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Chemistry
Dr. Jay Maron

Atoms

Hydrogen
Helium
Lithium

Elements are built from protons, neutrons, and electrons. The identity of an element is determined by the proton number. The heaviest naturally-occuring element is uranium with 92 protons.

```Particle     Charge   Mass (kg)       Mass / Proton mass

Proton         +1     1.673⋅10-27       1
Neutron         0     1.675⋅10-27       1.0012
Electron       -1     9.109⋅10-31        .000544
```
Proton number

Isotopes

Isotopes of hydrogen

An element has a fixed number of protons and a variable number of neutrons. Each neutron number corresponds to a different isotope. Naturally-occuring elements tend to be a mix of isotopes.

```Isotope   Protons   Neutrons   Natural fraction

Hydrogen-1    1        0        .9998
Hydrogen-2    1        1        .0002

Helium-3      2        1        .000002
Helium-4      2        2        .999998

Lithium-6     3        3        .05
Lithium-7     3        4        .95

Beryllium-9   4        5        1

Boron-10      5        5        .20
Boron-11      5        6        .80

Carbon-12     6        6        .989
Carbon-13     6        7        .011
```
Teaching simulation for isotopes at phet.colorado.edu
Atomic mass

Atom masses are measured in "atomic mass units" (AMU). One AMU is defined as 1/12 the mass of a carbon-12 atom and is approximately equal to the mass of a hydrogen-1 atom.

```                    Mass (Atomic mass units)

Proton               1.0072765
Neutron              1.0086649
Electron              .0005486
Atomic mass unit     1.000000  =  1.6605-27 kg
Hydrogen-1           1.007825
Hydrogen-2           2.014102
Hydrogen-3           3.016049
Hydrogen ave. mass   1.00798
Carbon-12           12.00000
```
The atomic mass for an element is the average over all isotopes. For hydrogen,
```Hydrogen-1 abundance     =  .9998
Hydrogen-2 abundance     =  .0002
Hydrogen-3 abundance     =  0          (Unstable)

Average mass of hydrogen =  (Hydrogen-1 fraction) * (Hydrogen-1 mass)  +  (Hydrogen-2 fraction) * (Hydrogen-2 mass)
=  .9998 * 1.007825  +  .0002 * 2.014102
= 1.00798
```

Density

Size of atoms
Dot size corresponds to atom size.

For gases, the density at boiling point is used.   Size data

Density

Copper atoms stack like cannonballs. We can calculate the atom size by assuming the atoms are shaped like either cubes or spheres. For copper atoms,

```Density         = D              =       8900 kg/m3
Atomic mass unit= M0             = 1.661⋅10-27 kg
Atomic mass     = MA             =      63.55 Atomic mass units
Mass            = M   =  MA⋅M0    = 9.785⋅10-26 kg
Number density  = N   =  D / M   = 9.096⋅1028  atoms/m3
Cube volume     = Υcube=  1 / N   = 1.099⋅10-29 m3            Volume/atom if the atoms are cubes
Cube length     = L   =  Υ1/3cube = 2.22⋅10-10  m             Side length of the cube
Sphere fraction = f   =  π/(3√2) =     .7405                Fraction of volume occupied by spheres in a stack o spheres
Sphere volume   = Υsph=  Υcube f  = 8.14⋅10-30  m3 = 4⁄3πR3    Volume/atom if the atoms are spheres
Sphere radius   = R              = 1.25⋅10-10  m
```

Electric force

Charges of the same sign repel and charges of opposite sign attract.

```Charge 1    Charge 2     Electric Force

+           +         Repel
-           -         Repel
+           -         Attract
-           +         Attract
```
The gravitational and electric forces follow the same equations. The fundamental unit of charge is the "Coulomb".
```Mass                     =  M
Charge                   =  Q       (Coulombs)
Charge on a proton       =  Qp = 1.602e-19 Coulombs
Distance between charges =  R
Gravity constant         =  G  = 6.67⋅10-11 Newton m2 / kg2
Electric constant        =  K  = 8.99⋅109   Newton m2 / Coulomb2

Gravity force            =  Fg =  -G M1 M2 / R2
Electric force           =  Fe =  -K Q1 Q2 / R2

Gravity energy           =  Eg =  -G M1 M2 / R
Electric energy          =  Ee =  -K Q1 Q2 / R
```

Energy

Energy is measured in either Joules or electron Volts (eV). An electron Volt is the energy gained by an electron upon falling down an electric potential of 1 Volt.

```1.6022⋅10-19 Joules     =  1   eV
Red photon             =  1.8 eV
Green photon           =  2.3 eV
Blue photon            =  3.1 eV
O2 molecule energy     =  5.2 eV    Energy released when two oxygens combine to O2
Hydrogen ionization    = 13.6 eV    Energy to remove the electron from hydrogen
```

Hydrogen atom

Calculating the energy levels of an electron in a hydrogen atom requires quantum mechanics, but we get useful results by oversimplifying and assuming the electron is on a circular orbit around the proton. Quantum mechanics tells us that the lowest energy level has an orbit radius of 5.29⋅10-11 meters and an energy of -13.6 eV.

```1 electron Volt (eV)            =  1.60⋅10-19 Joules        Unit of energy for particles
Electron mass             =  Me =  9.11⋅10-31 kg
Electron charge           =  C  = -1.60⋅10-19 Coulombs
Electron orbit speed      =  V  =  2190 km/s  =  .041 ⋅ Lightspeed
Electric force constant   =  K  =  8.99⋅109  Newtons meters2 / Coulombs2       "Coulomb constant"
Electric force            =  Fe = -K C2 / R2      Force between the electron and proton
Centripetal force         =  Fc =  M V2 / R
Electric potential energy =  Ee = -K C2 / R =  -27.2 eV      Potential energy between the electron and proton
Electron kinetic energy   =  Ek =  ½ M V2   =  +13.6 eV
Electron total energy     =  Et =  Ek + Ee  =  -13.6 eV  =  -½ Ee

Electric force = Centripetal force
Fe = Fc
K C2 / R = M V2
-Ee  = 2 Ek
```
This sets the characteristic length and energy of chemical bonds. Chemical bonds have energies ranging from 2 to 9 eV. Bonds that are weaker than this tend to be unstable.
Hydrogen energy levels

Electron energy levels in a hydrogen atom
Electrons can change levels by emitting or absorbing a photon

The lowest energy level is -13.6 eV and the higher levels are given by

```Energy level                 =  N
=  1 for the lowest energy level
=  2 for the next lowest level, etc.
Energy of lowest level       = -Eo  = -13.6 eV
Energy of level N            = -Eo N-2
Orbit radius of lowest level =  Ro  =  5.29⋅10-11 meters     "Bohr radius"
Orbit radius of level N      =  Ro N2
```
The "Bohr model" is an empirical way to calculate these levels. In quantum mechanics particles have an intrinsic wavelength and an electron orbital is interpreted as a vibrating string with this wavelength. The allowed wavelengths correspond to the overtones of the string and the number of wavelengths experienced by an electron in one orbit must be an integer.
```Particle momentum   =  S  =  M V
particle wavelength =  λ
Planck constant     =  h  =  6.62⋅10-34 Joule seconds
Orbit circumference =  C

De Broglie formula:  h = S λ
Overtone rule:       C = N λ    where N is an integer and this determines the orbital type

N   Orbital
1      S
2      P
3      D
4      F
```
Setting N=1 gives the lowest energy level.
```2 π R  =  λ  =  h / Q  =  h / (MV)

For a circular orbit,  K Q2 / R = M V2

Ro  =  (h/2π)2 / (K M Q^2)

Eo  =  ½ K2 Q4 M (2π/h)2
```

Electron energy levels

If a nucleus has multiple protons and one electron then the relative spacing between the levels is the same as for a nucleus with one proton. The electron energy levels are

```Energy level                 =  N
Number of protons            =  Z
Energy of the lowest level   = -Eo  =  -13.6 eV
Energy of level N            = -Eo Z2 N-2
Orbit radius of lowest level =  Ro  =  5.29⋅10-11 meters
Orbit radius of level N      =  Ro N2 / Z
```
If there are multiple electrons then the levels change. The electrons orbiting a nucleus are in discrete energy levels, each represented by a circle in the above figure. Each level can have 0, 1, or 2 electrons and not more. Electrons seek the lowest energy level and if it's occupied they settle in the next-highest energy level.
Electron packing

Each level can have 0, 1, or 2 electrons and not more. Electrons seek the lowest energy level and if it's occupied they settle in the next-highest energy level.

```Orbital  Number of   Maximum #
type    levels     of electrons

S         1          2
P         3          6
D         5         10
F         7         14
```
```           Protons   Max   S1  S2  P2  S3  P3
bonds
H   Hydrogen    1    1     1   0   0   0   0
He  Helium      2    0     2   0   0   0   0
Li  Lithium     3    1     2   1   0   0   0
Be  Beryllium   4    2     2   2   0   0   0
B   Boron       5    3     2   2   1   0   0
C   Carbon      6    4     2   2   2   0   0
N   Nitrogen    7    3     2   2   3   0   0
O   Oxygen      8    2     2   2   4   0   0
F   Fluorine    9    1     2   2   5   0   0
Ne  Neon       10    0     2   2   6   0   0
Na  Sodium     11    1     2   2   6   1   0
Mg  Magnesium  12    2     2   2   6   2   0
Al  Aluminum   13    3     2   2   6   2   1
Si  Silicon    14    4     2   2   6   2   2
P   Phosphorus 15    3     2   2   6   2   3
S   Sulfur     16    2     2   2   6   2   4
Cl  Chlorine   17    1     2   2   6   2   5
Ar  Argon      18    0     2   2   6   2   6
Fe  Iron       26   many   2   2   6   2   6
Au  Gold       79   many   2   2   6   2   6
U   Uranium    92   many   2   2   6   2   6
```
Max bonds:         Maximum number of chemical bonds that the element can form.
S1, S2, P2, etc.:    Number of electrons in each energy level.

Moles

Molecule number is measured in moles, which are defined such that one mole of Carbon-12 atoms has a mass of exactly 12 grams.

```Avogadro number           =  NAvo  =  6.022⋅1023  =  Number of molecules in one mole
One mole of carbon-12     = 12.000 grams    (exact)
One mole of hydrogen      =  1.008 grams  =  1.674⋅10-27 kg
One mole of water         = 18.015 grams  =  2.992⋅10-26 kg
1 electron Volt = 1 eV    =  E0  =  1.6022⋅10-19 Joules
Energy per mole           =  Emol     (Joules/mole)
Energy per particle in eV =  EeV = Emol / NAvo / 1.6022⋅10-19 = 1.0364⋅10-5 Emol = EMol / 96488    (eV)
```

Molecules

Diatomic molecules

If two atoms of hydrogen encounter each other they combine into a diatomic molecule, releasing energy. All elements that are gases at room temperature are diatomic.

Bonds

Metallic
Covalent
Ionic
Ionic solid

Bond dissociation energy

For the dissociation of water,

```OH + H      ↔  H2O +   5.12 eV     Remove the first hydrogen from the oxygen
O  + H      ↔  HO  +   4.41 eV     Remove the second hydrogen from the oxygen
O  + H + H  ↔  2HO + 2*4.76 eV     Remove both hydrogens from the oxygen

Water molecule energy  =  2*4.76 eV  =  5.12 eV + 4.41 eV
```
The first two rows are "bond dissociation energies" and the last row is a "mean bond energy" (4.76 eV). The mean bond energy is the total energy of the water molecule divided by the number of bonds.

For methane, the average bond energy is 4.31 eV.

```CH3 + H             ↔  CH4  +   4.52 eV
CH2 + H             ↔  CH3  +   4.61 eV
CH  + H             ↔  CH2  +   4.61 eV
C   + H             ↔  CH   +   3.52 eV
C   + H + H + H + H ↔  CH4  + 4*4.31 eV
```

Hydrogen molecules (hydrides)

LiH
BeH2
BH3
CH4
NH3
H2O
HF

Hydrogen forms molecules with all elements except the noble gases, osmium, iridium, promethium, francium, and radium. This makes it a useful benchmark for determining the number of bonds that each element forms, as well as the strength of each element's attraction for electrons.

Valence electrons

Valence sites

The "valence number" is the number of bonds that an element can form. The valence number for each element can be inferred from the table of hydrides. Elements in the same column of the periodic table have the same valence number. The following table shows the valence number for each column of the periodic table.

```   1           2        3          4           3          2          1          0

Hydrogen                                                                      Helium
Lithium    Beryllium  Boron      Carbon     Nitrogen    Oxygen    Fluorine    Neon
Sodium     Magnesium  Aluminum   Silicon    Phosphorus  Sulfur    Chlorine    Argon
Potassium  Calcium    Gallium    Germanium  Arsenic     Selenium  Bromine     Krypton
```

Electronegativity

Every atom attracts electrons and the electronegativity table shows the relative energy released when the atom captures an electron. The elements in the upper right are the most electron-hungry.

In the reaction   H + H + O   →   H2O,   The oxygen steals an electron from each of the two hydrogens. It is able to do this because the electrons are at a lower energy with oxygen than with hydrogen.

Most chemical reactions involve elements on the left side of the periodic table giving electrons to elements on the right side.

Hydrogen bond energy

The following table gives the energy to remove a hydrogen from a hydride molecule. This is the data used to construct the electronegativity table. Ionic solids such as LiH are considered to have a bond number of 1.

```Element  Molecule  Bonds  Bond energy
(eV)

H      H2         1    4.52
He     -          0     -       The noble gases don't react with hydrogen
Li     LiH        1    2.56
Be     BeH2       2    2.35
B      BH3        3    3.43
C      CH4        4    3.52
N      NH3        3    3.26
O      H2O        2    4.41
F      HF         1    4.90
Ne     -          0     -
Na     NaH        1    2.09
Mg     MgH2       2    2.04
Al     AlH3       3    2.96
Si     SiH4       4    3.10
P      PH3        3    3.56
S      H2S        2    3.57
Cl     HCl        1    4.48
Ar     -          0     -
K      KH         1    1.90
Ca     CaH2       2    1.74
Ga                3     ?
Ge                4    3.36
As                3    2.82
Se     SeH2       2    3.17
Br     HBr        1    3.80
Kr     -          0     -
```
If we arrange the bond energies by the columns of the period table,
```Row    Li    Be    B     C     N     O     F

Li    2.56  2.35  3.43  3.52  3.26  4.41  4.90
Na    2.09  2.04  2.96  3.10  3.56  3.57  4.48
Ca    1.90  1.74   ?    3.36  2.82  3.17  3.80
Rb                      2.77   ?    2.78  3.10
```
Bond energy is highest for Fluorine at the upper right and it decreases as one moves left or down.
Oxides

Fe2O3  paint

H2O
Li2O
BeO
B2O3
CO2
N2O
O2
OF2

The oxides of copper are:

```1 electron:       Cu2O   Copper(I) Oxide.  Cuprous oxide. Red paint
2 electrons:      CuO    Copper(II) Oxide.  Cupric oxide. Black color
3 electrons:      Cu2O3   Copper(III) Oxide
```
"Electrons" refers to the number of electrons that each copper atom gives to the oxygen atoms. Iron has an addition form Fe3O4 referred to as iron(II,III) oxide where the electron number is 8/3.

In the following table the "e-" column denotes the number of electrons given by the element to oxygen atoms.

```        e-

1  H   1   H2O    Water
2  He  0          Does not react with oxygen
3  Li  1   Li2O
4  Be  2   BeO    Beryllium oxide
5  B   3   B2O3   Boron trioxide. Most common form.  High conductivity
1/3  B6O    Boron suboxide.  High conductivity and hardness
6  C   4   CO2    Carbon dioxide
2   CO     Carbon monoxide.  Toxic.  Displaces oxygen from hemoglobin
7  N   1   N2O    Nitrous oxide.  Laughing gas
2   NO     Nitric oxide.  Gas.  Signaling molecule.  Decomposes in air to NO2
4   NO2    Nitrogen dioxide.  Toxic gas
4   N2O4   Dinitrogen tetroxide
5   N2O5   Dinitrogen pentoxide
8  O       O2     Oxygen
O3     Ozone
9  F  -2   OF2    Oxygen difluoride
10  Ne  0          Does not react with oxygen
11  Na  1   Na2O   Sodium oxide
12  Mg  2   MgO    Magnesium oxide
13  Al  3   Al2O3  Aluminum(III) oxide. Aluminum oxide. Most common form
2   AlO    Aluminum(II) oxide. Aluminum monoxide
1   Al2O   Aluminum(I) oxide
14  Si  4   SiO2   Quartz
15  P   4   P2O4   Diphosphorus tetroxide
3   P4O6   Phosphorus trioxide.  Phosphorus(III) oxide. Stable. Reacts with water
5   P4O10  Phosphorus pentoxide
16  S   6   SO3    Sulfur trioxide.  Component of acid rain
4   SO2    Sulfur dioxide.  Toxic gas
2   SO     Sulfur monoxide.  Unstable
17  Cl  4   ClO2   chlorine dioxide
2   ClO    Foe of the ozone layer
1   Cl2O   Dichlorine monoxide. Unstable. Explosive
18  Ar  0          Does not react with oxygen
19  K   1   K2O    Potassium oxide
20  Ca  2   CaO    Calcium oxide   Quicklime
21  Sc  3   Sc2O3  Scandium(III) oxide.  Ceramic
22  Ti  4   TiO2   Titanium dioxide.  Most common form
3   Ti2O3  Dititanium trioxide
2   TiO    Titanium monoxide.  Corundum structure.  Tistarite ore (extremely rare)
23  V   5   V2O5   Vanadium(V) oxide. Rare mineral
3   V2O3   Vanadium(III) oxide. Morphs in air to V2O4
24  Cr  2   CrO    Chromium(II) oxide
3   Cr2O3  Chromium(III) oxide.  Eskolaite ore
4   CrO2   Chromium dioxide
6   CrO3   Chromium trioxide
25  Mn  7   Mn2O7  Manganese(VII) oxide.  Extremely unstable
6   MnO3   Manganese(VI) oxide
4   MnO2   Manganese dioxide.  Most common form
3   Mn2O3  Manganese(III) oxide
8/3  Mn3O4  Manganese(II,III) oxide
2   MnO    Manganese(II) oxide.  Rare mineral
26  Fe  3   Fe2O3  Iron(III) Oxide.  Ferric oxide.  Most common form
2   FeO    Iron(II) oxide.  Rare
8/3  Fe3O4  Iron(II,III) Oxide.  Magnetite
27  Co  3   Co2O3  Cobalt(II) oxide.  Cobaltic oxide
2   CoO    Cobalt(II) oxide.  Cobaltous oxide
8/3  Co3O4  Cobalt(II,IIIs) oxide.  Cobaltous oxide
28  Ni  2   NiO    Nickel(II) oxide
29  Cu  1   Cu2O   Copper(I) Oxide.  Cuprous oxide. Red paint
2   CuO    Copper(II) Oxide.  Cupric oxide. Black color. Common ore
3   Cu2O3  Copper(III) Oxide
30  Zn  2   ZnO    Zinc oxide
```

Valence of metals

The following table gives the most common oxidation number for each metal.

```Potassium   1
Calcium     2
Scandium    3
Titanium    4
Chromium    4
Manganese   4
Iron        3
Cobalt      2
Nickel      2
Copper      3
Zinc        2
```

Oxide acids

Water
Carbonic acid
Nitric acid
Nitrous acid
Silicic acid
Phosphoric acid
Sulfuric acid

Hydroxide
Carbonate
Nitrate
Nitrite
Silicate
Phosphate
Sulfate

Potassium oxide
Selenium oxide
Fe2O3

```With         Hydrogens
hydrogen     removed

H2O          OH-       Water
H2CO3        CO3--     Carbonic acid
HNO2         NO2-      Nitrous acid
HNO3         NO3-      Nitric acid
H2O2         HO2-      Hydrogen peroxide
H4SiO4       SiO4----  Silicic acid
H3PO4        PO4---    Phosphoric acid
H2SO4        SO4--     Sulfuric acid
```

Carbides

Tungsten carbide drill
Tungsten carbide
Silicon carbide
Boron carbide

```      Carbon atoms per metal atom

Boron      1/4
Silicon     1
Titanium    1
Beryllium  1/2
Zirconium  1/2
Tantalum    1
Tungsten    1
Aluminum   3/4
```

Gases

Ideal gas law

Molecules in a gas
Brownian motion

```Pressure                          =  P             (Pascals or Newtons/meter2 or Joules/meter3)
Temperature                       =  T             (Kelvin)
Volume                            =  Vol           (meters3)
Total gas kinetic energy          =  E             (Joules)
Kinetic energy per volume         =  e  =  E/Vol   (Joules/meter3)
Number of gas molecules           =  N
Mass of a gas molecule            =  M
Gas molecules per volume          =  n  =   N / Vol
Gas density                       =  D  = N M / Vol
Avogadro number                   =  Avo=  6.022⋅1023  moles-1
Moles of gas molecules            =  Mol=  N / Avo
Boltzmann constant                =  k  =  1.38⋅10-23 Joules/Kelvin
Gas constant                      =  R  =  k Avo  =  8.31 Joules/Kelvin/mole
Gas molecule thermal speed        =  Vth
Mean kinetic energy / gas molecule=  ε  =  E / n  =  ½ M Vth2     (Definition of the mean thermal speed)
```
Gas pressure arises from the kinetic energy of gas molecules and has units of energy/volume.
The ideal gas law can be written in the following forms:
```P  =  2⁄3 e                    Form used in physics
=  R Mol T / Vol            Form used in chemistry
=  k N   T / Vol
=  1⁄3 N M Vth2/ Vol
=  1⁄3 D Vth2
=  k T D / M
```
Derivation of the ideal gas law
History

Boyle's law
Charles' law

```1660  Boyle law          P Vol     = Constant          at fixed T
1802  Charles law        T Vol     = Constant          at fixed P
1802  Gay-Lussac law     T P       = Constant          at fixed Vol
1811  Avogadro law       Vol / N   = Constant          at fixed T and P
1834  Clapeyron law      P Vol / T = Constant          combined ideal gas law
```

Boltzmann constant

For a system in thermodynamic equilibrium each degree of freedom has a mean energy of ½ k T. This is the definition of temperature.

```Molecule mass                =  M
Thermal speed                =  Vth
Boltzmann constant           =  k  =  1.38⋅10-23 Joules/Kelvin
Molecule mean kinetic energy =  ε
```
A gas molecule moving in N dimensions has N degrees of freedom. In 3D the mean energy of a gas molecule is
```ε  =  3⁄2 k T  =  ½ M V2th
```

Speed of sound

The sound speed is proportional to the thermal speed of gas molecules. The thermal speed of a gas molecule is defined in terms of the mean energy per molecule.

```Adiabatic constant  =  γ
=  5/3 for monatomic molecules such as helium, neon, krypton, argon, and xenon
=  7/5 for diatomic molecules such as H2, O2, and N2
=  7/5 for air, which is 21% O2, 78% N2, and 1% Ar
≈  1.31 for a triatomic gas such as CO2
Pressure            =  P
Density             =  D
Sound speed         =  Vsound
Mean thermal speed  =  Vth
K.E. per molecule   =  ε  =  ½ M Vth2

V2sound  =  γ  P / D  =  1⁄3  γ  V2th
```
The sound speed depends on temperature and not on density or pressure.

For air, γ = 7/5 and

```Vsound  =  .68  Vth
```
These laws are derived in the appendix.

We can change the sound speed by using a gas with a different value of M.

```                   M in atomic mass units

Helium atom                4
Neon atom                 20
Nitrogen molecule         28
Oxygen molecule           32
Argon atom                40
Krypton atom              84
Xenon atom               131
```
A helium atom has a smaller mass than a nitrogen molecule and hence has a higher sound speed. This is why the pitch of your voice increases if you inhale helium. Inhaling xenon makes you sound like Darth Vader. Then you pass out because Xenon is an anaesthetic.

In a gas, some of the energy is in motion of the molecule and some is in rotations and vibrations. This determines the adiabatic constant.

Ethane
Molecule with thermal vibrations

History of the speed of sound
```1635  Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660  Viviani and Borelli produce the first accurate measurement of the speed of
sound, giving a value of 350 m/s.
1660  Hooke's law published.  The force on a spring is proportional to the change
in length.
1662  Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
1687  Newton publishes the Principia Mathematica, which contains the first analytic
calculation of the speed of sound.  The calculated value was 290 m/s.
```
Newton's calculation was correct if one assumes that a gas behaves like Boyle's law and Hooke's law.

The fact that Newton's calculation differed from the measured speed is due to the fact that air consists of diatomic molecules (nitrogen and oxygen). This was the first solid clue for the existence of atoms, and it also contained a clue for quantum mechanics.

In Newton's time it was not known that changing the volume of a gas changes its temperature, which modifies the relationship between density and pressure. This was discovered by Charles in 1802 (Charles' law).

Gas data
```       Melt   Boil  Solid    Liquid   Gas      Mass   Sound speed
(K)    (K)   density  density  density  (AMU)  at 20 C
g/cm3    g/cm3    g/cm3            (m/s)

He        .95   4.2            .125   .000179    4.00  1007
Ne      24.6   27.1           1.21    .000900   20.18
Ar      83.8   87.3           1.40    .00178    39.95   319
Kr     115.8  119.9           2.41    .00375    83.80   221
Xe     161.4  165.1           2.94    .00589   131.29   178
H2      14     20              .070   .000090    2.02  1270
N2      63     77              .81    .00125    28.01   349
O2      54     90             1.14    .00143    32.00   326
Air                                   .0013     29.2    344     79% N2, 21% O2, 1% Ar
H2O    273    373     .917    1.00    .00080    18.02
CO2    n/a    195    1.56      n/a    .00198    44.00   267
CH4     91    112              .42    .00070    16.04   446
CH5OH  159    352              .79    .00152    34.07           Alcohol
```
Gas density is for 0 Celsius and 1 Bar. Liquid density is for the boiling point, except for water, which is for 4 Celsius.

Carbon dioxide doesn't have a liquid state at standard temperature and pressure. It sublimes directly from a solid to a vapor.

Height of an atmosphere

```M  =  Mass of a gas molecule
V  =  Thermal speed
E  =  Mean energy of a gas molecule
=  1/2 M V^2
H  =  Characteristic height of an atmosphere
g  =  Gravitational acceleration
```
Suppose a molecule at the surface of the Earth is moving upward with speed V and suppose it doesn't collide with other air molecules. It will reach a height of
```M H g  =  1/2  M  V^2
```
This height H is the characteristic height of an atmosphere.
```Pressure of air at sea level      =  1   Bar
Pressure of air in Denver         = .85  Bar      One mile high
Pressure of air at Mount Everest  = 1/4  Bar      10 km high
```
The density of the atmosphere scales as
```Density ~ (Density At Sea Level) * exp(-E/E0)
```
where E is the gravitational potential energy of a gas molecule and E0 is the characteristic thermal energy given by
```E0 = M H g = 1/2 M V^2
```
Expressed in terms of altitude h,
```Density ~ Density At Sea Level * exp(-h/H)
```
For oxygen,
```E0  =  3/2 * Boltzmann_Constant * Temperature
```
E0 is the same for all molecules regardless of mass, and H depends on the molecule's mass. H scales as
```H  ~  Mass^-1
```

Atmospheric escape
```S = Escape speed
T = Temperature
B = Boltzmann constant
= 1.38e-23 Joules/Kelvin
g = Planet gravity at the surface

M = Mass of heavy molecule                    m = Mass of light molecule
V = Thermal speed of heavy molecule           v = Thermal speed of light molecule
E = Mean energy of heavy molecule             e = Mean energy of light molecule
H = Characteristic height of heavy molecule   h = Characteristic height of light molecule
= E / (M g)                                   = e / (m g)
Z = Energy of heavy molecule / escape energy  z = Energy of light molecule / escape energy
= .5 M V^2 / .5 M S^2                         = .5 m v^2 / .5 m S^2
= V^2 / S^2                                   = v^2 / S^2

For an ideal gas, all molecules have the same mean kinetic energy.

E     =     e      =  1.5 B T

.5 M V^2  =  .5 m v^2  =  1.5 B T
```
The light molecules tend to move faster than the heavy ones. This is why your voice increases in pitch when you breathe helium. Breathing a heavy gas such as Xenon makes you sound like Darth Vader.

For an object to have an atmosphere, the thermal energy must be much less than the escape energy.

```V^2 << S^2        <->        Z << 1

Escape  Atmos    Temp    H2     N2      Z        Z
speed   density  (K)    km/s   km/s    (H2)     (N2)
km/s    (kg/m^3)
Jupiter   59.5             112   1.18    .45   .00039   .000056
Saturn    35.5              84   1.02    .39   .00083   .00012
Neptune   23.5              55    .83    .31   .0012    .00018
Uranus    21.3              53    .81    .31   .0014    .00021
Earth     11.2     1.2     287   1.89    .71   .028     .0041
Venus     10.4    67       735   3.02   1.14   .084     .012
Mars       5.03     .020   210   1.61    .61   .103     .015
Titan      2.64    5.3      94   1.08    .41   .167     .024
Europa     2.02    0       102   1.12    .42   .31      .044
Moon       2.38    0       390   2.20    .83   .85      .12
Ceres       .51    0       168   1.44    .55  8.0      1.14
```
Even if an object has enough gravity to capture an atmosphere, it can still lose it to the solar wind. Also, the upper atmosphere tends to be hotter than at the surface, increasing the loss rate.

The threshold for capturing an atmosphere appears to be around Z = 1/25, or

```Thermal Speed  <  1/5 Escape speed
```

Heating by gravitational collapse

When an object collapses by gravity, its temperature increases such that

```Thermal speed of molecules  ~  Escape speed
```
In the gas simulation at phet.colorado.edu, you can move the wall and watch the gas change temperature.

For an ideal gas,

```3 * Boltzmann_Constant * Temperature  ~  MassOfMolecules * Escape_Speed^2
```
For the sun, what is the temperature of a proton moving at the escape speed? This sets the scale of the temperature of the core of the sun. The minimum temperature for hydrogen fusion is 4 million Kelvin.

The Earth's core is composed chiefly of iron. What is the temperature of an iron atom moving at the Earth's escape speed?

```      Escape speed (km/s)   Core composition
Sun        618.             Protons, electrons, helium
Earth       11.2            Iron
Mars         5.03           Iron
Moon         2.38           Iron
Ceres         .51           Iron
```

Derivation of the ideal gas law

We first derive the law for a 1D gas and then extend it to 3D.

Suppose a gas molecule bounces back and forth between two walls separated by a distance L.

```M  = Mass of molecule
V  = Speed of the molecule
L  = Space between the walls
```
With each collision, the momentum change = 2 M V

Time between collisions = 2 L / V

The average force on a wall is

```Force  =  Change in momentum  /  Time between collisions  =  M  V^2  /  L
```
Suppose a gas molecule is in a cube of volume L^3 and a molecule bounces back and forth between two opposite walls (never touching the other four walls). The pressure on these walls is
```Pressure  =  Force  /  Area
=  M  V^2  /  L^3
=  M  V^2  /  Volume

Pressure * Volume  =  M  V^2
```
This is the ideal gas law in one dimension. For a molecule moving in 3D,
```Velocity^2  = (Velocity in X direction)^2
+ (Velocity in Y direction)^2
+ (Velocity in Z direction)^2

Characteristic thermal speed in 3D  =  3  *  Characteristic thermal speed in 1D.
```
To produce the 3D ideal gas law, replace V^2 with 1/3 V^2 in the 1D equation.
```Pressure * Volume  =  1/3  M  V^2        Where V is the characteristic thermal speed of the gas
```
This is the pressure for a gas with one molecule. If there are n molecules,
```Pressure  Volume  =  n  1/3  M  V^2            Ideal gas law in 3D
```
If a gas consists of molecules with a mix of speeds, the thermal speed is defined as
```Kinetic dnergy density of gas molecules  =  E  =  (n / Volume) 1/2 M V^2
```
Using this, the ideal gas law can be written as
```Pressure  =  2/3  E
=  1/3  Density  V^2
=  8.3  Moles  Temperature  /  Volume
```
The last form comes from the law of thermodynamics:
```M V^2 = 3 B T
```

Virial theorem

A typical globular cluster consists of millions of stars. If you measure the total gravitational and kinetic energy of the stars, you will find that

```Total gravitational energy  =  -2 * Total kinetic energy
```
just like for a single satellite on a circular orbit.

Suppose a system consists of a set of objects interacting by a potential. If the system has reached a long-term equilibrium then the above statement about energies is true, no matter how chaotic the orbits of the objects. This is the "Virial theorem". It also applies if additional forces are involved. For example, the protons in the sun interact by both gravity and collisions and the virial theorem holds.

```Gravitational energy of the sun  =  -2 * Kinetic energy of protons in the sun
```

Acids

Svante Arrhenius

For an acid dissolved in water,

```Mole of carbon-12         =  12    grams   (exact)
Mole of hydrogen          =  1.008 grams  =  1.674⋅10-27 kg
Mole of water             =  18.02 grams  =  2.992⋅10-26 kg
Avogadro number           =  NAvo  =  6.022⋅1023 molecules/moles-1
Water molecule density    =  NH2O  =  3.343⋅1028 molecules/meter3
Molecule concentration    =  C                   (moles/Litre)
Water concentration       =  CH2O  =  55.49 moles/Litre
H+ concentration          =  CH+   =  10-7 moles/Litre for pure water
OH- concentration         =  COH-  =  10-7 moles/Litre for pure water
Acid concentration        =  Cx
Acid ion concentration    =  Cx-
Acid molecule mass        =  Mx
Water molecule mass       =  MH2O
Water mass density        =  ρH2O  =  1000 g/Litre
Acid mass density         =  ρx    =  ρH2O (Mx/MH2O) (Cx/CH2O)
H2O dissociation rate     =  RH2O  =  2.36⋅10-5 seconds-1
H+ + OH- association rate =  ROH-  =  1.3⋅1011 Litres/Mole/second
H2O dissociation time     =  TH2O  =  R-1H2O  =  42370 seconds  =  11.77 hours
Acid dissociation rate    =  Rx
H+ + X- association rate  =  Rx-
Water constant            =  KH2O  =  RH2O / ROH-            (moles/Litre)
Acid constant             =  Kx    =  Rx  / Rx-
Boltzmann constant        =  k    =  1.381⋅10-23 Joules/Kelvin
Gibbs energy              =  E    =  - k NAvo T log10 K     (Joules/mole)
Acid ionization fraction  =  Fx   =  Cx- / Cx
=  (Kx/Cx-)½     if Cx ≪ Kx
≈  1             if Cx ≫ Kx

Water dissociation:  H+ + OH- → H2O       Rate  =  RH2O CH2O        moles/Litre/second
Water association:   H2O → H+ + OH-       Rate  =  ROH- CH+ COH-    moles/Litre/second
```
For pure water in equilibrium, the dissociation and association rates are equal.
```ROH- CH+ COH- = RH2O CH2O
CH2O = 55.49 moles/Litre
CH+  = COH-
C2H+ =  RH2O / ROH-  =  KH2O  =  10-14
```
For an acid,
```Rx- CH+ Cx-  =  Rx Cx
CH+ Cx- / Cx =  Kx  =  Rx / Rx-
```
If there is only one acid in the solution,
```CH+ = Cx-
CH+ = (Kx Cx)½
```
The ionization fraction of the acid   Cx-/Cx-   is
```If   Cx ≪ Kx   then    Cx-/Cx ≈  1               the acid is fully ionized
If   Cx ≫ Kx   then    Cx-/Cx = (Kx/Cx-)½ ≪ 1    the acid is partially ionized

K    log10K   Energy
(electron Volts)
Perchoric   HClO4 131.8       2.1   -.125
Nitric      HNO3   27.5       1.4   -.083
Hydronium   H3O+    1         0      0
Selenic     H2SeO4  Large
Sulfuric    H2SO4   Large
Chloric     HCL     Large
Chromic     H2CrO4  1.8e-1    -.74   .0439
Iodic       HIO3    1.7e-1    -.78   .0463
Phosphorous H3PO3   5.0e-2   -1.3    .077
Selenic     HSeO4-  2.2e-2   -1.66   .098
Sulfurous   H2SO3   1.4e-2   -1.85   .110
Chlorous    HClO2   1.1e-2   -1.94   .115
Sulfuric    HSO4-   1.0e-2   -1.99   .118
Phosphoric  H3PO4   6.9e-3   -2.14   .127
Fluoric     HF      6.3e-4   -3.20   .190
Citric      C6H8O7  7.4e-4   -3.13   .185
Nitrous     HNO2    5.6e-4   -3.25   .193
Formic      H2CO2   1.8e-4   -3.75   .222
Acetic      CH3CO2H 1.8e-5   -4.76   .281
Carbonic    H2CO3   4.5e-7   -6.35   .377
Sulfide     H2S     8.9e-8   -7.05   .418
Phosphoric  H2PO4-  6.2e-8   -7.20   .427
Carbonic    HCO3-   4.7e-11 -10.3    .611
Peroxide    H2O2    2.0e-12 -11.7    .694
Phosphoric  HPO4--  4.8e-13 -12.37   .734
Water       H2O     1.0e-14 -14.00   .830
```
All values are for 25 Celsius.
1 electron Volt = 1.602⋅10-19 Joules
Arrhenius units
```Water scale               =  LH2O  =  NH2O-1/3 = 3.10⋅10-10 m  size of a water molecule
Water volume              =  VH2O  =  L3H2O                   volume of a water molecule
Conc. relative to water   =  Ć    =  C / CH2O
Water concentration       =  ĆH2O  =  1
Arrhenius concentration   =  ĆArr  =  1.80⋅10-9               H+ concentration in pure water
Arrhenius scale           =  LArr  =  ĆArr-1/3 LH2O  =  822 LH2O  =  2.552⋅10-7 meters
Arrhenius volume          =  VArr  =  L3Arr
Arrhenius time            =  TArr  =  R-1H2O = 11.7 hours     time for a water molecule to dissociate
Conc. rel to Arrhenius vol=  C″    = Ć CArr
Acid const. in water units=  K′    =  K / CH2O                molecules per water molecule
Acid const. in Arr. units =  K″    =  K / CH2O / CArr         molecules per Arrhenius volume
Dissoc. rate in Arr. units=  R″x   =  Rx / TArr               molecules/Arrheniustime
Assoc. rate in Arr. units =  R″x-  =  Rx- ⋅ 1000 NAvo VArr / TArr  molecules/Arrheniustime
Water rate in Arr. units  =  R″H2O  =  RH2O / Tarr =  1        molecules/Arrheniustime
H+ + OH- rate in Arr. units= R″OH-  =  1                      molecules/Arrehniusvolume/Arrheniustime
Water const. in Arr. units=  K″H2O  =  1                      molecules/Arrheniusvolume

moles/   molecules per   molecules per
Litre    water molecule  Arrhenius volume

Pure water H+ concentration     10-7     1.80⋅10-9             1
Pure water H2O concentration    55.5        1               5.56⋅108
```

Organic chemistry

Propane with hydrogens included
Propane with hydrogen excluded

A molecule is organic if it contains carbon. Molecules are often depicted with the hydrogens excluded.

Alkanes

Methane
Ethane
Propane
Octane

An "Alkane" is a carbon chain with hydrocarbons attached. At standard temperature (300 K), alkanes are solid if they have more than 20 carbons. This is why lipids (long alkanes) are the optimal form of energy storage. Short alkanes are liquids or gases at STP and are hard to store.

In the following table, the first section shows properties of alkanes and the second section shows properties of other energy sources.

```Alkane   Carbons  Energy of   Melt  Boil  Solid    Liquid    Gas       Phase at
type              combustion  (K)   (K)   density  density   density   300 K
(MJ/kg)                 (g/cm^3) (g/cm^3)  (g/cm^3)

Hydrogen     0     141.8      14.0   20.3           .07      .000090   Gas
Methane      1      55.5      90.7  111.7           .423     .00070    Gas
Ethane       2      51.9      90.4  184.6           .545     .0013     Gas
Propane      3      50.4      85.5  231.1           .60      .0020     Gas
Butane       4      49.5     136    274             .60      .0025     Gas
Pentane      5      48.6     143.5  309             .63                Liquid
Hexane       6      48.2     178    342             .65                Liquid
Heptane      7      48.0     182.6  371.5           .68                Liquid
Octane       8      47.8     216.3  398.7           .70                Liquid
Dodecain    12      46       263.5  489             .75                Liquid
Hexadecane  16      46       291    560             .77                Liquid
Icosane     20      46       310    616     .79                        Solid
Alkane-30   30      46       339    723     .81                        Solid
Alkane-40   40      46       355    798     .82                        Solid
Alkane-50   50      46       364    848     .82                        Solid
Alkane-60   60      46       373    898     .83                        Solid

Gasoline   ~ 8      47                               .76               Liquid     Mostly alkanes with ~ 8 carbons
Natural gas         54        91    112                                Gas        Mostly methane
Coal                32         -      -                                Solid      Mostly carbon
Wood                22         -      -                                Solid      Carbon, oxygen, hydrogen
Pure carbon  1      32.8       -      -                                Solid      Pure carbon, similar to coal
Methanol     1     175.6  337.8           .79                          Liquid
Ethanol      2     159    351.5           .79                          Liquid
Propanol     3     147    370                                          Liquid
```

An alkane with 7 or more carbons has a heat of combustion of 46 MJoules/kg.

A nitrogen molecule is more tightly bound than an oxygen molecule, making it impossible to extract energy from hydrocarbons with nitrogen. Few things burn in a nitrogen atmosphere, lithium and magnesium being examples.

Hydrogen saturation

A chain is "saturated" if it contains the maximum number of hydrogen atoms and "unsaturated" if it contains less. Examples of unsaturated carbon chains:

Ethene
Acetylene
Propene

The hydrogens are required to stabilize the carbon chain.

Bond resonance

If there is a double or triple bond then the electrons can be mobile and assume different states. The molecule exists in a quantum-mechanical resonance between the possible states.

Non-carbon chains

Ammonia
Hydrazine
Triazane

Silane, spontaneously ignites in air
Disilane
Trisilane
Silene

Hydrogen peroxide
Diborane
Diphosphan

Suppose we make a chain of atoms that is saturated in hydrogen. The following table gives the longest stable chain for each element, and the longest stable chain in an oxygen environment. Only carbon is capable of making long chains. We can expect that aliens will be carbon-based.

```          Stable   Stable in an
oxygen environment

Lithium     1            1
Boron       0            0
Carbon      ∞            ∞
Nitrogen    1            1
Oxygen      1            1
Aluminum    1            1
Silicon     2            0
Phosphorus  1            0
Sulfur      1            0
```

Cycloalkanes

Cyclohexane comes in different conformations with different energies.

Cyclohexene

Benzene

Benzine is a resonance molecule.

Napthaline
Napthaline

3D

Tetrahedrane
Cubane
Methylcyclopropene
Propellane
Pagodane
Pagoda

Functional group

Organic molecules are classified by their functional group. "R" stands for an arbitrary molecule.

Alkyne
Alcohol
Thiol
Carboxyl

Aldehyde
Ketone group
Thial
Thioketone

Ether
Sulfide

Peroxy group
Organice disulfide
Azo group
Methylenedioxy group

Carboxyl group
Nitro group
Phosphate
Phosphonic acid

Phenyl group
Pyridyl group

Fuel

```                 MJoules/kg

Antimatter       90 billion
Hydrogen bomb      25000000    theoretical maximum yield
Hydrogen bomb      21700000    highest achieved yield
Uranium            20000000    as nuclear fuel
Hydrogen                143
Natural gas              53.6
Gasoline                 47
Jet fuel                 43
Fat                      37
Coal                     24
Carbohydrates & sugar    17
Protein                  16.8
Wood                     16
Lithium-air battery       9
TNT                       4.6
Gunpowder                 3
Lithium battery           1.3
Lithium-ion battery        .72
Alkaline battery           .59
Compressed air             .5        300 atmospheres
Supercapacitor             .1
Capacitor                  .00036
```
The chemical energy source with the highest energy/mass is hydrogen+oxygen, but molecular hydrogen is difficult to harness. Hydrocarbons + oxygen is the next best choice. Carbon offers a convenient and lightweight way to carry hydrogen around.

Reacting hydrocarbons in an oxygen atmosphere yields the optimal power-to-weight ratio.

Given the enormous power required by brains, if intelligent life exists in the universe, it likely gets its energy from reacting hydrocarbons in an oxygen atmosphere. Most likely we would be able to eat their food.

Food
```        MJ/kg  Calories/gram
Sugar    16        5
Protein  17        5
Alcohol  25        7
Fat      38        9
```
Humans can metabolize a wide range of fats and sugars.
Elements of single-cellular life

Life appeared on the Earth within a billion years of its formation. http://en.wikipedia.org/wiki/Timeline_of_evolutionary_history_of_life

Shortly after that, between 3500 and 3800 million years ago, the "Last Universal Common Ancestor" lived. http://en.wikipedia.org/wiki/Last_Universal_Common_Ancestor

The LUCA had the following properties: Single-cellular with a bilipid cell wall. ATP to power enzymes. A DNA codon system with 4^3=64 options coding for 20 proteins. This code hasn't changed since.

Building blocks for life
```
Abundance in  Mass frac in
Crust (ppm)   Human body
Oxygen      460000     .65
Carbon        1000     .18
Hydrogen      1500     .10
Nitrogen        20     .03
Calcium      45000     .014
Phosphorus    1100     .011
Potassium    20000     .0025
Sulfur         400     .0025
Sodium       25000     .0015
Chlorine       200     .0015
Magnesium    25000     .0005
Iron         60000     .00006
Fluorine       500     .000037
Zinc            75     .000032
Silicon     275000     .00002
Trace elements        <.00001
```
Among the elements required for life, nitrogen is the scarcest. The nitrogen in the first 250 km of the Earth's crust has the same mass as the nitrogen in the atmosphere.
```           Used by   Used by
humans    bacteria
Hydrogen      *      *
Helium
Lithium
Beryllium
Boron         *      *
Carbon        *      *
Nitrogen      *      *
Oxygen        *      *
Fluorine             *
Neon
Sodium        *      *
Magnesium     *      *
Aluminum
Silicon              *
Phosphorus    *      *
Sulfur        *      *
Chlorine      *      *
Argon
Potassium     *      *
Calcium       *      *
Scandium
Titanium
Chromium
Manganese     *      *
Iron          *      *
Cobalt        *      *
Nickel               *
Copper        *      *
Zinc          *      *
Gallium
Germanium
Arsenic              *
Selenium      *      *
Bromine       *      *
Krypton
Molybdenum           *
Tellurium            *
Iodine        *      *
Tungsten             *
```

Cell walls
Lipids and cell membranes

Cell walls are formed from a double layer of lipids. They are elastic and they self-assemble.

Each lipid has a polar and a non-polar end. The polar end faces the water and the non-polar end faces another lipid.

* Video of the self-assembly of a bilipid layer
* Video of an amoeba

If life were to exist in a non-polar solvent it would have to find another way to make cell walls.

ATP and ATP Synthase

Enzymes use ATP as an energy source to power chemical reactions. ATP and ATP synthase are common to all Earth life.

* Video of the ATP synthase enzyme in action

Amino acids

Amino acids have the above form, where R stands for an arbitrary molecule.

The 21 amino acids used by eucaryote life

Protein

Synthesis of two amino acids. Proteins are chains of animo acids with a backbone of the form:

```C-C-N-C-C-N-C-C-N-C-C-N-C-C-N
```

DNA and the genetic code

DNA codes a sequence of amino acids. The 64-element codon system is universal to Earth life.

The codon ATG both codes for methionine and serves as an initiation site: the first ATG in an mRNA's coding region is where translation into protein begins.

21 amino acids are used by eucaryote. More than 500 amino acids are known.

Sugar

Glucose

A sugar generally has the formula CN H2N ON, where N = 2, 3, etc. The common sugars are hexoses with N=6.

```         Number of   Number of
carbons     sugars
Diose        2          1
Triose       3          2
Tetrose      4          3
Pentose      5          4
Hexose       6         12       At least 6 carbons are required to form a ring
Heptose      7       many       Rarely observed in nature
Octose       8       many       Unstable.  Not observered in nature.
```
"Number of sugars" refers to the number of different types of sugar molecules for each carbon number.

Each sugar molecule has two mirror-symmetric forms, the "D" and "L" form. Only the D forms are found in nature.

The following figures show all sugars up to 6 carbons. All can be metabolized by humans.

2 carbons:

Glycolaldehyde

3 carbons:

Glyceraldehyde
Dihydroxyacetone

4 carbons:

Erythrose
Threrose
Erythrulose

5 carbons:

Ribose
Arabinose
Lyxose
Xylose

6 carbons:

Glucose
Galactose
Mannose
Allose
Altrose
Gulose
Idose
Talose

Fructose
Sorbose
Psichose
Tagatose

```         Energy  Sweetness

Succrose   1.00    1.00      Benchmark
Glucose             .74
Maltose             .32
Galactose           .32
Lactose             .16
Allose
Altrose
Mannose
Fructose           1.73
Psichose            .70
Tagatose    .38     .92
Sorbose            1.0
Honey               .97
```

Complex sugars
```Monosaccharde:   1 sugar molecule
Disaccharide:    2 monosaccharides
Polysaccharide:  More than 2 monosaccharides, such as starch and cellulose
```
Sucrose
Maltose
Lactose
Lactulose
Trehalose
```Sucrose    =  Glucose     + Fructose
Maltose    =  Glucose     + Glucose
Lactose    =  Galactose   + Glucose
Lactulose  =  Galactoce   + Fructose
Trehalose  =  Glucose     + Glucose
Cellobiose =  Glucose     + Glucose
Chitobiose =  Glucosamine + Glucosamine
```
Starch and cellulose are long chains of glucose molecules.

Starch
Cellulose

Synthesis

Metabolism

Fatty acid with 16 carbons
Sugar (glucose)
Acetyl
Pyruvic acid
H2O
CO2

Fatty acids and sugars are metabolized in the following stages, with each stage yielding energy.

```Fatty acid    →     Acetyl      →     CO2 and H2O

Sugar         →     Pyruvate    →     CO2 and H2O
```

Blood delivers fatty acids to cells.

The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2. Coenzyme-A carries the acetyl around.

Fat metabolism

A fat molecule is converted into a fatty acid by lipolysis, and then the fatty acid is converted into acetyl by beta oxydation, and then the acetyl is converted into H2O and CO2 by the citric acid cycle.

Beta oxidation cleaves 2 carbons from a fatty acid, which becomes acetyl. This process is repeated until te entire fatty acid has been converted into acetyls.

The steps of beta oxidation are:

Sugar metabolism (glycolysis)

Glycolysis converts a glucose molecule into 2 pyrovate molecules. A summary of the reaction showing only the starting and ending points is:

The full reaction is:

Citric acid cycle

Citric acid

The citric acid cycle (Krebs cycle) converts acetyl or pyrovate into H2O and CO2.

Fat metabolism oxidizes a carbon chain so that the chain can be split into acetyl. The strategy of the citric acid cycle is to further oxidize the acetyl (now a part of citrate) so that the remaining carbon bonds in the acetyl can be broken.

Alcohol

An alcohol is a carbon chain with one OH attached.

Methanol
Ethanol
Propanol
Isopropanol
Butanol

```          Carbons
Methanol     1       Toxic
Ethanol      2       Inebriating
Propanol     3       3 times more inebriating than ethanol
Isopropanol  3       Toxic
Butanol      4       6 times more inebriating than ethanol
```

Fatty acids (carboxylic acids)

Formic acid
Acetic acid
Palmitic acid

Palmitic acid has 16 carbons and is the most common fatty acid found in food.

```Carbons
1
2    Vinegar
3
4    Found in butter
8    Found in coconuts
10    Found in coconuts
12    Found in coconuts
16    Most common fatty acid.  Found in palm oil
18    Found in chocolate
20    Found in peanut oil
```

Metabolism molecules

Guanosine triphosphate
Glucosamine
Acetic acid
Citric acid
Vitamin C

Toxic molecules

Formaldehyde

```             LD50
(mg/kg)
CO                     Carbon monoxide
HCN             6.4    Hydrogen cyanide
CH2O                   Methanol
CH2O                   Formaldehyde
H2S                    Hydrogen sulfide
NO2                    Nitrite
Cl2                    Chlorine
Fl2                    Fluorine
Ethanol      7060
Salt         3000
Caffeine      192
Aspirin       200
NaNO2         180      Sodium nitrite
Cobalt         80
NaF            52
Capsaicin      47      Chili pepper
Mercury        41
Arsenic        13
Nicotine         .8
Bromine
C2N2
PH3
SiCl4
```
Almost anything with fluorine or bromine is toxic.

Weakly toxic:

```C2H2          Acetylene.  Inebriating
C3H6          Propene.  Inebriating
```

Opsins

```Opsin         Wavelength  Humans
(nm)
RH1               500     White  Black/White
RH2               600            Black/White.  Extinct in mammals
OPN1LW            564     Red    Once possessed by mammals, then lost by most
OPN1MW            534     Green  All mammals
OPN1SW            440     Blue   All mammals
SWS2              480            Extinct in mammals
VA                500            Vertebrates except mammals.  Vertebrae ancient opsin.
Parapinopsin UV   365            Catfish
Parapinopsin Blue 470            Catfish and lamphrey
Pareitopsin       522            Lizards
Panopsin Cyan     500            Fish vision.  Found in the brains of humans
Panopsin Blue     450            Fish vision.  Found in the brains of humans
Neuropsin         380            Bird vision.  Found in the brains of humans
Melanopsin        480            Found in the brains of humans
Retinal G                        Found in the brains of humans
```

Porphyrins

Heme cofactor carrying an iron atom
Pyrrole

Metals are held by a cofactor, which is held by a protein. Many cofactors are porphyrin rings conposed of 4 pyrroles. Examples of porphyrins:

Porphin (Iron)
Corrin (Cobalt)
Corphin (Nickel)
Chlorophyll building blocks (Magnesium)

Porphin resonance
Porphin is an aromatic molecule because it is flat and because it resonates between different electronic states.

Hemoglobin

Heme A
Heme B
Heme C
Heme O
Hemo B
Hemoglobin
Myoglobin

Superoxide

Oxygen bonds to the iron in a heme molecule and becomes superoxide.
Hemoglobin is a set of 4 helix proteins that carry 4 iron ligands, and each iron ligand carries 1 oxygen molecule.
Human hemoglobin is composed mostly of heme B.
The oxygen density of hemoglobin is 70 times the solubility of oxygen in water.

```Hemoglobin fraction of red blood cells   =  .96      (dry weight)
Hemoglobin fraction of red blood cells   =  .35      (including water)
Oxygen capacity of hemoglobin            = 1.34 Liters of oxygen / kg hemoglobin
Iron ligands per hemoglobin              =    4
O2 molecules per ion ligand              =    1
```

Chlorophyll

Chlorophyll A

Chlorophyll A
Chlorophyll B
Chlorophyll D

Chlorophyll C1
Chlorophyll C2
Chlorophyll F

All chlorophyll uses magnesium.

```A      Universal
B      Plants
C1     Algae
C2     Algae
D      Cyanobacteria
F      Cyanobacteria
```

Zinc fingers

Zinc stabilizes the proteins that manipulate DNA and RNA.

Metal
Carbonic anhydrase
```Element   Humans  Cofactor  Function

Hydrogen    *
Helium                      No biological role
Lithium                     No biological role
Beryllium                   Toxic becauseit displaces magnesium in proteins
Boron       *               Plant cell walls.  Metabolism of calcium in plants & animals
Magnesium   *     Chlorin   Chlorophyll
Scandium                    No biological role
Titanium                    No biological role
Vanadium                    Found only in rare bacteria.
Chromium                    No biological role
Manganese   *               Superoxide dimutase.  Converts superoxide to oxygen
Iron        *     Porphin   Hemoglobin
Cobalt      *     Corrin    Cobalamin (Vitamin B12)
Nickel            Corphin   Coenzyme F430 (Creates methane. Found only in archaea)
Copper      *     Heme      Cytochrome C oxidase. Electron transport chain
Hemocyanin, an alternative to hemoglobin used by some animals
Hemoglobin carries 4 times as much oxygen as hemocyanin
Plastocyanin protein, used in photosynthesis
Sometimes used in superoxide dimutase
Zinc        *               Component of proteins that manipulate DNA and RNA (Zinc fingers)
Component of carbonic anhydrase, which interconverts CO2 and HCO3
Metallothionein proteins, which bind to metals such as
zinc, copper, selenium cadmium, mercury, silver, and arsenic
Molybdenum                  Nitrogen fixase. Convert N2 to NH3
Selenium    *               Component of the amino acide selenocysteine
Bromine     *               Limited role
Iodine      *               Component of thyroxine and triiodotyronine, which
regulate metabolic rate
Lead                        Toxic because it displaces calcium in bones
```
Thyroxine
Triiodothyronine

Antioxidation

Superoxide dimutase
Superoxide dimutase, manganese in purple
Peroxidase

Bicarbonate
Carbonic acid
Hydrogen peroxide

Superoxide dimutase converts superoxide to oxygen or hydrogen peroxide.

The peroxidase enzyme decomposes hydrogen peroxide to water. Peroxidase contains the selenocysteine amino acid, which contains selenium.

Nitrogen fixation

Nitrogen fixase uses an iron-molybdenum cofactor.

Selenium

Selenocysteine

Selenium is a component of the amino acid selenocysteine.

Copper
Hemocyanin
Copper group without an oxygen
Copper group with an oxygen

The hemocyanin protein uses copper to carry oxygen. It has an oxygen density that is 1/4 of hemoglobin.

Plastocyanin is a copper-containing protein used in photosynthesis.

Plastocyanin

Lignin

Lignin is the structural component of wood.

Oxidizer clusters

Ozone
Trisulfur

Nitric oxide
Nitrous oxide (laughing gas)
Dinitrogen dioxide

Dinitrogen trioxide crystal

Sulfur monoxide
Sulfur dioxide
Disulfur dioxide

Phosphorus trioxide crystal
Phosphorus pentoxide

Potassium oxide
Selenium oxide

Metallurgy

Stone age
Copper age
Bronze age
Iron age
Carbon age

```      Discovery   Yield    Density
(year)    Strength  (g/cm3)
(GPascals)

Gold     Ancient   .20     19.3
Silver   Ancient   .10     10.5
Copper   -5000     .12      9.0
Bronze   -3200     .20      9      Copper + Tin.   Stronger than copper
Brass    -2000     .20      9      Copper + Zinc.  Stronger than copper
Iron     -1200     .25      7.9    Stronger than bronze and brass
Carbon    1987    1.4       1.75
```
The "yield strength" is the maximum stress a material can sustain before breaking.
The carbon age began in 1987 when Jimmy Connors switched from a steel to a carbon racquet.

Discovery of elements

The ancient metals such as iron, copper, tin, and zinc are obtained by carbon smelting minerals. Cobalt was the first metal discovered since iron and it's discovery inspired people to smelt every known mineral in the hope of yielding a new metal. By 1800 nearly all of the carbon smeltable metals had been discovered.

Some elements can't be carbon smelted and require electrolysis to isolate. Electrochemistry began in 1800 with the invention of the battery and most of the remaining metals were discovered soon after. Sodium and potassium were isolated by electrolysis in 1807 and these were used to smelt metals that couldn't be smelted with carbon.

```         Discovery   Method of
(year)     discovery

Carbon     Ancient   Naturally occuring     Coal, diamond
Gold       Ancient   Naturally occuring
Silver     Ancient   Naturally occuring
Sulfur     Ancient   Naturally occuring
Copper       -5000   Smelt with carbon
Bronze (As)  -4200                          Copper + Arsenic
Bronze (Sn)  -3200                          Copper + Tin
Tin          -3200   Smelt with carbon
Brass        -2000                          Copper + Zinc
Mercury      -2000   Heat the oxide
Iron         -1200   Smelt with carbon      In the form of steel
Zinc          1300   Smelt with carbon      Date first produced in pure form
Antimony      1540   Smelt with iron
Arsenic       1649   Heat the oxide
Phosphorus    1669   Heat the oxide
Cobalt        1735   Smelt with carbon      First metal discovered since iron
Platinum      1735   Naturally occuring
Nickel        1751   Smelt with carbon
Hydrogen      1766   Hot iron + steam
Oxygen        1771   Heat HgO
Nitrogen      1772   From air
Manganese     1774   Smelt with carbon
Molybdenum    1781   Smelt with carbon
Tungsten      1783   Smelt with carbon
Chromium      1797   Smelt with carbon
Osmium        1803
Iridium       1803
Rhodium       1804   Smelt with zinc        Smelt Na3RhCl6 with zinc
Sodium        1807   Electrolysis
Potassium     1807   Electrolysis
Magnesium     1808   Electrolysis
Lithium       1821   Electrolysis
Zirconium     1824   Smelt with potassium
Aluminum      1827   Smelt with potassium
Silicon       1823   Smelt with potassium
Beryllium     1828   Smelt with potassium
Thorium       1929   Smelt with potassium
Uranium       1841   Smelt with potassium
Ruthenium     1844   Smelt with carbon
Tantalum      1864   Smelt with hydrogen
Niobium       1864   Smelt with hydrogen
Fluorine      1886   Electrolysis
Helium        1895   From uranium ore
Titanium      1910   Smelt with sodium
Hafnium       1924
Rhenium       1928   From molybdenite
Scandium      1937

```
Gold was the densest element known until the discovery of platinun in 1735. It was useful as an uncounterfeitable currency until the discovery of tungsten in 1783, which has the same density as gold.

Wood fires are 200 Celsius short of the copper smelting temperature. Coal has to be used.

Titanium can't be smelted with carbon because it produces titanium carbide (TiC).

Discovery of the strong metals

The usefulness of a metal as a sword depends on its strength/density ratio. The table below shows all the metals with a ratio of at least 5 MJoules/kg. For these metals, strength tends to be proportional to density and the strength/density ratio has a characteristic value of 10 MJoules/kg. Beryllium is the sole outlier with a superlatively large value of 71 MJoules/kg.

The low density metals are ones up to vanadium on the periodic table. None are carbon smeltable and all require electrochemistry to isolate. The first low density metal to be produced was magnesium in 1808.

```        Protons  Strength  Density  Strength/Density   Carbon    Discovery
(GPa)    (g/cm3)   (MJoule/kg)      smeltable    year

Beryllium    4      132      1.85      71.4          no      1828
Magnesium   12       17      1.74       9.8          no      1808
Aluminum    13       26      2.70       9.6          no      1827
Scandium    21       29      3.0        9.7          no      1937
Titanium    22       44      4.5        9.8          no      1910
Vanadium    23       47      6.0        7.8          no      1831
Chromium    24      115      7.2       16.0          yes     1797
Manganese   25       75      7.2       10.4          yes     1774
Iron        26       82      7.9       10.4          yes    -1200
Cobalt      27       75      8.9        8.4          yes     1735
Nickel      28       76      8.9        8.5          yes     1751
Copper      29       48      9.0        5.3          yes    -5000
Zinc        30       43      7.1        6.0          yes     1746
Molybdenum  42      120     10.3       11.7          yes     1781
Ruthenium   44      173     12.4       14.0          yes     1844
Rhodium     45      150     12.4       12.1          yes     1804
Tungsten    74      161     19.2        8.4          yes     1783
Rhenium     75      178     21.0        8.5          yes     1928
Osmium      76      222     22.6        9.8          yes     1803
Iridium     77      210     22.6        9.3          yes     1803
Uranium     92      111     19.1        5.8          no      1841

Strength:          Shear modulus            (GPascals)
Density:           Density                  (grams/cm3)
Strength/Density:  Shear modulus / Density  (MJoules/kg)
```

Metals known since antiquity

For a metal, the stiffness is characterized by the "shear strength" and the sword worthiness is characterized by the shear strength over the density (the "strength to weight ratio"). For example for iron,

```Shear modulus    =  S         =   82 GJoules/meter3
Density          =  D         = 7900 kg/meter3
Sword worthiness =  Q  = S/D  = 10.4 MJoules/kg
```

Metals

This plot includes all metals with a strength/density at least as large as lead, plus mercury. Beryllium is beyond the top of the plot.

Wootz steel

```-600  Wootz steel developed in India and is renowned as the finest steel in the world.
1700  The technique for making Wootz steel is lost.
1790  Wootz steel begins to be studied by the British Royal Society.
1838  Anosov replicates Wootz steel.
```
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon), and cementite (iron carbide, Fe, 6.7% carbon).

Iron meteorites

In prehistoric times iron meteorites were the only source of metallic iron. They consist of 90% iron and 10% nickel.

Alloys

Copper
Orichalcum (gold + copper)
Gold

Alloy of gold, silver, and copper

Superstrong amorphous alloys

Crystal, polycrystal, amorphous

New alloys have been discovered that are stronger and ligher than diamond. These alloys have an amorphous structure rather than the crystalline structure of conventional alloys. A crystaline alloy tends to be weak at the boundaries between crystals and this limits its strength. Amorphous alloys don't have these weaknesses and can be stronger.

Pure metals and alloys consisting of 2 or 3 different metals tend to be crystaline while alloys with 5 or more metals tend to be amorphous. The new superalloys are mixes of at least 5 different metals.

A material's strength is characterized by the "yield strength" and the quality is the ratio of the yield strength to the density. This is often referred to as the "strength to weight ratio".

```Yield strength  =  Y            (Pascals)
Density         =  D            (kg/meter3)
Quality         =  Q  =  Y/D    (Joules/kg)
```
The strongest allyos are:
```       Yield strength   Density   Quality
(GPa)        (g/cm3)    (MJoule/kg)

Magnesium + Lithium             .14        1.43        98
Magnesium + Y2O3                .31        1.76       177
Aluminum  + Beryllium           .41        2.27       181
Amorphous LiMgAlScTi           1.97        2.67       738
Diamond                        1.6         3.5        457
Titanium  + AlVCrMo            1.20        4.6        261
Amorphous AlCrFeCoNiTi         2.26        6.5        377
Steel     + Cobalt, Nickel     2.07        8.6        241
Amorphous VNbMoTaW             1.22       12.3         99
Molybdenum+ Tungsten, Hafnium  1.8        14.3        126
```
The strongest pure metals are weaker than the strongest alloys.
```       Yield strength   Density   Quality
(GPa)        (g/cm3)    (MJoule/kg)

Magnesium                        .10       1.74        57
Beryllium                        .34       1.85       184
Aluminum                         .02       2.70         7
Titanium                         .22       4.51        49
Chromium                         .14       7.15        20
Iron                             .10       7.87        13
Cobalt                           .48       8.90        54
Molybdenum                       .25      10.28        24
Tungsten                         .95      19.25        49
```

Alloy types
```Beryllium + Li           →  Doesn't exist. The atoms don't mix
Beryllium + Al           →  Improves strength
Magnesium + Li           →  Weaker and lighter than pure Mg. Lightest existing alloy
Magnesium + Be           →  Only tiny amounts of beryllium can be added to magnesium
Magnesium + Carbon tubes →  Improves strength, with an optimal tube fraction of 1%
Aluminum  + Li,Mg,Be,Sc  →  Stronger and lighter than aluminum
Titanium  + Li,Mg,Sc     →  Stronger and lighter than titanium
Steel     + Cr,Mo        →  Stronger and more uncorrodable than steel. "Chromoly"
Copper    + Be           →  Stronger than beryllium and is unsparkable
```

High-temperature metals (refractory metals)
```          Melting point (Celsius)

Tungsten    3422
Rhenium     3186
Osmium      3033
Tantalum    3017
Molybdenum  2623
Niobium     2477
Iridium     2446
Ruthenium   2334
Hafnium     2233
Technetium  2157
Rhodium     1964
Chromium    1907
```

High-temperature superalloys

Most alloys weaken with increasing temperature except for a small subset called "superalloys" that strengthen with temperature, such as Ni3Al and Co3Al. This is called the "yield strength anomaly".

Nickel alloys in jet engines have a surface temperature of 1150 Celsius and a bulk temperature of 980 Celsius. This is the limiting element for jet engine performance. Half the mass of a jet engine is superalloy.

Current engines use Nickel superalloys and Cobalt superalloys are under development that will perform even better.

Yield strength in GPa as a function of Celsius temperature.

```                   20   600   800  900  1000  1100 1200  1400  1600 1800  1900  Celsius

VNbMoTaW          1.22         .84        .82       .75  .66   .48   .4
AlMohNbTahTiZr    2.0   1.87  1.60  1.2   .74  .7   .25
Nickel superalloy 1.05        1.20   .90  .60  .38  .15
Tungsten           .95   .42   .39        .34  .31  .28  .25   .10   .08  .04
```
Below 1100 Celsius AlMohNbTahTiZr has the best strength-to-mass ratio and above this VNbMoTaW has the best ratio. Both alloys supercede nickel superalloy and both outperform tungsten, the metal with the highest melting point. Data:
Entropy, nickel superalloy
Copper alloys
```                  Yield strength (GPa)

Copper                  .27
Brass                   .41     30% zinc
Bronze                  .30     5% tin
Phosphor bronze         .69     10% tin, .25% phosphorus
Copper + beryllium     1.2      2% beryllium, .3% cobalt
Copper + nickel + zinc  .48     18% nickel, 17% zinc
Copper + nickel         .40     10% nickel, 1.25% iron, .4% manganese
Copper + aluminum       .17     8% aluminum
```

Bells and cymbals

Bells and cymbals are made from bell bronze, 4 parts copper and 1 part tin.

Bond energy

Gibbs energy, enthalpy, and entropy
```Pressure         =  P
Volume           =  V
Entropy          =  S
Temperature      =  T
Internal energy  =  E
Enthalpy         =  H  =  E + P V
Gibbs energy     =  G  =  E + P V - T S
Helmholtz energy =  A  =  E - T S
```
The Gibbs energy is the energy required to assemble a molecule from raw elements at standard temperatue (298.2 Kelvin) and pressure (1 bar). The Gibbs energy is measured with respect to the most common form of the element. The Gibbs energy of each element is 0.
Gibbs energy of free atoms

The following table gives the energy required to extract one atom from an element in its most common form. For example, graphite is the most common form of graphite, and it takes 671 Joules/mole to extract a carbon atom from graphite. We also give the enthalpy and entropy for each element.

Table of Gibbs energies
```        Gibbs      Enthalpy       Entropy
kJoule/mole  kJoule/mole  kJoule/mole/K

H2          0          0      .131
C graphite  0          0      .00574
C diamond   2.90       1.90   .00238
N2          0          0      .1915
O2          0          0      .2050
Ne          0          0      .1464
Na          0          0      .0512
Mg          0          0      .0327
Al          0          0      .0283
Al          0          0      .0283
Si          0          0      .0188
P4          0          0      .1644
S           0          0      .0318
Cl2         0          0      .223
K           0          0      .0642
Ca          0          0      .0414
Ar          0          0      .155
Cr          0          0      .0238
Mn          0          0      .0327
Fe          0          0      .0273
Ni          0          0      .0299
Cu          0          0      .0332
Zn          0          0      .0416
Ag          0          0      .0426
Sn          0          0      .0516
Hg          0          0      .0760
Pb          0          0      .0648

H2O      -237.24   -285.83    .06995
CH4                 -74.87    .1862         Combustion =  -890.7
C2H6                -83.7                   Combustion = -1561
C3H8               -104.6
C4H10              -125.5
C5H12              -146.9
C6H14              -167.4
C7H16              -187.9
C8H18              -208.4
C12H26             -352.1     .4907         Combustion =-7901.7
C16H34             -456.3     .5862         Combustion =-10699
N2O                  82.05    .2200
H2O2               -187.80
N2O4                  9.16    .3043
N2H4                 50.63    .1215
NH4NO3
NH4ClO4
HNO3               -207       .146
Li2O     -561.9     -20.01    .03789
C4H8N8O8                                     HMX explosive
BeO      -579.1
B2O3    -1184
CO2      -394.4    -393.5     .214
CO       -137.2    -110.5     .198
NO                   90.2     .211
NO2                  33.2     .240
Na2O     -377
MgO      -596.3    -601.6     .0269
Al2O3   -1582.3    -1675.7    .0509
SiO2     -856.6    -910.9     .0418          Quartz
P2O5
SO2                -296.8     .2481
SO3                -395.7     .2567
K2O      -322.2
CaO      -533.0    -634.9     .0398
TiO2     -852.7
Ti2O3   -1448
VO       -404.2
V2O3    -1139.3
V2O4    -1318.4
Cr2O3   -1053.1   -1139.7     .0812
MnO2     -465.2
MnO      -362.9    -385.2     .0597
MnO2               -520.0     .0530
Fe2O3    -741.0    -824.2     .0874
Fe3O4   -1014     -1118.4     .0146
CoO      -214.2
Co3O4    -795.0
NiO      -211.7    -239.7     .0380
CuO      -129.7    -157.3     .0426
Cu2O     -146.0    -168.6     .0931
ZnO      -318.2    -350.5     .0436
MoO2     -533.0
MoO3     -668.0
Ag2O      -11.2
PdO
SnO2               -577.6     .0523
CdO      -228.4
WO2      -533.9
WO3      -764.1
HgO       -58.5     -90.8     .0703
PbO                -219.0     .0665
PbO2     -219.0    -277.4     .0686
UO2

CuS                  -53.1    .0665
Cu2S                 -79.5    .1209
ZnS2                -206.0    .0577

CaCO3   -1128      -1207      .090

H+ (aq)     0          0      0
OH- (aq) -157.2     -230.0   -.0108
H2O (l)  -237.2     -285.8    .0699
H2O (g)  -228.6     -241.8    .1888
Cu+                   71.7    .0406
Cu+2                  64.8   -.0996
Ca+2                -543.0   -.0531
Ag+ (aq)             105.8    .0727
Al+3 (aq)           -538.4   -.3217
CO3-2               -675.2   -.0569
NH3 (g)   -16.4      -46.1
NaCl (s) -384.1     -411.2    .0721

Gibbs      Enthalpy       Entropy
kJoule/mole  kJoule/mole  kJoule/mole/K
```

Bond energy of hydrides
```Target  Molecule  Bonds  Bond   1st   2nd   3rd   4th
atom                   energy  bond  bond  bond  bond
(eV)   (eV)  (eV)  (eV)  (eV)

H      H2         1    4.52   4.52
He     -          0     -      -
Li     LiH        1    2.56   2.56
Be     BeH2       2     ?     2.35   ?
B      BH3        3     ?     3.43   ?     ?
C      CH4        4    4.31   3.52  4.61  4.61  4.52
N      NH3        3    3.90   3.26  3.91  4.52
O      H2O        2    4.76   4.41  5.12
F      HF         1    5.90   4.90
Ne     -          0     -      -
Na     NaH        1    2.09   2.09
Mg     MgH2       2     ?     2.04   ?
Al     AlH3       3     ?     2.96   ?     ?
Si     SiH4       4     ?     3.10   ?     ?    4.08
P      PH3        3     ?     3.56   ?     ?
S      H2S        2    3.76   3.57  3.95
Cl     HCl        1    4.48   4.48
Ar     -          0     -      -
K      KH         i    1.90   1.90
Ca     CaH2       i     ?     1.74   ?
Ga                      ?      ?     ?     ?
Ge                      ?     3.36   ?     ?     ?
As                      ?     2.82   ?     ?
Se     SeH2       2     ?     3.17   ?
Br     HBr        1    3.80   3.80
Kr     -          0     -      -
In                      ?      ?     ?     ?
Sn                      ?     2.77   ?     ?     ?
Sb                      ?      ?     ?     ?
Te     TeH2       2     ?     2.78   ?
I      HI         1    3.10   3.10
Xe     -          0     -      -
```

Bond energies in eV
```      Single  Double  Triple  Quadruple

B  B    3.04
B  C    3.69
B  O    5.56
C  C    3.65   6.45    8.68   6.32
C  N    3.19   6.38    9.19
C  O    3.73   7.7    11.11
C  Si   3.30
C  P    2.74
C  S    2.82   5.94
N  N    1.76   4.33    9.79
N  O    2.08   6.29
N  Si   3.70
N  P
N  S
O  O    1.50   5.15
O  Si   4.69
O  P    3.47   5.64
O  S           5.41
Si Si   2.30
Si S    3.04
Si P
P  P    2.08
P  S           3.47
S  S    2.34   4.41
H  H    4.52
H  C    4.25
H  N    4.05
H  O    3.79
H  F    5.89
H  Si   3.30
H  P    3.34
H  S    3.76
H  Cl   4.48
```

Bond dissociation energies
```                eV   kJoules/mole

HO    -  H             493.4
O     -  H             424.4
CH3   -  H     4.52    435
CH2   -  H             444
CH    -  H             444
C     -  H             339
C2H5  -  H             423
C2H   -  H             556
C6H5  -  H             473
CH3   -  CH3   3.64    351
CH2   =  CH2           622
CH    ≡  CH            837
C2H3  -  H             464
CH2CHCH2 - H           372
```

Fuel for oxygen
```       Enthalpy
kJ/mole

H2O     -285.83
Li2O     -20.01
BeO     -609.4
CO2     -393.5
MgO     -601.6
Al2O3  -1675.7
Fe2O3   -824.2
```

Oxidizer
```       Enthalpy  Entropy   Boil   Density
kJ/mole   kJ/mole  Kelvin

O2          0       .2050
O3        142.67    .2389   161
H2O2     -187.80
NO         90.2     .211
NO2        33.2     .240
HNO3     -207       .146    356    1.51
N2O3       91.20    .3146   277    1.45
N2O4        9.16
N2O5      -43.1     .1782   320    1.64     solid
N2O        82.05    .2200
SO2      -296.8     .2481   265
SO3      -395.7     .2567
N2H4       50.63    .1215
NH4NO3   -365.6             483    1.72
NH4ClO4  -295.77    .1842
C4H8N8O8  296.16                            HMX explosive
NH3OHNO3
```

Metal smelting

Prehistoric-style smelter

Most metals are in oxidized form. The only metals that can be found in pure form are gold, silver, copper, platinum, palladium, osmium, and iridium.

Smelting is a process for removing the oxygen to produce pure metal. The ore is heated in a coal furnace and the carbon seizes the oxygen from the metal. For copper,

```Cu2O + C  →  2 Cu + CO
```
At low temperature copper stays in the form of Cu2O and at high temperature it gives the oxygen to carbon and becomes pure copper.

For iron, the oxidation state is reduced in 3 stages until the pure iron is left behind.

```3 Fe2O3 + C  →  2 Fe3O4 + CO
Fe3O4   + C  →  3 FeO   + CO
FeO     + C  →    Fe   + CO
```
```Oxidation state  =  Number of electrons each iron atom gives to oxygen

Oxidation state
CuO          2
Cu2O         1
Cu           0
Fe2O3        3
Fe3O4       8/3
FeO          2
Fe           0
```

Smelting temperature

The following table gives the temperature required to smelt each element with carbon.

```        Smelt  Method  Year  Abundance
(C)                   (ppm)

Gold        <0   *   Ancient      .0031
Silver      <0   *   Ancient      .08
Platinum    <0   *    1735        .0037
Mercury     <0  heat -2000        .067
Copper      80   C   -5000      68
Sulfur     200   *   Ancient   420
Nickel     500   C    1751      90
Cobalt     525   ?    1735      30
Tin        725   C   -3200       2.2
Iron       750   C   -1000   63000
Phosphorus 750  heat  1669   10000
Tungsten   850   C    1783    1100
Potassium  850   e-   1807   15000
Zinc       975   C    1746      79
Sodium    1000   e-   1807   23000
Chromium  1250   C    1797     140
Niobium   1300   H    1864      17
Manganese 1450   C    1774    1120
Silicon   1575   K    1823  270000
Titanium  1650   Na   1910   66000
Magnesium 1875   e-   1808   29000
Lithium   1900   e-   1821      17
Aluminum  2000   K    1827   82000
Uranium   2000   K    1841       1.8
Beryllium 2350   K    1828       1.9

Smelt:      Temperature required to smelt with carbon
Method:     Method used to purify the metal when it was first discovered
*:  The element occurs in its pure form naturally
C:  Smelt with carbon
K:  Smelt with potassium
Na: Smelt with sodium
H:  Smelt with hydrogen
e-: Electrolysis
heat:  Heat causes the oxide to decompose into pure metal. No carbon required.
chem:  Chemical separation
Discovery:  Year the element was first obtained in pure form
Abundance:  Abundance in the Earth's crust in parts per million
```
Elements with a low carbon smelting temperature were discovered in ancient times unless the element was rare. Cobalt was discovered in 1735, the first new metal since antiquity, and this inspired scientists to smelt every known mineral in the hope that it would yield a new metal. By 1800 all the rare elements that were carbon smeltable were discovered.

The farther to the right on the periodic table, the lower the smelting temperature, a consequence of "electronegativity".

The battery was invented in 1800, launching the field of electrochemistry and enabling the the isolation of non-carbon-smeltable elements. Davy used electrolysis in 1807 to isolate sodium and potassium and then he used these metals to smelt other metals. To smelt beryllium with potassium, BeO + 2 K ↔ Be + K2O.

Titanium can't be carbon smelted because it forms the carbide Ti3C.

Data

Thermite

Thermite is smelting with aluminum. For example, to smelt iron with aluminum,

```Fe2O3 + 2 Al  →  2 Fe + Al2O3
```

Smelting reactions

The following table shows reactions that change the oxidation state of a metal. "M" stands for an arbitrary metal and the magnitudes are scaled to one mole of O2. The last two columns give the oxidation state of the metal on the left and right side of the reaction. An oxidation state of "0" is the pure metal and "M2O" has an oxidation state of "1".

```                            Oxidation state   Oxidation state
at left          at right
2  M2O   ↔  4  M     + O2        1                0
4  MO    ↔  2  M2O   + O2        2                1
2  M3O4  ↔  6  MO    + O2       8/3               2
6  M2O3  ↔  4  M3O4  + O2        3               8/3
2  M2O3  ↔  4  MO    + O2        3                2
2  MO    ↔  2  M     + O2        2                0
2/3 M2O3  ↔ 4/3 M     + O2        3                0
1  MO2   ↔  1  M     + O2        4                0
2  MO2   ↔  2  MO    + O2        4                2
```

Gibbs energy

Let MO be a metal oxide for which the Gibbs energy of CO is larger than MO and the oxygen binds to the metal preferentially over carbon.

The entropies of most metal oxides are similar and so changing the temperature has little effect on their relative Gibbs energies. CO is special because it is a gas and hence has a larger entropy than the solid metal oxides. As temperature increases the Gibbs energy of CO decreases faster than that of MO and at the critical smelting temperature they are equal. Above this temperature the oxygen unbinds to the metal and binds to carbon.

For the smelting of cobalt,

```Standard temperature                 =  T0  =  298 Kelvin  =  25 Celsius
Smelting temperature                 =  Tsmelt
Temperature change                   =  t   =  Tsmelt - T0
Gibbs energy at standard temperature =  G
Entropy at standard temperature      =  S
Gibbs energy at temperature Tsmelt    =  g   =  G - t S
CoO Gibbs energy per mole O2         =  GCoO =  -428.4   kJoule/mole
CO  Gibbs energy per mole O2         =  GCO  =  -274.4   kJoule/mole
CoO entropy per mole O2              =  SCoO =      .12  kJoule/mole
CO  entropy per mole O2              =  SCO  =      .396 kJoule/mole
```
At the smelting temperature, the Gibbs energies of CoO and CO are equal and the reaction is in equilibrium. Below this temperature oxygen binds to cobalt and above this temperature it binds to carbon. The calculation is approximate because it assumes entropy is a constant as a function of temperature. To calculate the smelting temperature,
```    gCoO      =      gCO
GCoO - t SCoO  =  GCO - t SCO

t  =  (GCoO - GCO) / (SCoO - SCO)
=  558 Celsius

Tsmelt  =  583 Celsius  =  t + 25 Celsius      (The actual smelting temperature is 525 Celsius)
```

Smelting thermodynamics
```       Gibbs       Gibbs            Entropy       Entropy
kJoule/mole  kJoule/mole(O2)  kJoule/mole  kJoule/mole(O2)

Li2O     -561.9    -1123.8
Na2O     -377       -754
K2O      -322.2     -644.4
Cu2O     -146.0     -292.0
Ag2O      -11.2      -22.4

BeO      -579.1    -1158.2
CO       -137.2     -274.4     .198      .396
MgO      -596.3    -1192.6     .0269     .0538
CaO      -533.0    -1066.0     .0398     .0769
VO       -404.2     -808.4
MnO      -362.9     -725.8     .0597     .1194
CoO      -214.2     -428.4
NiO      -211.7     -423.4
CuO      -129.7     -259.4     .0426     .0852
ZnO      -318.2     -636.4
CdO      -228.4     -456.8
HgO       -58.5     -117.0

Fe3O4   -1014       -507       .0146     .0073
Co3O4    -795.0     -397.5

B2O3    -1184       -789
Al2O3   -1582.3    -1054.9     .0509     .0339
Ti2O3   -1448       -965.3
V2O3    -1139.3     -759.5
Cr2O3   -1053.1     -702.1     .0812     .0541
Fe2O3    -741.0     -494.0     .0874     .0583

CO2      -394.4     -394.4     .214      .214
SO2                            .2481     .2481
SiO2     -856.4     -856.4     .0418     .0418
TiO2     -852.7     -852.7
MnO2     -465.2     -465.2     .0530     .0530
MoO2     -533.0     -533.0
WO2      -533.9     -533.9
PbO2     -219.0     -219.0

MoO3     -668.0     -445.3
WO3      -764.1     -509.4

V2O4    -1318.4     -659.2

Cu          0
C (gas)   672.8
```

Minerals

We list the most abundant mineral for each element.

Spodumene: LiAl(SiO3)2
Beryl: Be3Al2(SiO3)6
Periclase: MgO
Magnesite: MgCO3
Dolomite: CaMg(CO3)2
Bauxite: Al(OH)3 and AlO(OH)

Quartz: SiO2
Rutile: TiO2
Chromite: FeCr2O4
Pyrolusite: MnO2
Hematite: Fe2O3

Hematite: Fe2O3
Pyrite: FeS2
Iron meteorite
Cobaltite: CoAsS
Millerite: NiS
Chalcocite: Cu2S

Chalcopyrite: CuFeS2
Sphalerite: ZnS
Germanite: Cu26Fe4Ge4S32
Zircon: ZrSiO4
Molybdenite: MoS2
Acanthite: Ag2S
Cassiterite: SnO2
Wolframite: FeWO4
Cinnabar: HgS
Platinum nugget
Gold nugget
Galena: PbS

More common minerals:

Fluorite: CaF2
Volcanic sulfur
Alumstone: KAl3(SO4)2(OH)6
Malachite: Cu2CO3(OH)l2
Azurite: Cu3(CO3)2(OH)2
Muscovite mica: KAl2(AlSi3O10)(F,OH)2 or KF2(Al2O3)3(SiO2)6(H2O)

```       grams/cm3

Osmium      22.6
Gold        19.3
Tungsten    19.2
Silver      10.5
Sperrylite  10.6   PtAs2
Thorianite  10     ThO2
Copper       8.9
Calaverite   9.2   AuTe2
Petzite      8.7   Ag3AuTe2
Minium       8.2   Pb3O4
Altaite      8.1   PbTe
Cinnabar     8.1   HgS
Iron         7.9
Epsomite     1.67  MgSO4(H2O)7
Carnallite   1.6   KMgCl3(H2O)6
```
ce1.html 0;256;0c
Spices

Turmeric: curcumin
Cumin: cuminaldehyde
Chili: capsaicin
Mustard: allyl isotyiolcyanate

Bay: myrcene
Garlic and onion: allicin
Clove: eugenol

Raspberry ketone
Tangerine: tangeritin
Lemon: citral
Lemon peel: limonene

Chocolate: theobromine
Smoke: guaiacol
Cardamom: terpineol
Wintergreen: methyl salicylate

```Hydrogen   White
Carbon     Black
Nitrogen   Blue
Oxygen     Red
Sulfur     Yellow
```
```        Scoville scale (relative capsaicin content)

Ghost pepper    1000000
Naga Morich     1000000
Habanero         250000
Cayenne           40000
Tabasco           40000
Jalapeno           6000
Pimento             400

Molecule        Relative hotness

Rresiniferatoxin   16000
Tinyatoxin          5300
Capsaicin             16         Chili pepper
Nonivamide             9.2       Chili pepper
Shogaol                 .16      Ginger
Piperine                .1       Black pepper
Gingerol                .06      Ginger
Capsiate                .016     Chili pepper
```
Caraway: carvone
Black tea: theaflavin
Cinnamon: cinnamaldehyde
Citrus: hesperidin
Fruit: quercetin

Mint: menthol
Juniper: pinene
Saffron: picrocrocin
Saffron: safranal
Wine: tannic acid

Black pepper: piperine
Oregano: carvacrol
Sesame: sesamol
Curry leaf: girinimbine
Aloe emodin
Whiskey lactone

Signalling molecules

Alcohol
Caffeine
Tetrahydrocannabinol
Nicotine

Dopamine
Seratonin

Aspirin
Ibuprofen
Hydrocodone
Morphone

Vitamin A (beta carotene)
Vitamin A (retinol)
Vitamin C (ascorbic acid
Vitamin D (cholecalciferol)
B

Opium

Opium poppies
Opium poppy

```              Strength   Half life   Dose
hours      mg

Carfentanil     30000        7.7       .0003
Ohmefentanil     6300
Dihydroetorphine 4000                  .03
Etorphine        2000                  .006
Sufentanil        750        4.4       .015
Ocfentanil        180                  .06
Fentanyl           75         .04      .1
Oxymorphone         7        8       10
Hydromorphone       5        2.5      1.5    Dilaudid
Heroine             4.5      <.6      2.2    Diamorphine
Oxycodone           1.5      4        6.7
Morphine            1        2.5     10
Hydrocodone         1        5       10      Vicodin
Codeine              .1      2.8    180
Naproxen             .0072  18     1380
Ibuprofen            .0045   2     2220
Aspirin              .0028   6     3600
```

Strength data

Poppy

The composition of a typical opium poppy is:

```                %    First isolated

Morphine        10       1817          Used to produce heroine
Codeine          2       1832
Thebaine         8                     Used to produce hydrocodone and hydromorphone
Papaverine      14       1848          Not psychoactive
Noscapine        5       1820          Not psychoactive
Other alkaloiods  .1
```

Opioids

Codein
Hydrocodone
Hydrocodone
Morphine
Morphine
Oxycodone
Oxycodone

Heroine
Heroine
Hydromorphone
Oxymorphone
Oxymorphone

Fentanyl
Fentanyl
Ocfentanil
Sufentanil
Sufentanil
Etorphine
Etorphine

Dihydroetorphine
Carfentanil

Explosives

Medieval-style black powder
Modern smokeless powder

```               MJoules  Rocket  Shock  Density  Boil
/kg     km/s   km/s   g/cm3  Kelvin

Beryllium+ O2    23.2   5.3
Aluminum + O2    15.5
Magnesium+ O2    14.8
Hydrogen + O2    13.2   4.56             .07    20
Kerosene + O3    12.9
Octanitrocubane  11.2          10.6     1.95
Methane  + O2    11.1   3.80             .42   112
Octane   + O2    10.4                    .70   399
Kerosene + O2    10.3   3.52             .80   410
Dinitrodiazeno.   9.2          10.0     1.98
C6H6N12O12        9.1                   1.96        China Lake compound
Kerosene + H2O2   8.1   3.2
Kerosene + N2O4   8.0   2.62
HMX (Octogen)     8.0   3.05    9.1     1.86
RDX (Hexagen)     7.5   2.5     8.7     1.78
Al + NH4NO3       6.9
Nitroglycerine    7.2           8.1     1.59        Unstable
PLX               6.5                   1.14        95% CH3NO2 + 5% C2H4(NH2)2
Composition 4     6.3           8.04    1.59        91% RDX. "Plastic explosive"
Kerosene + N2O    6.18
Dynamite          5.9           7.2     1.48        75% Nitroglycerine + stabilizer
PETN              5.8           8.35    1.77
Smokeless powder  5.2           6.4     1.4         Used after 1884. Nitrocellulose
TNT               4.7           6.9     1.65        Trinitrotoluene
Al + Fe2O3        4.0                               Thermite
H2O2              2.7   3.1             1.45   423  Hydrogen peroxide
Black powder      2.6   3.08     .6     1.65        Used before 1884
Al + NH4ClO4            2.6
NH4ClO4                 2.5
N2O               1.86  1.76
N2H4              1.6   2.2             1.02   387  Hydrazine
NH4NO3            1.4   2.0     2.55    1.12        Ammonium nitrate
Bombardier beetle  .4                               Hydroquinone + H2O2 + protein catalyst
N2O4               .10                  1.45   294

Rocket: Rocket exhaust speed
Shock:  Shock speed
```
Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Nitrocellulose
TNT
RDX
HMX
PETN
Octanitrocubane

Dinitrodiazenofuroxan
Nitromethane

High explosives

High explosives have a large shock velocity.

```
MJoules   Shock  Density
/kg     km/s    g/cm3

Octanitrocubane    11.2   10.6     1.95
Dinitrodiazeno.     9.2   10.0     1.98
C6H6N12O12          9.1            1.96    China Lake compound
HMX (Octogen)       8.0    9.1     1.86
RDX (Hexagen)       7.5    8.7     1.78
PLX                 6.5            1.14    95% CH3NO2 + 5% C2H4(NH2)2
Composition 4       6.3    8.04    1.59    91% RDX. "Plastic explosive"
Dynamite            5.9    7.2     1.48    75% Nitroglycerine + stabilizer
PETN                5.8    8.35    1.77
```

Liquid oxygen

The best oxidizer is liquid oxygen, and the exhaust speed for various fuels when burned with oxygen is:

```                Exhaust  Energy   Density of fuel + oxidizer
speed   /mass
km/s    MJ/kg      g/cm3

Hydrogen   H2      4.46   13.2    .32
Methane    CH4     3.80   11.1    .83
Ethane     C2H6    3.58   10.5    .9
Kerosene   C12H26  3.52   10.3   1.03
Hydrazine  N2H4    3.46          1.07
```
Liquid hydrogen is usually not used for the ground stage of rockets because of its low density.
Oxidizer

We use kerosene as a standard fuel and show the rocket speed for various oxidizers. Some of the oxidizers can be used by themselves as monopropellants.

```    Energy/Mass       Energy/Mass        Rocket           Rocket         Boil    Density
with kerosene   as monopropellant  with kerosene  as monopropellant  Kelvin   g/cm3
MJoule/kg         MJoule/kg          km/s             km/s

O3        12.9           2.97                                              161
O2        10.3           0                  3.52             0             110     1.14
H2O2       8.1           2.7                3.2              1.6           423     1.45
N2O4       8.00           .10               2.62                           294     1.44
N2O        6.18          1.86                                1.76          185
N2H4       -             1.58                                2.2           387     1.02
```

Solid rocket fuel
```               MJoules  Rocket   Density
/kg     km/s    g/cm3

C6H6N12O12        9.1             1.96        China Lake compound
HMX (Octogen)     8.0   3.05      1.86
RDX (Hexagen)     7.5   2.5       1.78
Al + NH4ClO4            2.6
NH4ClO4                 2.5
NH3OHNO3                2.5       1.84        Hydrxyammonium nitrate
Al + NH4NO3       6.9
NH4NO3            1.4   2.0       1.12        Ammonium nitrate
```

History
```~808  Qing Xuzi publishes a formula resembling gunpower, consisting of
6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850  Incendiary property of gunpower discovered
1132  "Fire lances" used in the siege of De'an, China
1220  al-Rammah of Syria publishes "Military Horsemanship and Ingenious War
Devices", describes the purification of potassium nitrate by
adding potassium carbonate with boiling water, to precipitate out
magnesium carbonate and calcium carbonate.
1241  Mongols use firearms at the Battle of Mohi, Hungary
1338  Battle of Arnemuiden.  First naval battle involving cannons.
1346  Cannons used in the Siege of Calais and the Battle of Crecy
1540  Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1610  First flintlock rifle
1661  Boyle publishes "The Sceptical Chymist", a treatise on the
distinction between chemistry and alchemy.  It contains some of the
earliest modern ideas of atoms, molecules, and chemical reaction,
and marks the beginning of the history of modern chemistry.
1669  Phosphorus discovered
1774  Lavoisier appointed to develop the French gunpowder program.  By 1788
French gunpowder was the best in the world.
1832  Braconnot synthesizes the first nitrocellulose (guncotton)
1846  Nitrocellulose published
1847  Sobrero discovers nitroglycerine
1862  LeConte publishes simple recipes for producing potassium nitrate.
1865  Abel develops a safe synthesis of nitrocellulose
1867  Nobel develops dynamite, the first explosive more powerful than black powder
It uses diatomaceous earth to stabilize nitroglycerine
1884  Vieille invents smokeless gunpowder (nitrocellulose), which is 3 times
more powerful than black powder and less of a nuisance on the battlefield.
1902  TNT first used in the military.  TNT is much safer than dynamite
1930  RDX appears in military applications
1942  Napalm developed
1949  Discovery that HMX can be synthesized from RDX
1956  C-4 explosive developed (based on RDX)
1999  Eaton and Zhang synthesize octanitrocubane and heptanitrocubane

Black powder           =  .75 KNO3  +  .19 Carbon  +  .06 Sulfur
```

Above 550 Celsius, potassium nitrate decomposes. 2 KNO3 ↔ 2 KNO2 + O2.

Black powder

Sulfur
Sulfur
Saltpeter
Saltpeter

Charcoal
Icing sugar and KNO3
Mortar and pestle
Mortar and pestle

```Potassium nitrate  KNO3     75%       (Saltpeter)
Charcoal           C7H4O    15%
Sulfur             S        10%

Oversimplified equation:  2 KNO3 + 3 C + S  →  K2S + N2 + 3 CO2

Realistic equation:       6 KNO3 + C7H4O + 2 S  →  KCO3 + K2SO4 + K2S + 4 CO2 + 2 CO + 2 H2O + 3 N2
```
Nitrite (NO3) is the oxidizer and sulfur lowers the ignition temperature.
Fuel air explosives
```                   MJoules
/kg

Hydrogen + Oxygen     13.16
Gasoline + Oxygen     10.4

Mass   Energy    Energy/Mass
kg      MJ         MJ/kg

MOAB    9800   46000        4.7               8500 kg of fuel
```

Phosphorus
White phosphorus
White, red, violet, and black phosphorus
Red phosphorus

Violet phosphorus
Black phosphorus
Black phosphorus

```Form      Ignition    Density
(Celsius)

White        30        1.83
Red         240        1.88
Violet      300        2.36
Black                  2.69
```
Red phosphorus is formed by heating white phosphorus to 250 Celsius or by exposing it to sunlight. Violet phosphorus is formed by heating red phosphorus to 550 Celsius. Black phosphorus is formed by heating white phosphorus at a pressure of 12000 atmospheres. Black phosphorus is least reactive form and it is stable below 550 Celsius.
Matches

Striking surface
P4S3

The safety match was invented in 1844 by Pasch. The match head cannot ignite by itself. Ignitition is achieved by striking it on a rough surface that contains red phosphorus. When the match is struck, potassium chlorate in the match head mixes with red phosphorus in the abrasive to produce a mixture that is easily ignited by friction. Antimony trisulfide is added to increase the burn rate.

```Match head                 Fraction             Striking surface   Fraction

Potassium chlorate    KClO3  .50                Red phosphorus      .5
Silicon filler        Si     .4                 Abrasive            .25
Sulfur                S      small              Binder              .16
Antimony3 trisulfide  Sb2S3  small              Neutralizer         .05
Neutralizer                  small              Carbon              .04
Glue                         small
```
A "strike anywhere" match has phosphorus in the match head in the form of phosphorus sesquisulfide (P4S3) and doesn't need red phosphorus in the striking surface. P4S3 has an ignition temperature of 100 Celsius.
Flint

Before the invention of iron, fires were started by striking flint (quartz) with pyrite to generate sparks. Flintlock rifles work by striking flint with iron. With the discovery of cerium, ferrocerium replaced iron and modern butane lighters use ferrocerium, which is still referred to as "flint".

```Cerium        .38      Ignition temperature of 165 Celsius
Lanthanum     .22
Iron          .19
Neodymium2    .04
Praseodymium  .04
Magnesium     .04
```

Nitrous oxide engine

Nitrous oxide is stored as a cryogenic liquid and injected along with gaoline into the combustion chamber. Upon heating to 300 Celsius the nitrous oxide decomposes into nitrogen and oxygen gas and releases energy. The oxygen fraction in this gas is higher than that in air (1/3 vs. .21) and the higher faction allows for more fuel to be consumed per cylinder firing.

```Air density                  =  .00122 g/cm3
Nitrous oxide gas density    =  .00198 g/cm3
Diesel density               =  .832   g/cm3
Gasoline density             =  .745   g/cm3
Diesel energy/mass           =  43.1   MJoules/kg
Gasoline energy/mass         =  43.2   MJoules/kg
Nitrous oxide boiling point  = -88.5   Celsius
Air oxygen fraction          =  .21
Nitrous oxide oxygen fraction=  .33
Nitrous oxide decompose temp =  300    Celsius
Nitrous oxide liquid pressure=   52.4  Bars     Pressure required to liquefy N2O at room temperature
```

Bombardier beetle

Hydroquinone
P-quinone

Hydroquinone and peroxide are stored in 2 separate compartments are pumped into the reaction chamber where they explode with the help of protein catalysts. The explosion vaporizes 1/5 of the liquid and expels the rest as a boiling drop of water, and the p-quinone in the liquid damages the foe's eyes. The energy of expulsion pumps new material into the reaction chamber and the process repeats at a rate of 500 pulses per second and a total of 70 pulses. The beetle has enough ammunition for 20 barrages.

```2 H2O2  →  2 H2O +  O2           (with protein catalyst)
C6H4(OH)2  →  C6H4O2 + H2        (with protein catalyst)
O2 + 2 H2  →  2 H2O

Firing rate                     = 500 pulses/second
Number of pulses in one barrage =  70
Firing time                     = .14 seconds
Number of barrages              =  20
```

Flame speed

A turbojet engine compresses air before burning it to increase the flame speed and make it burn explosively. A ramjet engine moving supersonically doesn't need a turbine to achieve compression.

Turbojet
Ramjet

```Airbus A350 compression ratio  =  52
Air density at sea level       = 1    bar
Air density at 15 km altitude  =  .25 bar
Air density in A350 engine     =  13  bar
```
From the thermal flame theory of Mallard and Le Chatelier,
```Temperature of burnt material    =  Tb
Temperature of unburnt material  =  Tu
Temperature of ignition          =  Ti
Fuel density                     =  Dfuel
Oxygen density                   =  Doxygen
Reaction coefficient             =  C
Reaction rate                    =  R  =  C Dfuel Doxygen
Thermal diffusivity              =  Q  = 1.9⋅10-5 m2/s
Flame speed                      =  V

V2  =  Q C Dfuel Doxygen (Tb - Ti) / (Ti - Tu)
```

Shocks

Spherical implosion
Mach < 1,    Mach = 1,     Mach > 1

If the pressure front moves supersonically then the front forms a discontinuous shock, where the pressure makes a sudden jump as the shock passes.

Energy boost

Metal powder is often included with explosives.

```        Energy/mass    Energy/mass
not including  including
oxygen         oxygen
(MJoule/kg)    (MJoule/kg)

Hydrogen    113.4      12.7
Gasoline     46.0      10.2
Beryllium    64.3      23.2
Aluminum     29.3      15.5
Magnesium    24.5      14.8
Carbon       12.0       3.3
Lithium       6.9       3.2
Iron          6.6       4.6
Copper        2.0       1.6
```

Fireworks

Li
B
Na
Mg
K
Ca
Fe

Cu
Zn
As
Sr
Sb
Rb
Pb

BaCl (green), CuCl (blue), SrCl (red)
Zero gravity
Bunsen burner, O2 increases rightward
Methane

Oxygen candle

Sodium chlorate

An oxygen candle is a mixture of sodium chlorate and iron powder, which when ignited smolders at 600 Celsius and produces oxygen at a rate of 6.5 man-hours of oxygen per kilogram of mixture. Thermal decomposition releases the oxygen and the burning iron provides the heat. The products of the reaction are NaCl and iron oxide.

Firearms

Walther PPK/E 9 mm
FN SCAR-H 7.6 mm

Barrett M82 13 mm
M2 Bradley, M242 Bushmaster 25 mm
GAU-8 Avenger 30 mm

A-10 Warthog, GAU-8 Avenger
M1 Abrams 120 mm
M777 howitzer 155 mm

M777 Howitzer
U.S.S. Iowa 406 mm

```                Bullet  Bullet   Speed   Energy   Barrel    Gun     Fire   Vehicle
diam    mass                                       rate    mass
mm      kg      m/s    kJoule   meters     kg     Hertz   tons

Walther PPK         5.6    .0020   530       .277   .083       .560
Walther PPK         5.6    .0030   370       .141   .083       .560
Walther PPK/S       7.65   .0050   318       .240   .083       .630
Walther PPK/E       9.0    .0065   323       .338   .083       .665
M4 Carbine          5.56   .0041   936      1.796   .370      2.88    15.8
FN SCAR-H Rifle     7.62   .011    790      3.506   .400      3.58    10.4           20 round magazine
Barrett M82        13.0    .045    908     18.940   .74      14.0                    10 round magazine
Vidhwansak         20      .13     720     33.7    1.0       26                      20x81 mm. 3 round magazine
RT-20              20      .13     850     47       .92      19.2                    1 round magazine
M621 cannon        20      .102   1005     51.5              45.5     13.3           20x102 mm
M61 Vulcan         20      .102   1050     56.2              92      110             20x102. 6 barrels
Oerlikon KBA       25      .184   1335    164      2.888    112       10
M242 Bushmaster    25      .184   1100    111      2.175    119        8.3    27.6   M2 Bradley
GAU-12 Equalizer   25      .184   1040     99.5             122       70       6.3   Harrier 2. 5 barrels
M230 chain gun     30      .395    805    128                55.9     10.4     5.2   Apache. 30x113 mm
Mk44 Bushmaster 2  30      .395   1080    230      2.41     160        3.3    27.6   M2 Bradley. 30x173 mm
GAU-8 Avenger      30      .395   1070    226      2.30     281       70      11.3   A-10 Warthog. 30x173 mm. 7 barrels
Bushmaster III     35             1180                      218        3.3           35x228 mm
Bushmaster IV      40     1.08                              198        3.3           40x365 mm
Rheinmetall 120   120     8.350   1750  12800      6.6     4500         .1    62     M1 Abrams tank
M777 Howitzer     155    48        827  16400      5.08    4200         .083
Iowa Battleship   406   862        820 290000     20.3   121500         .033  45000
2 bore rifle       33.7    .225    460     23.7     .711      4.5                    Historical big-game rifle
Cannonball 6 lb    87     2.72     438    261      2.4
Cannonball 9 lb    96     4.08     440    395      2.7
Cannonball 12 lb  110     5.44     453    558      2.4
Cannonball 18 lb  125     8.16     524   1120      2.6     2060
Cannonball 24 lb  138    10.89     524   1495      3.0     2500
Cannonball 32 lb  152    14.5      518   1945      3.4     2540
Cannonball 36 lb  158    16.33     450   1653      2.9     3250
```
Cannonball diameters are calculated from the mass assuming a density of 7.9 g/cm3.
For a pistol or rifle, the "vehicle mass" is the mass of the person wielding it. We use the mass of a typical person.
The "Metal Storm" gun has 36 barrels, 5 bullets per barrel, and fires all bullets in .01 seconds. The bullets are stacked in the barrel end-to-end and fired sequentially.

12 pound cannonballs
24 pound cannonballs

Bullet speed

25 mm
Excalibur 155 mm

The energy distribution for a 7.62 mm Hawk bullet is

```Bullet energy    .32
Hot gas          .34
Barrel heat      .30
Barrel friction  .02
Unburnt powder   .01
```
To estimate the velocity of a bullet,
```Energy efficiency  =  e  =  .32    (Efficiency for converting powder energy to bullet enery)
Bullet mass        =  M
Powder mass        =  m
Powder energy/mass =  Q  =  5.2 MJoules/kg
Bullet velocity    =  V
Bullet energy      =  E  =  ½ M V2  =  e Q m    (Kinetic energy = Efficiency * Powder energy)

V  =  (2 e Q m / M)2  =  1820 (m/M)½  meters/second
```

Muzzle break

M777 Howitzer
XD-40 V-10

The muzzle break at the end of the barrel deflects gas sideways to reduce recoil.

Ruby

Ruby in a green laser
Synthetic rubies

Emerald

Sapphire

Synthetic sapphire

Diamond

Raw diamond
Raw diamond
Synthetic diamond
Synthetic diamonds

Topaz

Quartz

Crystals
Crystal, polycrystal, and amorphous

Diamond
Diamond
Diamond
Diamond
Diamond

Diamond and graphite
Carbon phase diagram
Corundum (Al2O3)
Corundum
Corundum unit cell

Corundum
Tungsten Carbide
Metal lattice

Alpha quartz (SiO2)
Beta quartz
Glass (SiO2)
Ice
Salt (NaCl)

Corundum is a crystalline form of aluminium oxide (Al2O3). It is transparent in its pure orm and can have different colors when metal impurities are present. Specimens are called rubies if red, padparadscha if pink-orange, and all other colors are called sapphire, e.g., "green sapphire" for a green specimen.

```Metal impurity   Color

Chromium         Red
Iron             Blue
Titanium         Yellow
Copper           Orange
Magnesium        Green
```

Price
```1 Carat                     =  .2 grams
Price of a 1 Carat diamond  =  C  ≈  1000 \$     (This varies according to quality)
Mass of diamond in Carats   =  M
Price of diamond in dollars =  C M2
Pure gold                   =  24 Karats
3/4 pure gold               =  18 Karats

1837  Gaudin produces the first synthetic ruby.
1905  Bridgman invents the diamond anvil, which reached a pressure of 10 GPa.
He was awarded the Nobel prize for this in 1946.
1910  Synthetic ruby begins to be mass produced.
1928  Sir Parsons produces the first synthetic diamonds.
1954  Hall produces the first commercially successful synthetic diamonds.
1970  First gem-quality synthetic diamonds produced.
2015  Synthetic diamonds reach 10 carats in size.
```

Fullerines

Buckyball with 540 atoms
Buckyball with 60 atoms
Buckyballs in the liquid phase

Nanotube

Buckyballs in a nanotube
Graphene

Polymers

Zylon
Vectran
Aramid (Kevlar)
Polyethylene

Aramid
Nylon
Hydrogen bonds in Nylon

Spider silk
Lignin

Lignin comprises 30 percent of wood and it is the principal structural element.

Rope

```               Year   Young  Tensile  Strain  Density   Common
(GPa)  strength         (g/cm3)   name
(GPa)
Gut           Ancient           .2
Cotton        Ancient                   .1       1.5
Hemp          Ancient   10      .3      .023
Duct tape                       .015
Gorilla tape                    .030
Polyamide      1939      5     1.0      .2       1.14    Nylon, Perlon
Polyethylene   1939    117                       1.4     Dacron
Polyester      1941     15     1.0      .067     1.38
Polypropylene  1957                               .91
Carbon fiber   1968            3.0               1.75
Aramid         1973    135     3.0      .022     1.43    Kevlar
HMPE           1975    100     2.4      .024      .97    Dyneema, Spectra
PBO            1985    280     5.8      .021     1.52    Zylon
LCAP           1990     65     3.8      .058     1.4     Vectran
Vectran HT              75     3.2      .043     1.41    Vectran
Vectran NT              52     1.1      .021     1.41    Vectran
Vectran UM             103     3.0      .029     1.41    Vectran
Nanorope             ~1000     3.6      .0036    1.3
Nanotube              1000    63        .063     1.34
Graphene              1050   160        .152     1.0

Strain  =  Strength / Young
```
Carbon fiber is not useful as a rope.

A string ideally has both large strength and large strain, which favors Vectran.

Suppose Batman has a rope made out of Zylon, the strongest known polymer.

```Batman mass            =  M         =    100 kg               (includes suit and gear)
Gravity constant       =  g         =     10 meters/second2
Batman weight          =  F         =   1000 Newtons
Zylon density          =  D         =   1520 kg/meter3
Zylon tensile strength =  Pz        = 5.8⋅109 Newtons/meter2
Rope load              =  P         = 1.0⋅109 Newtons/meter2   (safety margin)
Rope length            =  L              100 meters
Rope cross section     =  A  = F/P  =1.0⋅10-6 meters2
Rope radius            =  R  =(A/π)½=     .56 mm
Rope mass              =  Mr = DAL  =     .15 kg
```

Wood

```         Density   Tensile   Young
strength
(g/cm^3)  (Gpa)     (Gpa)

Balsa         .12    .020      3.7
Corkwood      .21
Cedar         .32    .046      5.7     Northern white
Poplar        .33    .048      7.2     Balsam
Cedar         .34    .054      8.2     Western red
Pine          .37    .063      9.0     Eastern white
Buckeye       .38    .054      8.3     Yellow
Butternut     .40    .057      8.3
Basswood      .40    .061     10.3
Spruce, red   .41    .072     10.7
Aspen         .41    .064     10.0
Fir, silver   .42    .067     10.8
Hemlock       .43    .061      8.5     Eastern
Redwood       .44    .076      9.6
Ash, black    .53    .090     11.3
Birch, gray   .55    .069      8.0
Walnut, black .56    .104     11.8
Ash, green    .61    .100     11.7
Ash, white    .64    .110     12.5
Oak, red      .66    .100     12.7
Elm, rock     .66    .106     10.9
Beech         .66    .102     11.8
Birch, yellow .67    .119
Mahogany      .67    .124     10.8     West Africa
Locust        .71    .136     14.5     Black or Yellow
Persimmon     .78    .127     14.4
Oak, swamp    .79    .124     14.5     Swamp white
Gum, blue     .80    .118     16.8
Hickory       .81    .144     15.2        Shagbark
Eucalyptus    .83    .122     18.8
Bamboo        .85    .169     20.0
Oak, live     .98    .130     13.8
Ironwood     1.1     .181     21.0
Lignum Vitae 1.26    .127     14.1
```
Data #1     Data #2
Plastic

```           Density   Tensile   Young
strength
(g/cm^3)  (Gpa)     (Gpa)

Polyamide            .11       4.5
Polyimide            .085      2.5
Acrylic              .07       3.2
Polycarbonate        .07       2.6
Acetyl copoly        .06       2.7
ABS                  .04       2.3
Polypropylene  .91   .04       1.9
Polystyrene          .04       3.0
Polyethylene   .95   .015       .8
```

Valyrian steel

"Ice" is the sword with the red handle

Valyrian steel is a fictional substance from "Game of Thrones" that is stronger, lighter, and harder than steel. The only elements that qualify are beryllium, titanium, and vanadium, none of which were known in Earth history until the 18th century. Valyrian steel could be of these elements, an alloy, or a magical substance. According to George Martin, magic is involved.

The fact that it is less dense than steel means that it can't be a fancy form of steel such as Damascus steel or Wootz steel. Also, fancy steel loses its special properties if melted and hence cannot be reforged, whereas Valyrian steel swords can be reforged.

In Earth history, the first metal discovered since iron was cobalt in 1735. This launched a frenzy to smelt all known minerals and most of the smeltable metals were discovered by 1800. Then the battery and electrochemstry were discovered in 1800 and these were used to obtain the unsmeltable metals, which are lithium, beryllium, magnesium, aluminum, titanium, vanadium, niobium, and Uranium. Almost all of the strong alloys use these metals, and so the Valyrians must have used either electrochemistry or magic to make Valyrian steel.

Candidates for Valyrian steel

The following metals and alloys are both stronger and lighter than steel and could hypothetically be Valyrian steel.

```                Yield     Density  Strength/Density
strength  (g/cm3)   (GJoule/kg)
(GPascal)
Beryllium            .34     1.85     .186
Aluminum + Be        .41     2.27     .181
LiMgAlScTi          1.97     2.67     .738
Titanium             .22     4.51     .050
Titanium + AlVCrMo  1.20     4.6      .261
AlCrFeCoNiTi        2.26     6.5      .377
AlCrFeCoNiMo        2.76     7.1      .394
Steel                .25     7.9      .032     Iron plus carbon
Copper               .12     9.0      .013
```
"Yield strength" is the maximum pressure a material can sustain before deforming. "Strength/Density" is the strength-to-weight ratio. Steel is stronger and lighter than copper.
Lore

Petyr Baelish: Nothing holds an edge like Valyrian steel.

Tyrion Lannister: Valyrian steel blades were scarce and costly, yet thousands remained in the world, perhaps two hundred in the Seven Kingdoms alone.

George Martin: Valyrian steel is a fantasy metal. Which means it has magical characteristics, and magic plays a role in its forging.

George Martin: Valyrian steel was always costly, but it became considerably more so when there was no more Valyria, and the secret of its making were lost.

Ned Stark's stord "Ice" is melted down and reforged into two smaller swords, "Oathkeeper" and "Widow's Wail". This rules out Valyrian steel being Wootz steel because Wootz steel loses its special properties when reforged.

Appearances of Valyrian steel in Game of Thrones:

```        Name          Owner

Sword   Longclaw      Jon Snow
Sword   Heartsbane    Samwell Tarly
Dagger                Petyr Baelish
Sword   Ice           Eddard Stark         Reforged into Oathkeeper and Widow's Wail
Sword   Oathkeeper    Brienne of Tarth
Sword   Widow's Wail  The Crown
Sword   Lady Forlorn  Ser Lyn Corbray
Sword   Nightfall     Ser Harras Harlow
Sword   Red Rain      Lord Dunstan Drumm
Arakh                 Caggo
Armor                 Euron Greyjoy
Horn    Dragonbinder  The Citadel of The Maesters
```
Some Maesters carry links of Valyrian steel, a symbol of mastery of the highest arts.
Wildire

Copper

The burn rate of gasoline is limited by the supply of oxygen.

`C8H18 + 12.5 O2  →  8 CO2 + 9 H2O`
Gunpowder has oxygen in the mixture in the form of KNO3 which makes it burn faster.
```3 C + S + 2 KNO3  →  K2S + N2 + 3 CO2
```
We know that wildfire contains an oxidizer otherwise it wouldn't be able to explode as it did on the show. Wildfire is made from manure, which contains KNO3.

Copper burns with a green flame. Adding copper powder to the explosive adds energy to the blast.

Three types of incendiaries are:

```Gasoline:          Flame spreads slowly. Needs oxygen from the air.
Gunpowder:         Contains oxygen. Buns faster than gasoline. Subsonic pressure wave.
Plastic explosive: Pressure wave spreads supersonically as a shock.
```

Chemistry
```~808    Qing Xuzi publishes a formula resembling gunpower, consisting of
6 parts sulfur, 6 parts saltpeter, and 1 part birthwort herb (for carbon).
~850    Incendiary property of gunpower discovered
1540    Biringuccio publishes "De la pirotechnia", giving recipes for gunpowder
1661    Boyle publishes "The Sceptical Chymist", a treatise on the
distinction between chemistry and alchemy.  It contains some of the
earliest modern ideas of atoms, molecules, and chemical reaction,
and marks the beginning of the history of modern chemistry.
1662    Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
1663    Guericke invents the first electrostatic generator, which uses
mechanical work to separate charge.  Generators were refined until
they were superceded by the battery.
1671    Boyle discovers that combining iron filings and acid produces hydrogen gas.
1754    Black isolates CO2
1758    Black formulates the concept of latent heat to explain phase transitions
1766    Cavendish identifies hydrogen as a colorless, odourless gas that burns
in air.
1772    Scheele produces pure oxygen gas by heating HgO.
1774    Priestly produces pure oxygen gas by focusing sunlight on HgO.
He noted that it is combustible and that it gives energy when breathed.
1745    von Kleist invents the capacitor, a device for storing charge generated
by an electrostatic generator.
1746    van Musschenbroek refines the capacitor, which comes to be known as a
"Leyden jar".
1777    Lavoisier finds that in the reaction tin+oxygen, mass is conserved.
He also finds that oxygen is not the only component of air, that air also
consists of something else.
1780    Galvani observes that when a frog leg is touched by an iron scalpel,
it twitches.  This was the inspiration for Volta to invent the battery.
1781    Cavendish finds that buring hydrogen + oxygen produces water.
1787    Charles finds that for air at constant pressure,
Volume = Constant * Temperature
He also finds that this applies for O2, N2, H2, and CO2.
1789    Lavoisier publishes "Traite Elementaire de Chimie", the first modern
chemistry textbook.  It is a complete survey of (at that time) modern
chemistry, the law of conservation of mass.
1791    Volta develops the first electrochemical cell, consisting of two different
metals separated by a moist intermediary.
1797    Proust proposes the law of definite proportions, that elements
combine in small whole number ratios to form compounds.
1800    Volta constructs the first "battery" by connecting multiple electrochemical
cells in parallel, increasing the output power and voltage.
1800    Volta constructs the first battery, a set of electrochemical cells wired
in serial to increase the voltage.
1801    Dalton publishes the law of partial pressures.
The pressure of a mix of gases is equal to the sum of the pressures
of the components.  He also finds that when a light and heavy gas are mixed,
the heavy gas does not drift to the bottom but rather fills the space
uniformly.
1805    Gay-Lussac and Humboldt find that water is formed of two volumes of
hydrogen gas and one volume of oxygen gas.
1809    Gay-Lussac finds that for an ideal gas at constant volume,
Pressure = Constant * Temperature
1811    Avogadro finds that equal volumes of different gases have the same number
of particles.  At constant temperature and pressure,
Volume = Constant * NumberOfParticles
1811    Avogadro arrives at the correct interpretation of water's composition,
based on what is now called Avogadro's law and the assumption of diatomic
elemental molecules
1840    Hess finds that energy is conserved in chemical reactions
1848    Lord Kelvin establishes concept of absolute zero, the temperature at
which all molecular motion ceases.
1860    Cannizzaro publishes a table of atomic weights of the known elements
1864    Gulberg and Waage propose the law of mass action
1869    Mendeleev publishes a periodic table containing the 66 known elements
1876    Gibbs publishes the concept of "Gibbs free energy"
1877    Boltzmann defines entropy and develops thermodynamics
1877    Pictet freezes CO2 and liquefies oxygen.
Liquification enables the purification of gases.
1894    Ramsay discovers the noble gases, filling a large and unexpected gap in
the periodic table
```

Atoms
```1635   Gassendi measures the speed of sound to be 478 m/s with 25% error.
1660   Viviani and Borelli produce the first accurate measurement of the speed of
sound, giving a value of 350 m/s.
1660   Hooke's law published.  The force on a spring is proportional to the change
in length.
1662   Boyle discovers that for air at fixed temperature,
Pressure * Volume = Constant
Hence, air obey's Hooke's law
1687   Newton publishes the Principia Mathematica, which contains the first analytic
calculation of the speed of sound.  The calculated value was 290 m/s
and the true value is 342 m/s (at 20 Celsius).
```
Newton's result was the first solid evidence for the existence of atoms. His result differed from the correct value because it had not yet been discovered that air heats when compressed. If you add this effect you get the right value.

The reason air heats when compressed is because it is composed of atoms. You can see this in action with the "Gas" simulation at phet.colorado.edu. You can also see how atoms in a gas can carry a sound wave, and why the sound speed has the same order-of-magnitude as the thermal velocity of the atoms.

```1789  Lavoisier publishes "Traite Elementaire de Chimie", the first modern
chemistry textbook.  It is a complete survey of (at that time) modern
chemistry, the law of conservation of mass.
1797  Proust proposes the law of definite proportions, that elements
combine in small whole number ratios to form compounds.
1801  Dalton publishes the law of partial pressures.
The pressure of a mix of gases is equal to the sum of the pressures
of the components.  He also finds that when a light and heavy gas are mixed,
the heavy gas does not drift to the bottom but rather fills the space
uniformly.
1805  Gay-Lussac and Humboldt find that water is formed of two volumes of
hydrogen gas and one volume of oxygen gas.
1809  Gay-Lussac finds that for an ideal gas at constant volume,
Pressure = Constant * Temperature
1811  Avogadro finds that equal volumes of different gases have the same number
of particles.  At constant temperature and pressure,
Volume = Constant * NumberOfParticles
1811  Avogadro arrives at the correct interpretation of water's composition,
based on what is now called Avogadro's law and the assumption of diatomic
elemental molecules
1860  Cannizzaro publishes a table of atomic weights of the known elements
1869  Mendeleev publishes a periodic table containing the 66 known elements
1877  Boltzmann defines entropy and develops thermodynamics
```
All of these results support the hypothesis that matter is composed of atoms, but there was no known experiment sensitive enough to measure the size and mass of an individual atom.
```Wavelength of violet light = 4e-7 meters
Diameter of an iron atom   = 2e-10 meters
```
Violet photons are much larger than atoms and so you can't see atoms in an optical microscope.
```1905  Einstein publishes a method for measuring the mass of an atom using
Brownian motion
1908  Perrin uses Einstein's method to produce the first measurement of the mass of
an atom.  This is equivalent to measuring the value of Avogadro's number.
```
Minutephysics atoms
Periodic table of cupcakes

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