Gases

Gas laws

Constant temperature (Boyle's law)
P₁V₁ = P₂V₂
P₂ = P₁V₁/V₂
V₂ = P₁V₁/P₂
Constant pressure (Charles's law)
V₁/T₁ = V₂/T₂
T₁/V₁ = T₂/V₂
V₂ = V₁T₂/T₁
T₂ = T₁V₂/V₁
Constant volume (Gay-Lussac's law)
P₁/T₁ = P₂/T₂
P₂ = P₁T₂/T₁
T₂ = T₁P₂/P₁
Combined Gas law
P₁V₁/T₁ = P₂V₂/T₂
V₂ = P₁V₁T₂/T₁P₂
pressure and temperature are absolute
Avogadro's law
V₁/n₁ = V₂/n₂
n = number of moles

Ideal gas law
PV = nRT
n = number of moles
R = gas constant = 0.08206 (atm∙L)/(mol∙K)
                   8.314 L∙kPa/mol∙K
                   0.08314 L∙bar/mol∙K
                   62.36 L∙torr/mol∙K
                   62.36 L∙mmHg/mol∙K
T = temperature in kelvins
P = absolute pressure in atm, kPa, bar, torr
V = volume in liters

PV = kRT
k is the Boltzmann constant (1.381e−23 J/K
N is the number of gas molecules

PM = ρRT
ρ = density in g/L
M is molar mass in g/mol

alternate:
8.314 m³•Pa/K•mol
  Volume in m³, Pressure in Pa
62.36 L•Torr/K•mol
  Volume in Liters, Pressure in Torr
8.206e-5 m³•atm/K•mol
  Volume in m³, Pressure in atm

One mole of any ideal gas at STP has a volume of 22.41L
  (old def of STP, 1 atm)
One mole of any ideal gas at STP has a volume of 22.71L
  (new def of STP, 100 kPa)
One mole of any ideal gas at RTP has a volume of 24.47L
  (old def of RTP, 1 atm)
One mole of any ideal gas at RTP has a volume of 24.79L
  (new def of RTP, 100 kPa)

  STP = 0ºC & 1 ATM   (new 100 kPa)
  RTP = 25ºC & 1 ATM  (new 100 kPa)

Work on a gas at constant pressure
Volume increases with temperature. Take a cylinder with
the top a piston of area A moving up by distance d
W = Fd = (F/A)(Ad)
W = P(Ad) = PΔV

Work on a gas at constant volume
no work is done

Work on a gas at constant temperature
Take a cylinder with the top a piston of area A moving up
by distance d. We can keep the temperature constant by having
the system in contact with a heat reservoir.
W = nRT ln(Vf/Vi)
n = number of moles
R = gas constant = 0.08206 (atm∙L)/(mol∙K)
T = temperature in kelvins
P = absolute pressure in atm
V = volume in liters

Graham's Law
Graham's law states that the rate at which gas molecules diffuse is
inversely proportional to the square root of its density. Combined
with Avogadro's law (i.e. since equal volumes have equal number of
molecules) this is the same as being inversely proportional to the
root of the molecular weight.

Dalton's law of partial pressures states that the pressure of a
mixture of gases simply is the sum of the partial pressures of the
individual components. Dalton's Law is as follows:
  Ptotal = P₁ + P₂ + P₃ + ... Pn
or
  Ptotal = Pgas + Ph₂o
where PTotal is the total pressure of the atmosphere, Pgas is the
pressure of the gas mixture in the atmosphere, and Ph₂o is the water
pressure at that temperature.

KE/velocity of molecules
Kinetic Energy of a gas per mole = 12.47T J
where T is temperature in kelvins
at STP
Kinetic Energy of a gas per mole = 3406 J
Vrms = √(3kʙT/m)
  T is temp in kelvins
  m is the mass of one molecule
  kʙ = Boltzmann constant, 1.381×10^−23 J/K

Speed of molecules

Vrms = √(3kʙT/m)
kʙ = Boltzmann constant, 1.381×10^−23 J/K
m is mass of molecule in kg
T is temp in kelvins

Units of Pressure
1 Pa = 1 N/m²
1 torr = 1/760 of a standard atmosphere
1 standard atmosphere = 101.325 kPa = 1.01325 bar = 14.7 PSI
    = 10.33 meters of water = 29.92 inch of mercury
1 bar = 100 kPa = 14.5 PSI
1 PSI (lb/in²) = 6,894.8 Pa = 6.895x10^-3 N/mm² = 0.06895 bar
Vacuum, 100 micron = 13 Pa = 0.1 mm Hg

Air
specific heat of dry air is 1.006 kJ/kgC
Density of Air 1.164 kg/m³ at 30ºC and 101.325kPa
Density of Air 1.204 kg/m³ at 20ºC and 101.325kPa
Density of Air 1.247 kg/m³ at 10ºC and 101.325kPa
Density of Air 1.292 kg/m³ at 0ºC and 101.325kPa
Density of Air 1.341 kg/m³ at –10ºC and 101.325kPa
Density of Air 1.394 kg/m³ at –20ºC and 101.325kPa

Oxygen
Atomic Number 8
Atomic weight 16.00 g/mol
1 mole = 16 g
Density	(0°C, 101.325 kPa) 1.429 g/L
Liquid density at b.p.	1.141 g/cm³
Melting point 54.36 K, –218.79 °C, –361.82 °F
Boiling point 90.20 K, –182.95 °C, –297.31 °F
Heat of fusion (O₂) 0.444 kJ/mol
Heat of vaporization (O₂) 6.82 kJ/mol
Specific heat capacity (25 °C) (O₂) 29.378 J/mol·K

Nitrogen
Atomic Number 7
Atomic weight 14.01 g/mol
1 mole = 14.01 g
density 1.251 g/cm³ at 0°C
Melting point -210°C  63.05K
Boiling point -195.8°C  77.36K
Heat of Vaporization 199.1 kJ/kg
Liquid density at BP 0.808 g/cm³
liquid specific heat at BP 2.042 kJ/kgK

Other
Density of Hydrogen gas 0.089 kg/m³
Specific Heat of Hydrogen gas at 28C 14.31 kJ/kgC
Density of Helium gas 0.18 kg/m³
Density Helium is (0 °C, 101.325 kPa) 0.1786 kg/m³
Ammonia liquid density: 682 kg/m³



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