Ideal Gas Law: PV = nRT
R = 0.0821 liter· atm/mole· K
= 8.31 liter· kPa/mole· K
= 8.31 J/mole· K
= 8.31 V· C/mole· K
= 8.31 x 10^{-7} g· cm^{2}/sec^{2}· mole· K
(for calculating the average speed of molecules)
= 6.24 x 10^{4} L· mm Hg/mole· K
= 1.99 cal/mole· K
Molecular Weight: MW = g· R· T
P· V
van der Waal's (P + a/V^{2})(V - b) = R· T
(real gases) or
(P + n^{2}a/V^{2}))V - nb) = n· R· T
Here "a" corrects for force of attraction between gas molecules,
and "b" corrects for particle volume.
Graham's Law of Effusion:
__ __
r_{1} \/d_{2} \/MW_{2} t_{2} u_{1}
= __ = __ = =
r_{2} \/d_{1} \/MW_{1} t_{1} u_{2}
where, r = rate of diffusion
d = density
MW = molecular weight
t = time
u = average speed
Kinetic Molecular Theory
- Gases are composed of tiny, invisible molecules that are widely separated from one another in empty space.
- The molecules are in constant, continuous, random, and straight-line motion.
- The molecules collide with one another, but the collisions are perfectly elastic (no net loss of energy).
- The pressure of a gas is the result of collisions between the gas molecules and the walls of the container.
- The average kinetic energy of all the molecules collectively is directly proportional to the absolute temperature of the gas. Equal number of molecules of any gas have the same average kinetic energy at the same temperature.
E_{t} = m· u^{2} = cT
2
c = 3R
2N_{a}
u^{2} = 3· R· T = 3· R· T
m· N_{a} MW
where, E_{t} = average kinetic energy of translation
m = mass (of particle)
u = velocity (average speed)
c = constant
N_{a} = Avogadro's number
R = 8.31 x 10^{-7} g· cm^{2}/sec^{2}· mole· K
T = temperature in K