Gas and Stoichiometry
ABCD of gas laws
Ideal gas law and Dalton's law of parial pressures
From the Ideal Gas law to Dalton's law
P V = n R T
= n_{Total} R T
= (n_{1} + n_{2} +
n_{3} + ...) R T
= (P_{1} + P_{2} +
P_{3} + ...)
Mole fraction of gas 1, X_{1}
n_{1}
X_{1} = 
n_{Total}
Example:
A 1.0L cylinder contains 0.5 g each of N_{2}, O_{2}
and CO_{2} at 273 K. Calculate the total pressure, partial pressure, and
mole fractions.
Hint
See the table of results
Gas  Amount /mol  P = n R T /atm  Mole fraction


N_{2}  0.5/28 = 0.179 mol  P = 0.40  0.40

O_{2}  0.5/32 = 0.156 mol  P = 0.35  0.35

CO_{2}  0.5/44 = 0.114 mol  P = 0.254  0.25

Collecting Gases over Water
The vapour pressure of water is a function of temperature, and a plot
is shown.



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Example:
On July 1, the atmosphere pressure was 745 mmHg kPa at 30 C and the air is
saturated with water vapor, 31.8 mmHg. Estimate the mole fraction
of water vapour.
Hint
X = 31.8 / 745 = 0.043 (4.3 %)
The partial pressure of dry air would have been 745  31.8 = 713 mmHg.
Kinetic Theory of Gases
Postulates:
 Molecular size, attraction, & repulsion negligible
 Average kinetic energies of gases are the same at the same T
 Pressure due to kinetic energy
P V = N m u^{2}/2
= (3/2) R T
u = (3 R T / N M)^{1/2}
= (3 k T / M)^{1/2}
M_{1} u_{1}^{2} = M_{2} u_{2}^{2}.
Thus,
M_{1} u_{2}
 = ()^{2
} M_{2} u_{1}
The Graham's law of effusion is
k k '
rate of effusion =  = 
d^{1/2} M^{1/2}
Applications:
 Ratio of effusion rates
 Balloon business
 Separation of isotopes
Real Gases
van Der Waals Equation
(P + (n/V)^{2} a) (V  nb) = n R T
nb  Volume of n moles molecules.
(n/V)^{2} a  Pressure correction term.