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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
= (n1 + n2 + n3 + ...) R T
= (P1 + P2 + P3 + ...)

Mole fraction of gas 1, X1

n1
X1 = -----
nTotal
Example: A 1.0-L cylinder contains 0.5 g each of N2, O2 and CO2 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
N2 0.5/28 = 0.179 mol P = 0.40 0.40
O2 0.5/32 = 0.156 mol P = 0.35 0.35
CO2 0.5/44 = 0.114 mol P = 0.2540.25

## Collecting Gases over Water

The vapour pressure of water is a function of temperature, and a plot is shown.
```|
|
|
|________

```
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 u2/2
= (3/2) R T

u = (3 R T / N M)1/2
= (3 k T / M)1/2

```        M1 u12  =  M2 u22.
Thus,
M1     u2
-- = (---)2
M2     u1```

The Graham's law of effusion is

k             k '
rate of effusion = ------ = ------
d1/2       M1/2

Applications:

• Ratio of effusion rates