Non-Ideal Behaviour of Gases

Deviations from Ideal Behavior 

All real gasses fail to obey the ideal gas law to varying degrees


The ideal gas law can be written as:

For a sample of 1.0 mol of gas, n = 1.0 and therefore:

Plotting PV/RT for various gasses as a function of pressure, P:

• The deviation from ideal behavior is large at high pressure
• The deviation varies from gas to gas
• At lower pressures (<10 atm) the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error

Deviation from ideal behavior is also a function of temperature:

• As temperature increases the deviation from ideal behavior decreases
• As temperature decreases the deviation increases, with a maximum deviation near the temperature at which the gas becomes a liquid

Two of the characteristics of ideal gases included:

• The gas molecules themselves occupy no appreciable volume
• The gas molecules have no attraction or repulsion for each other

Real molecules, however, do have a finite volume and do attract one another

• At high pressures, and low volumes, the intermolecular distances can become quite short, and attractive forces between molecules becomes significant
• Neighboring molecules exert an attractive force, which will minimize the interaction of molecules with the container walls. And the apparent pressure will be less than ideal (PV/RT will thus be less than ideal).
• As pressures increase, and volume decreases, the volume of the gas molecules becomes significant in relationship to the container volume
• In an extreme example, the volume can decrease below the molecular volume, thus PV/RT will be higher than ideal (V is higher)
• At high temperatures, the kinetic energy of the molecules can overcome the attractive influence and the gasses behave more ideal
• At higher pressures, and lower volumes, the volume of the molecules influences PV/RT and its value, again, is higher than ideal

The van der Waals Equation

• The ideal gas equation is not much use at high pressures
• One of the most useful equations to predict the behavior of real gases was developed by Johannes van der Waals (1837-1923)
• He modified the ideal gas law to account for:
• The finite volume of gas molecules
• The attractive forces between gas molecules

van der Waals equation:

• The van der Waals constants a and b are different for different gasses
• They generally increase with an increase in mass of the molecule and with an increase in the complexity of the gas molecule (i.e. volume and number of atoms)

Substance	a (L2 atm/mol2)	b(L/mol)
He	0.0341	0.0237
H2	0.244	0.0266
O2	1.36	0.0318
H2O	5.46	0.0305
CCl4	20.4	0.1383

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Example
Use the van der Waals equation to calculate the pressure exerted by 100.0 mol of oxygen gas in 22.41 L at 0.0°C
V = 22.41 L
T = (0.0 + 273) = 273°K
a (O₂) = 1.36 L² atm/mol²
b (O₂) = 0.0318 L /mol

P = 117atm - 27.1atm

P = 90atm

• The pressure will be 90 atm, whereas if it was an ideal gas, the pressure would be 100 atm
• The 90 atm represents the pressure correction due to the molecular volume. In other words the volume is somewhat less than 22.41 L due to the molecular volume. Therefore the molecules must collide a bit more frequently with the walls of the container, thus the pressure must be slightly higher. The -27.1 atm represents the effects of the molecular attraction. The pressure is reduced due to this attraction.