Gases

Deviation from Ideal Behavior

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

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.

1996 Michael Blaber