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 (L^{2} atm/mol^{2}) |
b(L/mol) |
He |
0.0341 |
0.0237 |
H_{2} |
0.244 |
0.0266 |
O_{2} |
1.36 |
0.0318 |
H_{2}O |
5.46 |
0.0305 |
CCl_{4} |
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 (O_{2}) = 1.36 L^{2} atm/mol^{2}
b (O_{2}) = 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