9.7 Behavior of Real Gases

Real Gases differ from the ideal gases to the extent that do not always fit the assumption of kinetic molecular theory.

The assumptions tends to break at high pressure where the volume is higher than predicted for an ideal gas. Because the partial pressures are no longer negligibly small compared to the space between them.

The assumptions also break at low temp where the pressure is lowered than predicted because the attraction between molecules combined with low kinetic energy causes partially elastic collisions. Several experiments show the deviation of real gases from ideal behavior.

Figure 9.88 real Gas Behavior

Ref: commons.wikimedia.org/

.The above diagram shows how real gases tend to behave ideally when volume is very high.

Figure 9.89 PV/nRT vs. P Graph for Real Gases

Ref: commons.wikimedia.org/

 Above diagram shows the plot of PV/RT (Z) versus P for 1 mol of different gases. For ideal gases, the value of PV/RT is equal to 1 at any pressure. The values on the horizontal axis are the external pressures at which the PV/RT ratios are calculated. The pressure ranges from normal to very high (~600 atm) and PV/RT>1.

For example, in case of methane gas, it deceases below the ideal value at moderately high pressure and then rises above it as the pressure increases.

This observation can be summarizes as mentioned:

1. At moderately high pressure, values of PV/RT lower than ideal (less than 1) are mainly due to intermolecular attractions.
2. At very high pressure, values of PV/RT greater than ideal ( more than 1) are mainly due to molecular volume.

Intermolecular attraction: Attractive forces between molecules are much weaker than covalent bonding. Most intermolecular attractions occur within a very short distance between the molecules.  At lower temperature, molecules have less kinetic energy and they are relatively closer to each other. Attractive force between the molecules lower the number of collisions between the molecules and pressure decreases, Therefore a smaller numerator in PV/RT ratio. At low enough temperature, the attraction among molecules become overwhelming and gas may condense to a liquid.

Molecular volume: At normal pressures, the space between molecule of a real gas (free volume) is large enough to consider container volume. As the applied pressure increases, free volume decreases, the molecular volume makes up the greater portion of the container volume. Therefore at high pressure free volume is less than container volume and the ratio PV/RT is  high compared to the ideal volume “V”. Molecular volume effect becomes very significant as pressure increase and eventually PV/RT rises above the ideal value.

Vander Waal equation: The Ideal Gas Law redesigned:

Figure 9.90 Van der Waals

Ref: commons.wikimedia.org/

To describe the real gas more accurately, we need to redesign the ideal gas equation to do two things:

1. Adjust the measured pressure up by adding a factor that accounts for intermolecular attractions, and
2. Adjust the measured volume down by subtracting a factor that accounts from the entire container volume that accounts for the molecular volume.

P= observed pressure

V= observed volume

T, n = Temp and moles respectively

“a” and “b” are called Van der Waal’s constant. The constant “a” relates to the number of electrons which in turn relates to the complexity of the molecules and strength of its intermolecular attractions. The constant “b” relates to the molecular volume.

According to kinetic molecular theory, the constants a, b are zero for an ideal gas because the particles do not attract each other and have no volume. Even for a real gas at ordinary pressures, the molecules are very far apart. Thus observed pressure and volume become ideal pressure and volume. At  ordinary condition, Vander Waals equation becomes the ideal gas equation.

*** Adapted from Chem I Virtual textbook  http://www.chem1.com/acad/webtext/virtualtextbook.html