Gases:  Deviations from Ideal Gas Law Behavior: Van der Waals Equation
Two problems with the Kinetic Molecular Theory of "Ideal" Gases
1. Gas particles are much smaller than the distance between particles, therefore the volume of a gas is mostly empty space and the volume of the gas molecules themselves is negligible.
2. There is no force of attraction between gas particles or between the particles and the walls of the container.
"Real" Gases: van der Waals Equation
a: Constant to correct for intermolecular attractive forces

b: Constant to correct for volume of individual gas molecules

P: Pressure - Atmospheres (atm), torr, mmHg

• V: Volume - Liters (L)
• n: Amount of gas - moles (mol)
• T: Temperature - Kelvin (K)
• R: Ideal gas constant = 0.0820057 L-atm/mol-K = 62.3243 L-torr/mol-K = 62.3243 L-mmHg/mol-K
 Compound a (L2-atm/mol2) b (L/mol) He 0.03412 0.02370 Ne 0.2107 0.01709 H2 0.2444 0.02661 Ar 1.345 0.03219 O2 1.360 0.03803 N2 1.390 0.03913 CO 1.485 0.03985 CH4 2.253 0.04278 CO2 3.592 0.04267 NH3 4.170 0.03707
Deviations are greater if :
1. Intermolecular attractive forces (IMF) of gas molecules are greater.
2. Mass (and subsequently volume) of gas molecules is greater.
Conditions are "Ideal" at:            Conditions are "Real" at:

High Temperature                         Low Temperature

Low Pressure                             High Pressure

WHY?
• At High T, the gas molecules have a higher average kinetic energy (KEavg) which overcomes the IMF.
• At Low P, the gas molecules are spread further apart and can therefore avoid IMF.
• P of a real gas < P of an ideal gas because the actual paths of gas molecules are curved (not straight) due to the IMF.
• V of a real gas > V of an ideal gas because V of gas molecules is significant when P is high.  Ideal Gas Equation assumes that the individual gas molecules have no volume.
Relationship between Boiling Point and the "a" Constant

Boiling Point - The temperature at which the vapor pressure of the liquid equals the pressure on the liquid (usually atmospheric pressure).

• In other words, the temperature at which the molecules have enough energy to escape the forces of attraction that hold a liquid from becoming a gas.
•  Since the "a" constant corrects for the existing forces of attraction between gas molecules, it is easy to understand why there is a correlation  between this constant and the boiling point.  A substance with a higher boiling point has stronger forces of attraction which hold the molecules together.  Likewise, this substance would have a higher "a" constant value also because of these stronger forces of attraction.