Non-Ideal Behavior of Gases (College Board AP® Chemistry): Revision Note

Non-Ideal Behavior of Gases

• The kinetic molecular theory and gas laws assume that molecules in the gaseous state have two important properties:

  • They exert no attractive or repulsive force on one another

  • They have negligible volumes compared to that of the container

• Rearranging the ideal gas equation for n shows what ideal behavior means:

n = PV/RT

• This means that for 1 mol of an ideal gas, the quantity PV/RT equals 1 at all pressures

  • Hence, a graph plot of PV/RT against pressure should give a straight line parallel to the pressure axis

Graph Representation of an Ideal Behavior

A graph showing an ideal gas behavior for one mole of a gas at different pressures

Deviation from Ideal Behavior

• Real gases can often be treated as ideal, but not under all conditions

  • For example, without intermolecular forces present, gases will not condense to form liquids

• Hence the ideal behavior described by the assumptions of the kinetic molecular theory and the ideal gas equation are only true under certain conditions

  • For real gases, this is true only at moderately low pressures and high temperatures

• However, at high pressures and low temperatures, real gases deviate from the ideal behavior

  • At low temperatures, gas molecules have lower kinetic energy and begin to experience some intermolecular attraction

  • At high pressures, the molecules are crowded close together, so attractions between them become significant

    • Separately, the molecules' own volume is no longer negligible compared with the container volume

Effect of High Pressure on Volume of Real Gases

At high pressure, the volume of molecules of real gases is not negligible

• For real gases, a graph plot of PV/RT against pressure does not have the same shape as that of an ideal gas

  • The graph below shows that at pressures below about 400 atm, cooling (lower temperatures) increases the extent to which a gas deviates from ideal behavior

    • This is because lower temperatures mean the gas molecules do not have sufficient kinetic energy to overcome the intermolecular force of attraction

    • Attractions pull neighboring molecules toward one another, so they hit the walls less often and with less force, and the pressure is lower than the ideal value

  • As temperature increases,

    • The negative deviation from the ideal value of 1 decreases, as seen in the graph from 200 K to 1000 K

    • This is because the molecules have enough kinetic energy to overcome intermolecular attractions, so the attractions lower the pressure less

  • At very high pressures, PV/RT rises above 1 (a positive deviation): the molecules' own volume is no longer negligible, so the space they can move in is smaller than the container volume

Effect of temperature and pressure on PV/RT

A graph showing the effect of temperature and pressure on real gases. The deviation is more significant at higher pressures and lower temperatures as seen by the direction of the curve away from the ideal gas.