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
- From the ideal gas equation, we can see what it means for a gas to have an ideal behavior by rearranging the ideal-gas equation to solve for n:
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
- Although we can assume that real gases behave like an ideal gas, they do not do so 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 temperature
- 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, intermolecular attraction also comes into play because of the shorter distance seen when gas molecules are crowded
- This means the combined volume of the gas molecules is not negligible relative to 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
- From the graph below, we can observe 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
- This makes them stick to one another rather than bounce off each other
- 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 gas molecules begin to behave ideally as they have sufficient kinetic energy to overcome intermolecular attraction and their volumes become negligible
- The negative deviation from the ideal value of 1 decreases, as seen in the graph from 200 K to 1000 K
- From the graph below, we can observe that at pressures below about 400 atm, cooling (lower temperatures) increases the extent to which a gas deviates from ideal behavior
Deviation from Ideal Behavior
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.
Worked example
Which of the following conditions will make a gas behave more ideally?
- Large volume and high average kinetic energy
- High temperature and high average kinetic energy
- Low volume and low average kinetic energy
- Low temperature and low average kinetic energy
Answer:
Option A is correct because:
- Gases tend towards ideal behavior at high temperatures and low pressures
- Under these conditions, the gas molecules have energy energy to overcome intermolecular force and their actual volume tends to become negligible because of the distance between them
- This is synonymous with high average kinetic energies and large volumes
Options B and D are incorrect because
- Both conditions mean the same thing given that temperature is directly proportional to average kinetic energy
Option C is incorrect because
- Low volume means high pressure while low average kinetic energy means the molecules are at low temperatures and cannot overcome the intermolecular force between them.
