As stated in a previous study guide, there is no such thing as an ideal gas. Gases deviate from ideality, in other words they deviate from the gas laws, under conditions of high pressure and low temperatures. Many gases follow ideal behavior at moderate pressures and higher temperatures. Real gases have a real volume. The measured pressure is greater than predicted by the ideal gas law. Gas particles are not points of mass, but they have volumes determined by the sizes of their atoms as well as the bonds between them. Real gases experience both attractive and repulsive forces between their particles. Again, real gases deviate most from ideal behavior at low temperatures (below or around their boiling point) and high pressures. A pressure of 100 atm is considered a substantial pressure. Most gases behave ideally at lower pressures of a few atmospheres.
In the plot below, we see at higher pressures, the gases deviate from ideality. Ideal behavior is when PV/nRT is equal to one.
Many chemists work at lower pressures, therefore, the ideal gas laws are used in the lab. But, gases do have a real volume and gas particles have both repulsive and attractive forces. These become apparent at low temperatures and high pressures.
At high pressures, the gas particles are pushed closer together resulting in the volume of the gas no longer being negligible. The actual volume for the particles to move about in decreases, and this causes the measured pressure to be greater than the pressure predicted from the ideal gas law. In the plot above, we can see the deviations due to higher pressure above the ideal gas line. We also see some deviations below the ideal gas line. These deviations are due to attractive forces of attraction between the gas particles. The attractions between particles will lower the pressure because the particles will not hit the container walls with as much force.
In the plot below is PV/nRT verses pressure for nitrogen gas at three different temperatures.
Note, at 200 K and 500 K the deviations are below the ideal gas line due to attractive forces. At higher pressures, the deviation is above the line. Gases that are at least 100° above the boiling point and at moderate pressures tend to follow the ideal gas law. The conditions must be far from the pressure and temperature where the gas can condense to a liquid.
Van der Waals Equation
The ideal gas law can be modified to correct for the deviations due to molecular volume and the interparticle attractions. The correction factors, a and b, are shown for some common gases in the following table.
The Van der Waals equation is
The constants a and b are determined via experiment. Constants for some gases are listed in the table above.
Worksheet: Real Gases: Deviations From Ideality
Exercises
Exercise 1. Calculate the pressure of 1.000 mole of water vapor at 118.00°C if it occupies a volume of 28.65 L. Use both the ideal gas law and the van der Waals equation to compare your answers. (a = \(5.46\frac{L^2⋅atm}{mol^2}\), and b = 0.0305 L/mol)
Exercise 2. Use the van der Waals equation to calculate the pressure of 1.000 mole of methane gas if it occupies a volume of 31.50 L at 75.5°C. Compare your answer to the one using the ideal gas law.
Exercise 3. Use both the van der Waals equation and the ideal gas law to determine the pressure of 1.000 moles CO2 gas at 153 K in a volume of 31.50 L.
Check Solution to Exercise 3
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