Kaplan MCAT General Chemistry Review

Then calculate the partial pressure.

P_A = X_AP_T

Real Gases

Throughout our discussion of the laws and theory that describe and explain the behavior of gases, we have stressed that the fundamental assumption is a gas that behaves ideally. However, our world is not one of ideal gases but rather real ones, and real gases have volumes and interact with each other in measurable ways. In general, the ideal gas law is a good approximation of the behavior of real gases, but all real gases deviate from ideal gas behavior to some extent, particularly when the gas atoms or molecules are forced into close proximity under high pressure and at low temperature. Under these “nonideal” conditions, the molecular volume and intermolecular forces become significant.

You can think of these nonideal conditions as the degree to which human populations are “forced” to interact with each other in high-population density regions. In 2007, for example, the population density of Washington, D.C., was 9,581 people per square mile, whereas that of Alaska (the least densely populated state in the Union at that time) was 1.2 people per square mile. Quite literally, the personal space of an individual living in the nation’s capital cannot be ignored, whereas the vast physical separation between people living in Alaska (on average) makes the notion of “personal space” so insignificant as to be almost laughable. Continuing the human-as-real-gas analogy, how often do people say to each other on a hot and humid day, “Ugghh, don’t come near me. It’s too hot!”? And how many romantic songs include imagery of lovers snuggling together on a cold evening trying to keep warm?

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At high temperature and low pressure, deviations from ideality are usually small; good approximations can still be made from the ideal gas law.

DEVIATIONS DUE TO PRESSURE

As the pressure of a gas increases, the particles are pushed closer and closer together. As the condensation pressure for a given temperature is approached, intermolecular attraction forces become more and more significant, until the gas condenses into the liquid state (see “Gas-Liquid Equilibrium” in Chapter 8).

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On the MCAT, an understanding of nonideal conditions will help with determining how gases’ behavior may deviate.

At moderately high pressure (a few hundred atmospheres), a gas’s volume is less than would be predicted by the ideal gas law due to intermolecular attraction. At extremely high pressure, however, the size of the particles becomes relatively large compared to the distance between them, and this causes the gas to take up a larger volume than would be predicted by the ideal gas law.

DEVIATIONS DUE TO TEMPERATURE

As the temperature of a gas is decreased, the average velocity of the gas molecules decreases, and the attractive intermolecular forces become increasingly significant. As the condensation temperature is approached for a given pressure, intermolecular attractions eventually cause the gas to condense to a liquid state (see “Gas-Liquid Equilibrium” in Chapter 8).

As the temperature of a gas is reduced toward its condensation point (which is the same as its boiling point), intermolecular attraction causes the gas to have a smaller volume than that which would be predicted by the ideal gas law. The closer the temperature of a gas is to its boiling point, the less ideal is its behavior.

VAN DER WAALS EQUATION OF STATE

Key Concept

Note that if a and b are both zero, the van der Waals equation reduces to the ideal gas law.

There are several gas equations, or gas laws, that attempt to correct for the deviations from ideality that occur when a gas does not closely follow the ideal gas law. The van der Waals equation of state is one such equation:

where a and b are physical constants experimentally determined for each gas. The a term corrects for the attractive forces between molecules (a for attractive) and as such will be smaller for gases that are small and less polarizable (such as helium), larger for gases that are larger and more polarizable (such as Xe or N₂), and largest for polar molecules such as HCl and NH₃. The b term corrects for the volume of the molecules themselves. Larger values of b are thus found for larger molecules. Numerical values for a are generally much larger than those for b.

Example: Find the correction in pressure necessary for the deviation from ideality for 1 mole of ammonia in a 1 liter flask at 0°C. (For NH₃, a = 4.2, b = 0.037)

Solution: According to the ideal gas law,

P = nRT/V = (1)(0.0821)(273)/(1) = 22.4 atm, while according to the van der Waals equation,

The pressure is thus 3.3 atm less than would be predicted from the ideal gas law, or an error of 15 percent.