Real Gases Exhibit Deviations from Ideal Behavior at High Pressures

The kinetic theory of gases can be used to understand a number of phenomena relevant to chanistry. In Chapter 14, we will use the kinetic theory to determine the collision frequency of gas-phase reacting molecules, which will be used to calculate the rate of gas-phase reactions. Problans 5.57 and 5.58 illustrate the use of kinetic theory in gas diffusion the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic motion) and effusion (escape of a gas through a small hole in a container). 

5 Real Gases Exhibit Deviations from Ideal Behavior at High Pressures 

As discussed in Section 4.6, attractive intermolecular forces are the dominant interactions at intermediate intermolecular separations, whereas repulsive forces dominate when molecules are very close. When molecules are very far apart, as is the case at very low pressure, the attractive force is neghgible, and the ideal gas approximation works well. As the pressure is iuCTeased, the average intermolecular separation decreases and attractive forces wpiBcdp. n inggyiiHwW ga apf ssure 

Another way to observe the nonideal behavior of gases is to lower the temperature. Cooling a gas decreases the average kinetic energy of the molecules, which in a sense deprives the molecules of the drive they need to break away from their mutual attraction. 

Because of the intermolecular interactions, the ideal gas equation of state does not adequately describe the behavior of gases at high pressure, and alternate equations of state must be developed for real gases. In this section, we will discuss two important such equations of state for real gases the van der Waals equation and the virial equation of state. 

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FIGURE5.19 Plot of PV/RT versus P of 1 mole of a gas at CPC. For 1 mole of an ideal gas, PV/RT is equal to I, no matter what the pressure of the gas is. For real gases, we observe various deviations from ideality at high pressures. At very low pressures, all gases exhibit ideal behavior that is, their PV/RT values all converge to I as P approaches zero. 

At very high pressures or low temperatures, all gases deviate greatly from ideal behavior. As pressure increases, most real gases exhibit first a lower and then a higher PV/RT ratio than the value for the same amount (1 mol) of an ideal gas. These deviations are due to attractions between molecules, which lower the pressure (and the ratio), and to the larger fraction of the container volume occupied by the molecuies, which increases the ratio. By including parameters characteristic of each gas, the van der Waals equation corrects for these deviations. 

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