Equilibria Involving Real Gases

Up to this point in our discussion of the equilibrium phenomenon, we have assumed ideal behavior for all substances. In fact, the value of K calculated from the law of mass action is the true value of the equilibrium constant for a given reaction system only if the observed pressures (concentrations) are corrected for any nonideal behavior. 

To gain some appreciation for the effect of nonideal behavior on the calculation of equilibrium constants, consider the data in Table 6.5, which show the values of Kp (at 723 K) for the reaction 

One common method for finding the limiting value (the true value) of fCp is to measure Kp at various values of total pressure (constant temperature) and then to extrapolate the results to zero pressure. Another way to obtrin the true value of Kp is to correct the observed equilibrium pressures for y 

In general, for equilibrium pressures of 1 atm or less, the value of Kp calculated from the observed equilibrium pressures is expected to be within about 1 % of the true value. However, at high pressures the deviations can be quite severe, as illustrated by the data in Table 6.5. 

These questions are designed to be considered by groups of students in class. Often these questions work well for introducing a particular topic in class.,  

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Later, we will make equilibrium calculations that involve activities, and we will see why it is convenient to choose the ideal gas as a part of the standard state condition, even though it is a hypothetical state/ With this choice of standard state, equations (6.94) and (6.95) allow us to use pressures, corrected for non-ideality, for activities as we make equilibrium calculations for real gases.s... 

In solution the barriers to conformational change are often small, even when the molecule has a built-in restriction on motion. Conformational barriers calculated for isolated molecules in the gas phase that reveal the nature of some of these barriers are likely to be good reflections of the real barriers in solvents such as chloroform. There usually are many conformations present at any time in such solutions and they are in equilibrium. The equilibria are likely to be much more restricted in polar media. It is very important for us to discover the extent of the equilibrium, that is, the number of conformations involved, the relative proportion of each, and the rate of transformation between them. Such a task is virtually impossible from theoretical considerations, and two major approaches using physical techniques, mainly nmr, are possible. These have been discussed in some detail for small molecules and can be summarized as follows. 

Up to this point the equilibrium constants have been expressed in terms of partial pressures. However, for real gases the fugacities of the species should be used. If the pressures are low enough, the pressures themselves can be used, because at low pressures the pressure is approximately equal to the fugacity But many chemical reactions involve phases other than the gas phase. Solids, liquids, and dissolved solutes also participate in chemical reactions. How are they represented in equilibrium constants ... 

The two methods of computer simulation are known by the labels of Molecular Dynamic (MD) and Monte Carlo (MQ simulation. In the fimt the evolution of an assembly of N molecules is followed by numerical solution of Newton s equations of motion. The system is one of fixed N, V, and U and so is the simulation of a micro-canonical ensemble, but since the sequence of states is that of real time both equilibrium and dynamic information can be obtained. In the second method a sequence of states is generated such that each state occurs with a probability proportional to its Boltzmann factor, exp(-%(i )/fcT0. The sequence is (usually) specified by fixed values of N, V, and T, and so the ensemble represented is canonical. The ordering of the steps of the sequence is arbitrary (that is, it contains no information) and so only thermodynamic properties can be calculated. The principles and practice of these techniques are described elsewhere " both have been used to study the liquid-gas surface and here we describe only the special problems which these studies involve. 

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