Imperfect gases fugacity

So far we have assumed that the gases we have been dealing with are perfect. This is found to be a remarkably good approximation. For water vapour just 

We may define a new thermodynamic function, the fugacity / such that for real gases 

We could regard/as the effective pressure just as activities were introduced as effective concentrations . As all gases tend to perfect behaviour as P - 0, under these conditions/will tend to become equal to P. The standard state is strictly the state of the perfect gas at one atmosphere pressure where P = 1 atm and / = 1 atm. This is illustrated in Fig. 8.4. For practical purposes, as many gases are virtually ideal at 1 atm, no great error is introduced if the standard state is characterized by the properties of the real gas at 1 atm. 

Recalling the calculations of gas equilibria carried out earlier, we have for imperfect gases 

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The relationship between the fugacity and the second virial coefficient of a slightly imperfect gas may be expressed in several ways. 

Fig. 8.4. Definition of the standard state of unit fugacity for an imperfect gas.

For the ith component of an imperfect gas mixture the fugacity /i is chosen in such a way as to replace the partial pressure in equation (3 19). It is therefore defined by the following relations in which /ej... 

The relative values of are usually tabulated in the literature at a standard pressure of 1 atm. With this convention it follows that the partial pressures which appear in Kp should also be expressed in atmospheres, In the case of an imperfect gas mixture the quantity as discussed in 3 7, actually refers to unit fugacity. However, for most gases and vapours this differs very little from the value at 1 atm because deviations from the perfect gas laws are small in the range 0-latm. In using (4 19) to evaluate iS y it is usually a sufficiently good approximation to use the tabulated /li s at atmospheric pressure. For the sake of comparability with other thermodynamics texts it may be added that if the equation ln/ had been... 

The true equilibrium constant for imperfect gas mixtures is not Kp but Kf. By using the fugacity coefficient, Xi filPo ... 

There is an extremely simple specifie ease of the ealculation of the fiigaeity of the gas / when we consider that the mixture of gases forms a perfect solution of imperfect gases, because then we have = 1, the fugacity is written as ... 

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