Answer Happy

Consider a nonideal binary gas mixture with the simple equation of state V=pnRT​+nB (a) The rule of Lewis and Randall states that the value of the mixed second virial coefficient BAB​ is the average of BAA​ and BBB​. Show that when this rule holds, the fugacity coefficient of A in a binary gas mixture of any composition is given by lnϕA​=BAA​p/RT By comparing this expression with lnϕ≈RTBp​ for a pure gas, express the fugacity of A in the mixture as a function of the fugacity of pure A at the same temperature and pressure as the mixture. (b) The rule of Lewis and Randall is not accurately obeyed when constituents A and B are chemically dissimilar. For example, at 298.15 K, the second virial coefficients of H2​O(A) and N2​( B) are BAA​=−1158 cm3 mol−1 and BBB​=−5 cm3 mol−1, respectively, whereas the mixed second virial coefficient is BAB​=−40 cm3 mol−1. When liquid water is equilibrated with nitrogen at 298.15 K and 1bar, the partial pressure of H2​O in the gas phase is pA​=0.03185 bar. Use the given values of BAA​,BBB​, and BAB​ to calculate the fugacity of the gaseous H2​O in this binary mixture. Compare this fugacity with the fugacity calculated with the value of BAB​ predicted by the rule of Lewis and Randall.