Consider a binary mixture of species 1 and 2 that obeys the Peng–Robinson equation of state with van der Waals mixing rules. Show that the fugacity coeffi cient for species 1 is given by the “Species 1 in a binary mixture” row in Table 7.1.

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TABLE 7.1 Fugacity Coefficients for Three Cubic Equations of State Pure species i Species 1 in a binary mixture Species i in a mixture Van der Waals Equation of State (v - b)P RT In 4 = In 1 In Pi - bi v - b b b b v-b - - In In In (v b)P RT - b)P RT 2a RTvi 2(ya + ya12) RTV 2 m yka ik RTv