Calculate the compressibility factor, apparent fugacity coefficients, and the true vapor phase mole fractions in a mixture at 298.

a) A gas-phase A+B system solvates A + B ⇄ AB with K_a = 0.5 at 298.15 K.  Calculate the compressibility factor, apparent fugacity coefficients, and the true vapor phase mole fractions in a mixture at 298.15 K and 2 bar when the apparent concentration is yA = 0.45 using ideal chemical theory.

(b) A liquid-phase A+B system solvates A + B ⇄ AB with K_a = 0.7 at 298.15 K.  Calculate the true liquid-phase mole fractions in a mixture at 298.15 K and 1 bar when the apparent  concentration is x_A = 0.45 using ideal chemical theory.

(c) A gas-phase A+B system associates 2A ⇄ A₂ with K_a = 0.5 at 298.15 K.  Calculate the compressibility factor, apparent fugacity coefficients, and the true vapor phase mole fractions in a mixture at 298.15 K and 2 bar when the apparent concentration is y_A = 0.45 using ideal chemical theory.