The liquid phase activity coefficients of the ethanol(1) + toluene(2) system at 55°C are given by the two-parameter Margules equation, where A₁₂ = 1.869 and A₂₁ = 1.654.

(a) Show that the pure saturation fugacity coefficient is approximately 1 for both components.

(b) Calculate the fugacity for each component in the liquid mixture at x₁ = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. Summarize your results in a table. Plot the fugacities for both components versus x₁. Label your curves. For each curve, indicate the regions that may be approximated by Henry’s law and the ideal solution model.

(c) Using the results of part (b), estimate the total pressure above the liquid mixture at 55°C when a vapor phase coexists. Assume the gas phase is ideal for this calculation. Also estimate the vapor composition.

(d) Comment on the validity of the ideal gas assumption used in part (c).