# The volume change on mixing for the liquid methyl formate(1) + liquid

11.1. The volume change on mixing for the liquid methyl formate(1) + liquid ethanol(2) system at 298.15 K may be approximately represented by J. Polack, Lu, B.C.-Y. 1972. J. Chem Thermodynamics, 4:469: ∆Vmix = 0.8x1x2 cm3/mol a. Using this correlation, and the data V1 = 67.28 cm3 /mol, V2 = 58.68 cm3 /mol, determine the molar volume of mixtures at x1 = 0, 0.2, 0.4, 0.6, 0.8, 1.0 in cm3/mol. b. Analytically differentiate the above expression and show that and plot these partial molar excess volumes as a function of x1.

11.4. A stream containing equimolar methanol(1) + benzene(2) at 350 K and 1500 mmHg is to be adiabatically flashed to atmospheric pressure. The two-parameter Margules model is to be applied with A12 = 1.85, A21 = 1.64. Express all flash equations in terms of Ki values and Ki values in terms of Modified Raoult’s law. a. List all the unknown variables that need to be determined to solve for the outlet. b. List all the equations that apply to determine the unknown variables.

11.7. The excess Gibbs energy for a liquid mixture of n-hexane(1) + benzene(2) at 30°C is represented by GE = 1089 x1x2 J/mol. a. What is the bubble pressure for an equimolar mixture at 30°C? b. What is the dew pressure for an equimolar mixture at 30°C? c. What is the bubble temperature for an equimolar mixture at 760 mmHg? d. What is the dew temperature for an equimolar mixture at 760 mmHg?

11.15. The (1) + (2) system forms an azeotrope at x1 = 0.75 and 80°C. At 80°C, , . The liquid phase can be modeled by the one-parameter Margules equation. a. Estimate the activity coefficient of component 1 at x1 = 0.75 and 80°C. [Hint: The relative volatility (given in problem 11.2) is unity at the azeotropic condition.] b. Qualitatively sketch the P-x-y and T-x-y diagrams that you expect

11.21. Suppose a vessel contains an equimolar mixture of chloroform(1) and triethylamine(2) at 25°C. The following data are available at 25°C: a. If the pressure in the vessel is 90 mmHg, is the mixture a liquid, a vapor, or both liquid and vapor? Justify your answer. b. Provide your best estimate of the volume of the vessel under these conditions. State your assumptions.