CH353
 Physical Chemistry I Spring 2015, Unique 51170 Homework, Week 9 
Homework,
week 9 Answer key 1. Based on
your general chemistry knowledge, determine whether the chemical
potential of the reactants in the following balanced equations is
greater than, less than, or equal to the chemical potential of the
products. You may assume each reaction is taking place under
standard conditions unless otherwise indicated. 2. Consider a system consisting of n_{1} moles of component 1 and n_{2} moles of component 2. Derive an expression for the Gibbs free energy of this system. 3. At 25˚C, the density of a 50% (m/m) solution of ethanol and water is 0.914 g cm^{3}. Given that the partial molar volume of water in the solution is 17.4 cm^{3} mol^{1}, determine the partial molar volume of the ethanol. 4. What proportions of hexane and heptane should be mixed by mole fraction to achieve the greatest entropy of mixing? 5. The molar enthalpy of fusion of ice at 273.15 K and 1.0 atm is 6010 J mol1. The change in volume caused by the fusion of ice under the same conditions is 1.63 cm3 mol1. You may assume that these values remain constant as a function of pressure. Estimate the melting temperature of ice at 1000 atm. 6. When a solution of acetone (A) and methanol (M) are in equilibrium at 57.2˚Cat 1.0 atm, the mole fraction of acetone in the liquid phase was found to be 0.40, while the mole fraction of acetone in the vapor phase wasfound to be 0.516. Determine the vapor pressures of both liquids and comment on your answer. For these two components, P*A = 105kPa and P*M = 73.5 kPa. 7. A liquid mixture is composed of two liquids A and B. At 60 ˚C, the pure vapor pressure of A is 400 Torr and the pure vapor pressure of B is 800 Torr. The total mixture contains 1 mole of A and 4 moles of B. At 60 ˚C and a total pressure of 650 Torr, is the mixture all liquid, all vapor, or in a liquidvapor equilibrium? Justify your answer. 8. Draw a temperaturecomposition diagram of a binary system in terms of the mole concentration of species 1 in which species 1 is the more volatile component. Label the regions of the diagram in which liquid and vapor phases exist. 9. In class, we examined an ideal solution formed between 1propanol and 2propanol: P*(1propanol) = 20.9 Torr P*(2propanol) = 45.2 Torr (at 25˚C) Construct a pressurecomposition diagram for this solution in terms of the mole fraction of 2propanol in both the liquid and vapor phases. Label the regions of the diagram in which liquid, vapor, and liquidvapor phases exist. If the mole fraction of 2propanol in the liquid phase is 0.6, what is the composition of the vapor phase?

