Physical Chemistry for Engineers
Question 1
A Carnot cycle uses 1.00 mol of a monatomic perfect gas as the working substance from an initial state of 10.0 atm and 600 K. It expands isothermally to a pressure of 1.00 atm (Step 1), and then adiabatically to a temperature of 300 K (Step 2). This expansion is followed by an isothermal compression (Step 3), and then an adiabatic compression (Step 4) back to the initial state. Determine the values of q, w, ΔU, ΔH, ΔS, ΔStot, and ΔG for each stage of the cycle and for the cycle as a whole. Express your answer as a table of values.
Question 2
The heat capacity of chloroform (trichloromethane, CHCl3) in the range 240 K to 330 K is given by Cp,m/(J K-1 mol-1) = 91.47 + 7.5 × 10-2 (T/K). In a particular experiment, 1.00 mol CHCl3 is heated from 273 K to 300 K. Calculate the change in molar entropy of the sample.
Question 3
A gaseous sample consisting of 1.00 mol molecules is described by the equation of state pVm = RT(1 + Bp). Initially at 373 K, it undergoes Joule-Thomson expansion from 100 atm to 1.00 atm. Given that Cp,m = (5R)/2, μ = 0.21 K atm-1, B = -0.525 (K/T) atm-1, and that these are constant over the temperature range involved, calculate ΔT and ΔS for the gas.
Question 4
The volume of an aqueous solution of NaCl at 25 °C was measured at a series of molalities b, and it was found that the volume fitted the expression v = 1003 + 16.62x + 1.77x3/2 + 0.12x2 where v = V/cm3, V is the volume of a solution formed from 1.000 kg of water, and x = b/bθ. Calculate the partial molar volume of the components in a solution of molality 0.100 mol kg-1.
Question 5
Comelli and Francesconi examined mixtures of propionic acid with various other organic liquids at 313.15 K. They report the excess volume of mixing propionic acid with oxane as VE = x1x2{a0 + a1(x1 − x2)}, where x1 is the mole fraction of propionic acid, x2 that of oxane, a0 = -2.4697 cm3 mol-1 and a1 = 0.0608 cm3 mol-1. The density of propionic acid at this temperature is 0.97174 g cm-3; that of oxane is 0.86398 g cm-3.
(a) Derive an expression for the partial molar volume of each component at this temperature.
(b) Compute the partial molar volume for each component in an equimolar mixture.
Question 6
At 90 °C, the vapour pressure of methylbenzene is 53.3 kPa and that of 1,2-dimethylbenzene is 20.0 kPa. What is the composition of a liquid mixture that boils at 90 °C when the pressure is 0.50 atm? What is the composition of the vapour produced?