P15.1. Repeat all the practice problems from Chapter 10, this time applying the Peng-Robinson equation.
P15.2. Acrolein (C3H4O) + water exhibits an atmospheric (1 bar) azeotrope at 97.4 wt% acrolein and 52.4°C. For acrolein: Tc = 506 K; Pc = 51.6 bar; and ω = 0.330; MW = 56.
a. Determine the value of kij for the Peng-Robinson equation that matches this bubble pressure at the same liquid composition and temperature. (ANS. 0.015)
b. Tabulate P, y at 326.55 K and x = {0.57, 0.9, 0.95, 0.974} via the Peng-Robinson equation using the kij determined above. (ANS. (1.33, 0.575), (1.16, 0.736), (1.06, 0.841), (1.0, 0.860))
P15.3. Laugier and Richon (J. Chem. Eng. Data, 40:153, 1995) report the following data for the H2S + benzene system at 323 K and 2.010 MPa: x1 = 0.626; y1 = 0.986.
a. Quickly estimate the vapor-liquid K-value of H2S at 298 K and 100 bar. (ANS. 0.21)
b. Use the data to estimate the kij value, then estimate the error in the vapor phase mole fraction of H2S. (ANS. 0.011, 0.1%)
P15.4. The system ethyl acetate + methanol forms an azeotrope at 27.8 mol% EA and 62.1°C. For ethyl acetate, Tc = 523.2 K; Pc = 38.3 bar; and ω = 0.362.
a. What is the estimate of the bubble-point pressure from the Peng-Robinson equation of state at this composition and temperature when it is assumed that kij = 0? (ANS. 0.98 bars)
b. What value of kij gives a bubble-point pressure of 1 bar at this temperature and composition? (ANS. 0.0054)
c. What is the composition of the azeotrope and value of the bubble-point pressure at the azeotrope estimated by the Peng-Robinson equation when the value of kij from part (b) is used to describe the mixture? (ANS. xEA = 0.226)
a. Assuming zero for the binary interaction parameter (kij = 0) of the Peng-Robinson equation, predict whether an azeotrope should be expected in the system CO2 + ethylene at 222 K. Estimate the bubble-point pressure for an equimolar mixture of these components. (ANS. No, 8.7 bar)
b. Assuming a value for the binary interaction parameter (kij = 0.11) of the Peng-Robinson equation, predict whether an azeotrope should be expected in the system CO2 + ethylene at 222 K. Estimate the bubble-point pressure for an equimolar mixture of these components. (ANS. Yes, 11.3 bar)
a. Assuming zero for the binary interaction parameter (kij = 0) of the Peng-Robinson equation, estimate the bubble pressure and vapor composition of the pentane + acetone system at xp = 0.728, 31.9°C. (ANS. 0.78 bars, y1 = 0.83)
b. Use the experimental liquid composition and bubble condition of the pentane + acetone system at xP = 0.728, T = 31.9°C, P = 1 bar to estimate the binary interaction parameter (kij) of the Peng-Robinson equation, and then calculate the bubble pressure of a 13.4 mol% pentane liquid solution at 39.6°C. (ANS. 0.117, 1.12 bar)
P15.7. Calculate the dew-point pressure and corresponding liquid composition of a mixture of 30 mol% carbon dioxide, 30% methane, 20% propane, and 20% ethane at 298 K using
a. The shortcut K-ratios (ANS. 32 bar)
b. The Peng-Robinson equation with kij = 0 (ANS. 44 bar)
P15.8. The equation of state below has been suggested for a new equation of state. Derive the expression for the fugacity coefficient of a component.
Z = 1 + 4cbρ/(1 – bρ)
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