For the compounds specified by your instructor in problem 1

Question

1. This problem reinforces the concepts of phase equilibria for pure substances.

a. Use steam table data to calculate the Gibbs energy of 1 kg saturated steam at 150°C, relative to steam at 150°C and 50 kPa (the reference state). Perform the calculation by plotting the volume data and graphically integrating. Express your answer in kJ. (Note: Each square on your graph paper will represent [pressure-volume] corresponding to the area, and can be converted to energy units.)

b. Repeat the calculations using the tabulated enthalpies and entropies. Compare your answer to part (a).

c. The saturated vapor from part (a) is compressed at constant T and 1/2 kg condenses. What is the total Gibbs energy of the vapor liquid mixture relative to the reference state of part (a)? What is the total Gibbs energy relative to the same reference state when the mixture is completely condensed to form saturated liquid?

d. What is the Gibbs energy of liquid water at 600 kPa and 150°C relative to the reference state from part (a)? You may assume that the liquid is incompressible.

e. Calculate the fugacities of water at the states given in parts (a) and (d). You may assume that f = P at  50 kPa.

2. Derive the formula for fugacity according to the van der Waals equation.

3. Use the result of problem 2 to calculate the fugacity of ethane at 320 K and at a molar volume of 150 cm³/mole. Also calculate the pressure in bar.

4. Compare the Antoine and shortcut vapor-pressure equations for temperatures from 298 K to 500 K. (Note in your solution where the equations are extrapolated.) For the comparison, use a plot of log₁₀P^sat versus 1/T except provide a separate plot of P^sat versus T for vapor pressures less than 0.1 MPa.

a. n-Hexane

b. Acetone

c. Methanol

d. 2-propanol

e. Water

5. For the compound(s) specified by your instructor in problem 1, use the virial equation to predict the virial coefficient for saturated vapor and the fugacity of saturated liquid. Compare the values of fugacity to the vapor pressure.

6. Compare the Peng-Robinson vapor pressures to the experimental vapor pressures (represented by the Antoine constants) for the species listed in problem 4.