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Unformatted text preview: Problem Set 7 Chem 3900: Physical Chemistry II
Spring 2011 Due: Class, Friday, April 8th Please make sure to write your name and the recitation you’ll attend. When you print out your work, try to minimize the number of pages. You can do this by printing multiple pages per sheet and/or by using a duplex printer. Problem 1. Let’s approximate the equation of state of n‐pentane by: /
, with b given by the van der Waals “b” coefficient in Table 16.3. i)
Calculate the fugacity coefficient and the fugacity for n‐pentane at T = 600 K for two pressures, P = 60 bar and P = 200 bar. What do these calculations tell you about intermolecular interactions in pentane under these conditions? How does this agree with the equation of state? ii)
Calculate ∆ for isothermally changing the pressure of pentane gas from 60 to 200 bar at T = 600 K. Repeat your calculation assuming that pentane behaves as an ideal gas, and compare the results. Does this agree with your conclusion about the intermolecular forces in question (i)? Problem 2. i) The previous problem treats the calculation of ∆ for an isothermal process. We could calculate ∆ for such a process if only we could compute the quantity /
. Relate / for any material to quantities that can be calculated from the equation of state. ii) Evaluate your expression in (i) for a substance with the equation of state of problem 1. Use your answer in (ii) to calculate ∆ for the compression of pentane from 60 bar to 200 bar at T = 600 K, the process of problem 1(i). Redo this calculation for an ideal gas, and compare the answers. iii) iv) Determine ∆ for compressing pentane from 60 bar to 200 bar at T = 600 K by combining over your answers to 1(ii) and 2(iii). Redo the calculation by directly integrating /
volume to check your result. 1 Problem 3. i) ii) iii) Using the data given in McQ&S, problem 22.29, calculate and plot the fugacity coefficient for ethane over the pressure range 0 ≤ P ≤ 600 bar, at T = 600 K. Plot the fugacity over the pressure range 0 ≤ P ≤ 600 bar. For reference, also plot the pressure. Calculate G for changing the pressure of 1 mol of ethane isothermally from P = 1 bar to P = 400 bar at T = 600 K, and compare with the IG result. Problem 4. Given what you know about water and the following data, estimate the melting and boiling temperatures of water at an applied pressure of 200 bar: 19.7 cm /
18.0 cm /mol, ∆
6.008 kJ/mol, ∆
40.66 kJ/mol. Problem 5. i) Consider a mixture of the two volatile liquids CS2 (component A) and benzene (component B). At T = 25oC, the vapor pressures of the pure liquids are PA* = 360.924 Torr, PB* = 95.137 Torr. (Torr is a unit of pressure; 760 Torr = 1 bar.) Assuming ideal solution behavior, calculate the pressure/composition diagram for the mixture at the constant temperature: T = 25oC. That is, in two graphs plot the total vapor pressure of the solution as a function the liquid and vapor composition (mole fraction of component A), respectively. Also calculate and plot the partial pressures PA and PB as a function of liquid and vapor composition. ii) Compare your ideal solution predictions for the total vapor pressure of the solution with the experimental data given in the file PS7_solutiondata.nb by plotting the data on the same graph. What does this comparison tell you about the intermolecular interactions in the CS2/benzene solution? The empirical Antoine equation is often used to fit the dependence of vapor pressure on temperature: log where pressure P is given in Torr and temperature T is given in oC. For CS2 A = 6.94279, B = 1169.110, C = 241.593, and for benzene A = 6.87987, B = 1196.760, C = 219.161. 2 iii) Calculate the boiling temperatures of CS2 and benzene at P = 760 Torr. iv) Again assuming ideal behavior, calculate and plot the temperature/composition diagram for the mixture at the constant pressure P = 760 Torr. In principle you need to solve for the T value that satisfies P(T) = PA(T) + PB(T) = 760 Torr for given xA or yA. In practice it is much easier to take a grid of temperature values between the boiling points TA and TB and calculate the corresponding xA and yA values; a ListPlot of the resulting data then gives the required curves. v) Compare your ideal solution predictions with the experimental data given in PS7_solutiondata.nb for temperature T versus composition at fixed pressure. Explain briefly how your results are consistent with your comparison for the constant temperature diagram. vi) You have a mixture of CS2 and benzene at P = 760 Torr and T = 57.9 oC. The total number of moles of the mixture is n = 10, and the total mole fraction of CS2 is zA = 0.48. Using the given experimental data together with the lever rule, calculate the numbers of moles of CS2 and benzene present in the liquid and vapor phases at equilibrium. 3 ...
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