Part 1. Determine the liquid and vapor molar volumes, V₁^{^} and V_v^{^} , of pure n-butane and pure n-hexane at 5 bar and 300 K using the Redlich-Kwong equation of state:

P = RT/(V^{^}-b) - α(T)/V^{^}(V^{^}+b) where α(T) = 0.42748T_r^-1/2R²T_c²/P_c and b = 0.08664RT_c/P_c

P is pressure, T is temperature, R is the ideal gas constant, Tr is reduced temperature, Tc is critical temperature, and Pc is critical pressure. Note that the Redlich-Kwong equation of state is a cubic equation and will have three real roots. One root will correspond to the liquid phase molar volume (V₁^{^}) and one root will correspond to the vapor phase molar volume (V_v^{^} ). The intermediate root is unstable and hence meaningless. Use your 201 textbook to look up the critical parameters for n-butane and n-hexane.

Part 2. Assuming Raoult's Law to be valid, prepare a Txy diagram for a mixture n-butane (1) and n-hexane (2) at 1 atm. Make the plot in terms of n-butane and be sure to clearly label the bubble line and the dew line. Use the following increments for T:

T (°C) 68.74  65  60  55  50  45  40  35  30  25  20  15  10  5  -0.5

Part 3. If a liquid mixture containing 54.20 mol% n-butane and 45.80 mol% n-hexane (x_1,initial = 0.5420) is heated in a kettle until the liquid mole fraction of butane, x1,final, drops to 0.0448, the relationship between the starting number of moles, L1 and the ending number of moles, L2 in the kettle is given by the Rayleigh equation

In(L1/L2) = _x1,final∫^x1,initial dx/y1 - x1

where y1 and x1 in the expression refer to the y1 and x1 data calculated for your Txy diagram (T will be changing, but disregard that). Use Excel to perform a numerical integration to find the number of moles remaining given there were initially 10 moles in the kettle. Compare the values obtained using left-sided rectangles, right-sided rectangles, and trapezoids. Which method do you think gave the most accurate result and why?

Prepare a short write-up in the form of a technical memorandum presenting your analysis and explaining the results. Be sure to include a table of molar volumes for Part 1, a plot with Txy data for Part 2, and a table with L2 values for Part 3. Also attach a clear, readable and understandable printout of your Excel sheet, showing the data and equations used to solve the problem. Again, follow the guidelines presented in the first tutorial for formatting the spreadsheet.