Determine the liquid and vapor molar volumes

Question

The paper must be clear and concise. Proper organization of the information is essential. A typical report is divided into the following sections:

• Executive Summary

• Introduction or Purpose

• Theory and Analysis

• Results and Discussion

• Conclusions and Recommendations

• References

• Attachments and/or Appendices(This could include a printout of a spreadsheet)

The section headings are aligned with the left-hand margin in a memo and might be simply capitalized and/or given bold or italicized font. Keep the 12 point type size. Identify that the format itself is as well flexible; though, all the critical elements or information require to be comprised. The Results and Discussion and Conclusions sections are at times combined. The essential supporting documentation is included as Attachments or in Appendices. Frequently the supporting information may include a print out (mightbe comprising multiple pages) of a formatted spreadsheet.

Part 1:

Determine the liquid and vapor molar volumes, Vˆ_l and Vˆ_v, of pure n-butane and pure n-hexane at 5 bar and 300 K using the Redlich-Kwong equation of state:

P = (RT/Vˆ -b)  - d(T)/Vˆ(Vˆ + b) where d(T) = 0.42748 [Tr-^1/2 R² T_c²]/P_c and b = 0.08664 RT_c/P_c

P is pressure, T is temperature, R is the ideal gas constant, T_r is reduced temperature, T_c is critical temperature, and P_c 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 (Vˆ_L) and one root will correspond to the vapor phase molar volume (Vˆ_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, x_1,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

ln(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 T_xy 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.