HW8

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North Carolina State University *

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205

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Chemistry

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Jan 9, 2024

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ChE 205 – Fall 2023 Homework Set 8 Due: Friday, November 3 at noon. This assignment is to be completed in your homework groups. Be sure to include the group number as well as first and last names of all contributing group members in addition to the assignment number and instructor name on the group cover sheet (see template in Moodle). Gradescope will ask you to associate the names of all group members when you submit the assignment. The entire (Gradescope) assignment must be in one person’s handwriting . If you use an equation solving tool (calculator, APEx, Solver, MATLAB), write out the equation(s) and note the tool that you used; otherwise, show all hand calculations in equation solving. In addition to the usual Gradescope submission, please have one team member submit the Excel file that includes work from problem 4 as a separate document in Moodle. 1. ( 5 pts ) As a team, review the team expectations document on the Moodle site. Develop a list of the rules and expectations you agree as a team to adopt. You should deal with any or all aspects of the responsibilities outlined in the team document: preparation for and attendance at group meetings, making sure everyone understands all the solutions, cooperating with the team effort, communicating frankly but with respect when conflicts arise, etc. Submitting this as the response to Problem 1 indicates each team membe r’s acceptance of these expectations and intention to fulfill them. This should be typed out. These expectations are for your use and benefit. Note, however, that if you make the list fairly thorough without being unrealistic you'll be giving yourselves the best chance. For example, "We will each solve every problem in every assignment completely before we get together" or "We will never miss a meeting" are probably unrealistic, but "We will try to set up the problems individually before meeting" and "We will make sure that anyone who misses a meeting for good cause gets caught up on the work" are reasonable. 2. (5 pts) State whether you would use Raoult’s law or Henry’s law to perform vapor– liquid equilibrium calculations for each component in the following liquid mixtures: (a) water and dissolved nitrogen; (b) hexane, octane, and decane; and (c) CO 2 and water in club soda or any other carbonated beverage. 3. ( 10 pts ) Three moles of benzene and 7 moles of toluene are placed in a closed cylinder equipped with a piston. The cylinder is immersed in a bath of boiling water that maintains the temperature at 100°C. The force exerted on the piston can be varied to adjust the cylinder pressure to any desired value. The pressure is initially 1000mm Hg and is gradually lowered to 600mm Hg. Use the Pxy diagram of Figure 6.4-1 to convince yourself that the cylinder initially contains only liquid benzene and toluene and to answer the following questions. (a) At what pressure does the first vapor bubble form? What is its composition? (b) At what pressure does the last droplet of liquid evaporate? What is its composition? (c) What are the liquid and vapor compositions in equilibrium with each other when the pressure is 750mm Hg? What is the ratio (moles vapor/mole liquid) at this point? (d) Estimate the volume of the cylinder contents when the pressure is (i) 1000mm Hg, (ii) 750mm Hg, and (iii) 600mm Hg.

4. ( 20 pts ) Use an Excel spreadsheet to create a Txy diagram for the benzene-chloroform system at 1 atm. Once the spreadsheet has been created, it can be used as a template for vapor – liquid equilibrium calculations for other species. The calculations will be based on Raoult’s law ( y i P = x i p i * ), although we recognize that this relationship may not produce accurate results for benzene-chloroform mixtures. (a) Begin by establishing bounds on the system behavior. Look up the normal boiling points of chloroform and benzene and, without performing any calculations, sketch the expected shape of a Txy diagram for these two species at 1 atm, with the x-axis representing the mole fraction of chloroform. (b) Using APEx or Table B.4, estimate the normal boiling points of the two species and compare them to the results in Part (a). (c) Make a Txy diagram in Excel using Raoult’s Law : In Row 1, place the title “ Txy Diagram for Ideal Binary Solution of Chloroform and Benzene.” In Row 2, place the label “ P (mm Hg) =” and in the adjacent cell enter the system pressure, which for this case is 760. Below the title and pressure labels, place headings for columns: x C , x B , T , p C * , p B * , p C , p B , P , y C , y B , and y C +y B . Not all of these columns are essential but help provide a complete picture of the system and a final check of calculations. Use the following procedures to calculate the variables: ▪ x C : enter values for the liquid mole fraction chloroform from 0 to 1.00. Include at least 20 different values of x C . ▪ x B : calculate the mole fraction of benzene for each corresponding value of x C . ▪ T : enter an estimate of the equilibrium temperature that is between the two pure- component boiling points. This is the variable we will adjust using GoalSeek, so just provide an initial guess. ▪ p C * and p B * : calculate the vapor pressure corresponding to the estimated temperature using APEx or Table B.4 (Antoine’s constants) . ▪ p C and p B : calculate partial pressures based on Raoult’s law ( p i = y i P = x i p i * ). ▪ P : Calculate pressure by summing partial pressures. ▪ Use GoalSeek to correct T : Check whether the calculated pressure is equal to the known pressure (760 mmHg) – the calculated pressure is likely not equal to 760 mmHg since the temperature was an estimate. Adjust T to make the calculated pressure correct by using GoalSeek. ▪ y C and y B : calculate vapor phase mole fractions using partial pressures and P ( p i = y i P ). ▪ y C +y B : sum the mole fractions to check the sum is 1.00. Once you have completed a row for the first value of x C , copy formulas into subsequent rows and use GoalSeek to correct each temperature (GoalSeek must be done manually each time). When the calculation has been completed for all rows (for all x C values spanning 0 to 1), draw the Txy diagram by plotting two curves: one with x C and T and one with y C and T .

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