Homework Problems

Level 1 Problems
These problems are suitable for students in a material and energy balance course

 

Problem 1. By gradually increasing the temperature, determine the bubble-point temperature of a 50 mol% acetaldehyde + 50 mol% ethanol mixture. What is the composition of the vapor that is in equilibrium with this liquid?

Problem 2.  If a mixture containing 60 mol% acetaldehyde and 40 mol% ethanol is thermostatted at 324 K, what phase(s) is/are present? What are the compositions and relative amounts of each phase?

Problem 3.  If a mixture containing 60 mol% n-pentane and 40 mol% n-heptane is contained in a cylinder at 1 atm, determine from the simulator what phases are present at each of the following temperatures: (a) 308 K (b) 316 K (c) 324 K (d) 332 K.

Problem 4.  Run a simulation for 60 mol% n-pentane + 40 mol% n-heptane at 322 K. Click on the recorder tab. At some point where the liquid and vapor phases seem to be clearly defined, pause the simulation by clicking the STOP button. Now by counting the appropriate red and blue molecules, verify the instantaneous values shown on the strip-chart recorder for the mole fraction of pentane in the vapor, the mole fraction of pentane in the liquid, and the fraction of molecules that are in the vapor phase.

Problem 5.  Run a simulation for a mixture containing 30 mol% n-pentane and 70 mol% n-heptane at a high enough temperature that the fluid is 100% vapor. Now cool the vapor down until it starts to condense. What is the dew point temperature for this mixture? Perform the same simulation sequence for a mixture containing 50 mol% n-pentane. What is the dew point temperature? Comment on why the second dew point temperature is either higher or lower than the first.

Problem 6.  Run  a simulation for a mixture containing 80 mol% n-pentane and 20 mol% n-heptane. Adjust the temperature to achieve 50 mol% separation of the fluid into the vapor phase. At what temperature should a flash tank be operated if a feed containing 80 mol% n-pentane is to be 50% vaporized? Using a ruler measure the relative volumes of the liquid and vapor phases. Why is the one phase so much larger than the other if there is an equal number of moles in each phase?

Problem 7.  Run  a simulation for a mixtures of ethanol and n-heptane at 356 K. Vary the overall mole fraction from 10 mol% ethanol to 30 mol% ethanol in increments of 5 mol% noting after equilibration in each case the compositions of the vapor and liquid phases in equilibrium. Are they all the same? If so, explain how the compositions in the liquid and vapor can be the same when the overall composition changes. If they are not all the same, explain any trend in values that you observe.

Level 2 Problems
These problems are suitable for students in a thermodynamics course

• Problem 1. Run a simulation for a mixture of acetaldehyde + ethanol at 330 K and a composition in the two-phase region. Which component is more volatile? Does this mixture display positive or negative deviations from Raoult's Law? Explain how you can tell this from the Gibbs energy tab and from the activity coefficient tab. Explain why the observed deviations from Raoult's Law (positive or negative) are observed. Use the relative strengths of the interactions in your explanation.
• Problem 2. Run a simulation for the acetone + chloroform system. From a chemical view point, explain why the cross attractions are larger than either of the like (red-red or blue-blue) attractions. Examine the relative volatility. Can you get two phases in equilibrium for a mixture of 38 mol% acetone? Why or why not? Explain why the relative volatility is unity at this composition. The volatility is greater than one above this composition but less than one below it. What does this mean in terms of the compositions of acetone in the vapor phase relative to the liquid phase for compositions greater than 38 mol%? For compositions less than 38 mol%? Show how your explanations are consistent with the xy diagram.
• Problem 3. Run a simulation for ethanol (90 mol%) + n-heptane (10 mol%) at 348 K. Observe in the simulation the number of blue molecules in the vapor and liquid phases. Which component is the more volatile in this mixture? Which pure component boils at a lower temperature? Explain why in this mixture the more volatile component is the one whose normal boiling point is higher. Use molecular interactions to explain this phenomenon as well as the activity coefficients and excess Gibbs energy. Are these positive or negative deviations from Raoult's law?

Level 3 Problems
These problems are suitable for more advanced students in a graduate thermo. course or a statistical mechanics course

• Problem 1.
• Problem 2.  
• Problem 3.