Problem Set #33: Entropy of Mixing for Ideal and Real Gases

University:
The Pennsylvania State University
Course:
CHEM 450 | Thermodynamics
Academic year:

2024
Views:

84

Pages:

2
Author:

Alexis H.

Problem Set #33 Assigned: March 25, 2024 Due: March 27, 2024 at 2:30 pm 1. In class we found mixG and mixS for ideal gases. What should the value of mixH be under these circumstances? Are there circumstances under which real gases would not mix? (Hint: ideal gases assume that all the collisions between the gas molecules are elastic. In other words, there are no attractive or repulsive forces between the molecules.) 2. Consider a 5 L container that is divided into two compartments of equal size. N2(g) is placed on the left side at 25 °C and 1 atm. On the right side, H2(g) is present at 25 °C and 1 atm. Find mixS and mixG for this situation. You may assume the gases behave ideally. 3. Consider a 10 L container that is divided into two compartments of equal size. N2(g) is placed on the left side at 25 °C and 1 atm. On the right side, H2(g) is present at 25 °C and 1 atm. Find mixS and mixG for this situation. You may assume the gases behave perfectly. 4. Consider an entropy of mixing problem in which 1 mole of perfect gas A is placed on the left side of a container and 1 mole of perfect gas B is placed on the right side of a container. In this problem, the container is divided into two compartments of equal size before the gases are mixed and the temperature, 295 K, is the same on both sides. (A) Do you need to know the volume of the container to find mixS and mixG? Please explain your answer. (B) Explain this answer in light of the results you obtained in problems #2 and #3 above. 1. Since the gases are ideal the molecules don’t interact during the mixing process which leads the delta H to be zero. The circumstances in which real gases wouldn’t mix is if they interact and the value of delta H is anything but zero. 2. PV NRT n n n latm 2.5L 008206 298k Anitrogen s p 0.102MOI n latm 2.5L 0.08206 298K hydrogen 0.102mol 10.202mol 0.08206 298 5L p 0.988atm ΔmixS nR xInx 1 In 1 xD 0.202 0.51h105 ΔmixS 1.1641 K 0.51 0 5 ΔmixG Tomas 298710.0877 ΔmixG 489J 4. (a) You don’t need to know the volume because you already know the amount of moles of each of the gases and the volume is usually used in the ideal gas equation to nd the amount of moles, which is not needed in this case. (b) In both question 2 and 3 the only thing the volume was needed for was to nd how many moles are in the combined sample but the amount of moles was already given in this case. 3 PV MRT n P i.io i n n 0409mol Δmix5 nR xn Inxn xH in it 0.409 Δmixs 2356 8314 Int ΔmixG TLS 298k2.356 ΔmixG 702.088 Int