Thermodynamics Exam #1 Summary

Name_______________________ Chem. 450 Feb. 10, 2022 Midterm I Paul Cremer Olivia Fiebig Maximum score is 100 points. Exam time is 50 minutes. Some potentially useful information: 1 liter=0.001 m3 R=8.314 J/K*mol R=8.314 x 10-2 L*bar/K*mol R=8.206 x 10-2 L*atm/K*mol k=1.38 x 10-23 J/K Na=6.022 x 1023/mol 100 J = 1 L•bar pV=NkT pV=nRT T/K = T/°C + 273.15 Vf w Vi U p ex dV Cp q w H T p CV U T V vrms = (3RT/M)1/2 vmean = (8RT/ M)1/2 Tf=Ti(Vi/Vf)1/c H U pV c=Cv,m/R Cp,m=Cv,m + R pV =constant =(Cp,m/CV,m) 1 atm = 760 Torr = 1.01 x 105 Pa 1 bar = 105 Pa 1 Pa = 1 N/m2 1 L = 10-3 m3 N2 is 28.0 amu H2O is 18.1 amu NH3 is 17.0 amu He is 4.00 amu F = ma and P = F/A vrel = (2)1/2vmean (1) (20 points) Consider a system consisting of 1 mol of He at 22 °C in a volume of 25 L. (a) Find rms for He under these conditions. (b) Now consider a system consisting of N2 under initially similar conditions. To what temperature does this system need to be heated for the N2 to have the same rms that He has? (c) Plot the Maxwell-Boltzmann distribution of both He and N2 at 22 °C as a function of speed. (d) Did you need all the information you were given in the first three parts of the problem to answer the questions? If not, what information wasn’t needed? a V.ms Et F4 b rims Vms rms 1356.3 m s t C Vms M 13563 28.103 3 8.314 T 2065k probability density d speed No, the volume of 25L was not needed (2) (15 points) The mass density of a gas was found to be 1.23 kg/m3 at 330 K and 20 kPa. What is the molar mass of the molecule? PV NRT PV My RT p F E P d PT M I µ 1.23 8.314 330 20 103 68.791m (3) (15 points) Make a plot of the compression factor, Z, of a gas against pressure for a gas that has both attractive and repulsive interactions. Label the region on the graph that corresponds to the attractive interactions. Next, label the region that corresponds to the repulsive interactions. Also, show the behavior of an ideal gas on this graph. Finally, label your axes. repulsive Z 1 0 ideal gases pressure attractive (4) Consider a system that consists of 1.00 mol Ar gas at 3.00 atm of pressure. This closed system is placed inside a room with adjustable pressure. The temperature of the air in the room is 295 K and the Ar in the system is also initially at 295 K. (a) (15 points) If the system undergoes a reversible expansion (pex always equals pin) of 2 L and has diathermic walls, please find the values for U, q, and w in joules. Δ0 0 W PLV W W NRT W 2.45 k I Mol 8.314 295k 9 2.45K (b) (5 points) If the system undergoes reversible expansion and has adiabatic walls, please find the signs (positive, negative, or zero) for U, q, and w. ΔU 9 w t (5) (15 points) Consider a sample consisting of 2 mol of H2 sitting in a 24 L box at 283 K. (a) Determine the value of Cv for this system if the vibrational modes are not active. (b) Determine the value of CV for this system if the vibrational modes are active. a C C R 8.314 Cr 20.785 b vibrational modes ΔH NRT ACT NRT Cr R Cv 8.314 (6) (10 points) What is the difference in energy between Hm and Um at 298 K for the conversion of hydrogen and oxygen gas to water at 1 bar of pressure? Please give your answer in Joules. O2 (g) + 2 H2 ΔH 241.82 DH 483.64J 2O 2 (g) OH OH DO PV ΔU NRT 483.64 ΔU 483.64 ΔU Δ0 1 8.314 298 2477.57 2961J (7) (5 points) Consider a gas that is allowed to freely expand at a constant temperature. During this process, heat is transferred from the surroundings to the system. Circle the answer that is correct: (a) The molecular interactions in the gas are dominated by attractive forces. (b) The molecular interactions in the as are dominated by repulsive forces I (c) The gas is behaving ideally. (d) The attractive and repulsive forces between the gas molecules are exactly offset.