Problem Set #11: Thermodynamic Calculations and Analysis

Problem Set #11 Assigned: February 2, 2024 Due: Feb. 5, 2024 at 2:30 pm 1. Consider 3.0 mol O2(g) that is heated at a constant pressure of 3.25 atm, so that its temperature increases from 260 K to 285 K. Calculate q, H, and U for this process. Note: the molar constant pressure heat capacity of O2 is 29.4 J/mol K. 2. When 179 J of energy is supplied as heat at constant pressure to 1.9 mol of gas molecules, the temperature of the sample increases by 1.78 K. Find the molar heat capacity at constant volume and constant pressure. What can you say about the number of atoms per gas molecule in this gas? 3. The constant pressure heat capacity, Cp,m of a gas sample was found to vary with temperature according to the expression: Cp (J/K) = 20.17 + 0.3665 (T/K) Find q, w, U, and H when the temperature is raised from 25 °C to 100 °C at (a) constant pressure and (b) constant volume. 4. What is the difference in energy between Hm and Um at 298 K for the Haber-Bosch reaction? N2(g) + 3 H2(g) 2 NH3(g) 5. At 100 °C, it takes 1800 J to boil 0.798 g H2O at 1.0 atm. Find Hm and Um for this process. Note that you can write H = U + p V = U + ( n)RT under constant pressure conditions. 6. Consider the function, f(x,y) = 6x3 + 4xy2 + 6x + y2 (a) Find the total differential associated with this function. (Hint: read over Chemist Toolbox 9 on p. 44) (b) Does this function meet the criterion of exactness? 7. Consider the functions: (a) Find: (b) Find: , = and , and (c) Does the equation of state for a perfect gas meet the criterion for exactness? (d) Explain you answer to (c) = 8. For an ideal gas, consider the total differential: (a) Find: (b) Find: + and and (c) Does the expression for dq meet the criterion for an exact differential? (d) Explain you answer to (c) 9. Estimate the internal pressure of water vapor at 1.00 bar and 400 K, treating it as a van der Waals gas, when = . You may simplify the problem by assuming that the molar volume can be predicted from the perfect gas equation. Also, a = 5.464 atm L2/mol2 for water. 10. As noted above, for a van der Waals gas, = = . Starting from this equation, will the internal energy of a van der Waals gas go up, go down or remain unchanged as the volume is increased at constant temperature? Explain your answer in 40 words or less. Note: we will prove that 1 q = H ΔH nCpΔT 3.0mol 29.4mh.is 15k 9 2205 W PΔV POV NRT W NRT 3.00mol 8314 15k W 623.6J 9 ΔU w ΔU 9 w 2205 623.6 Δ0 1581.4J on page 106 in Topic 3E. 2 H nCpΔT Cp HIT Cp 1.9 9.78 Cp 52.9 Cp Cv R 52.9 Cv 8.314 Cr 44.61 d f 3 20.17 0.3665T at Cv 20.17 463 20.17T 03665 20.17 463 322 b Cv Cp R 0.36265 4632 3222 11.856 03665T 11.856T ΔH 23.1 103J 23.1kt W nRdT W 1m01 8.314 463322 6 1,172.274 W 1 172 103J 1.172k Δ0 9 w DO 23.1 k 1 172k Δ0 24.272K 8.314 Cv 11 856 0.3665 322k 2,843.97 20.283.026 9 0.3665T at 03665 0 6514632 322 11.856 463 322 1671.696 20,283.026 9 00 21,954.722J 21.95k W pdV W 0 ΔH DO NROT 21.95k Cimon 8.314 103 463322 21.95141 1.17k DH 23.12KJ 4 At 298K the delta H for the reaction is -92.3 kJ/mol and the delta U is -90.6 kJ/ mol meaning that the difference between the 2 is the amount of work done by the system in the reaction which is approximately -1.7 kJ/mol 5 DO 9 Δ0 9 0 ΔH ΔU PΔV 1800 ΔH 2134.04 NRT g MCLT 9 0.798 4.186 ΔH 2134.04 100 9 334.04 Δ 0 334.04 1800 Δ0 2134.04J 0.044 8.314 2134.04 36.58 ΔH 2170.62J 100 6 a f xy 6 3 4 42 6 42 6 3 4xy 6 42 0 b yes it meetsthecriterionofexactness 18 2 4xy 6 42 of 6 6 3 4xy 6 3 4xy 6 29 92 Of 18 2 4 6 92 dx 6 3 4xytox 2gdy 9 7 8 8 b c 8 Dnp 3 a h at CBI II In f MI 2 1 If yes d thesecond derivative bothequaleach other 400 Vm 9m 334.6246 2 b 2 star 33.26dm mott 4 96 103 Cordt par Cudt pdv CAT Pdr CAT par 229 9 Vm IT 8 a Gt Cudt par 2V Cudt Pc Cudt pdv c no d theequationswould cancel eachotherout 10 cvdttpa.lv It will go down because the higher the volume gets the lower the overall number will be because the volume is increasing, but in the denominator.