CH302 Worksheet 13c—Problems related to lecture on entropy Listed below are a collection of problems lifted from the entropy chapter in the text book. Although you have already seen some of the entropy material, specifically Worksheet 11 material that includes Hess’ law-like calculations of ΔSrxn and assigning the sign of entropy for a physical process based on changes in complexity, and Chapter 13a material on statistical thermodynamics, in this worksheet I provide a collection of entropy calculations in sequence that tie together the majors themes of this profoundly important concept. 1. First the simple definition of the change in entropy based on the amount of heat involved at a constant temperature Calculate the change in entropy of a large block of ice when 50. J of energy is removed reversibly from it as heat at 0°C in a freezer. 2. Now, given that the definition of the change in entropy corresponds nicely to a phase change, you can use the same equation (with ΔH representing the amount of heat to prompt every molecule in the system to undergo a phase change) Calculate the standard entropy of vaporization of argon at its boiling point of 87.3 K given an enthalpy of vaporization of 6.5 kJ/mol. (Note another variation of this problem allows you to calculate a phase change temperature give the entropy and enthalpy of the phase change.) 3. And now a refresher on calculating the ideal positional entropy at 0K. What is the entropy of a sample of a solid in which the molecules can take any one of three orientations with the same energy. Suppose there are 30 molecules in the sample. 4. One can successfully rank absolute molar entropies by looking at the complexity of the system. Complete the sentences below to create simply rules of thumb that will help you remember how to predict relative entropies. As the temperature of a system increases, the molar entropy of a compound _________________ As the pressure of a system increases, the molar entropy of a compound _________________ As the volume of a system increases, the molar entropy of a compound _________________ As the number of particles in a system increases, the molar entropy of a compound _________________ As the perfection of a compound’s crystal structure increases, the molar entropy of a compound _________________ 5. Apply the concepts in the question above to rank the molar entropy of the pairs of systems below: (a) 1 mol CO2 (g) at 25°C and 1 bar or 1 mol CO2 (g) at 25°C and 3 bar; (b) 1 mol He(g) at 25°C or 1 mol He(g) at 100°C in the same volume; (c) Br2 (l) or Br2 (g) at the same temperature? Explain your conclusions. 6. Tables of absolute entropies allow a ready comparison between compounds. Use the information below to determine which compound in a pair is the more ordered form, (a) diamond or graphite at 25°C. (b) nitrogen or oxygen at 25°C. .7. Without doing any calculations, estimate the sign of the entropy change for the reaction N2(g) + 3 H2(g) → 2 NH3 and explain your answer. 8. Use data from Table 7.3 to calculate the standard entropy of the reaction in problem 7. 9. Global changes in entropy. We know that reactions like the formation of ammonia from nitrogen and hydrogen actually do happen despite the decrease in entropy of the system. What is the reason? 10. Calculate the change in entropy of the surroundings when water freezes at −10.°C; use ΔHfus(H2O) = 6.0 kJ·mol−1 at −10.°C. 11. Calculate the entropy change of the surroundings when 1.00 mol H2O(l) vaporizes at 90°C and 1 bar. Take the enthalpy of vaporization of water as 40.7 kJ·mol−1. 12. Is the formation of hydrogen fluoride from its elements in their most stable forms spontaneous under standard conditions at 25°C? For the reaction H2(g) + F2(g) → 2 HF(g), ΔH° = −542.2 kJ and ΔS° = +14.1
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