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Solutions_Ch10

Solutions_Ch10 - CHAPTER 10 SPONTANEITY ENTROPY AND FREE...

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369 CHAPTER 10 SPONTANEITY, ENTROPY, AND FREE ENERG Y Spontaneity and Entropy 12. a. A spontaneous process is one that occurs without any outside intervention. b. Entropy is how energy is distributed among energy levels in the “particles” that constitute a given system. Entropy is closely associated with probability, where the most probable arrangement (state) is the highest entropy state. c. Positional probability is a type of probability that depends on the number of arrangements in space that yield a particular state. d. The system is the portion of the universe in which we are interested. e. The surroundings are everything else in the universe besides the system. f. The universe is everything; universe = system + surroundings. 13. We draw all the possible arrangements of the two particles in the three levels. 2 kJ x x xx 1 kJ x xx x __ 0 kJ xx x x __ Total E = 0 kJ 1 kJ 2 kJ 2 kJ 3 kJ 4 kJ The most likely total energy is 2 kJ. 14. 2 kJ AB B A B A 1 kJ AB B A A B 0 kJ AB A B A B E total = 0 kJ 2 kJ 4 kJ 1 kJ 1 kJ 2 kJ 2 kJ 3 kJ 3 kJ The most likely total energy is 2 kJ. 15. Processes a, b, d, and g are spontaneous. Processes c, e, and f require an external source of energy in order to occur since they are nonspontaneous.
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370 CHAPTER 10 SPONTANEITY, ENTROPY, AND FREE ENERGY 16. Of the three phases, gases have the greatest positional probability (greatest entropy), followed by liquids, with solids having the smallest positional disorder (smallest entropy). Thus a, b, c, e, and g involve an increase in entropy. All lead to an increase in positional probability. 17. a. Positional probability increases; there is a greater volume accessible to the randomly moving gas molecules, which increases disorder. b. The positional probability doesn't change. There is no change in volume and thus no change in the numbers of positions of the molecules. c. Positional probability decreases because the volume decreases (P and V are inversely related). 18. a. H 2 at 100°C and 0.5 atm; higher temperature and lower pressure mean greater volume and hence greater positional probability. b. N 2 ; N 2 at STP has the greater volume. c. H 2 O(l) has greater positional probability than H 2 O(s). 19. There are more ways to roll a seven. We can consider all the possible throws by constructing a table. One die 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 Sum of the two dice There are six ways to get a seven, more than any other number. The seven is not favored by energy; rather, it is favored by probability. To change the probability, we would have to expend energy (do work). 20. Arrangement I: S = k ln ; = 1; S = k ln 1 = 0 Arrangement II: = 4; S = k ln 4 = (1.38 × 10 23 J/K) ln 4, S = 1.91 × 10 23 J/K Arrangement III: = 6; S = k ln 6 = 2.47 × 10 23 J/K
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CHAPTER 10 SPONTANEITY, ENTROPY, AND FREE ENERGY 371 Energy, Enthalpy, and Entropy Changes Involving Ideal Gases and Physical Changes 21. 1.00 × 10 3 g C 2 H 6 × g 07 . 30 mol 1 = 33.3 mol q v = Δ E = nC v Δ T = 33.3 mol(44.60 J K 1 mol 1 )(48.4 K) = 7.19 × 10 4 J = 71.9 kJ At constant volume, 71.9 kJ of energy is required, and Δ E = 71.9 kJ.
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