# 2. Predict which of the following spontaneous reactions increase the entropy of the system.

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1 Spontaneity and Entropy DCI Name Section 1. Entropy (S) is a second driving force for chemical reactions. Define the word entropy. How is the sign of S for a chemical reaction interpreted? Entropy is a measure of the randomness of a chemical system. Randomness is measure in terms of the number of possible positions matter has in a chemical system, and the number of energy states the matter has. The greater the number of possible states in position and energy (number of microstates) the higher/greater the entropy. In a chemical or physical change a positive S means the products are more random, have a greater number of microstates compared to the reactants. If S is negative than the products are less random, have fewer number of microstates compared to the reactants. 2. Predict which of the following spontaneous reactions increase the entropy of the system. a) H 2 O(l) H 2 O(g) at 25 C The products have a greater number of positional microstates possible because gases are mostly empty space and the gas particles can occupy any of the available positions. In the liquid phase, while the molecules are mobile, the phase is condensed so there is considerably less empty space so there are many fewer positional microstates. b) 2Mg(s) + O 2 (g) 2MgO(s) The products phase is solid and the reactants are a solid and a gas. So the reactants are less ordered compared to the products. Gases have high entropies because the particles are well separated in space, so there are many more microstates possible. Also there are fewer numbers of product particles compared to the reactants. When there are fewer moles of products there are fewer arrangements/microstates possible. So both the phase change and the number of particles point to a more ordered products compared to reactants. c) Ba(OH). 2 8H 2 O(s) + 2NH 4 Cl(s) BaCl 2 (aq) + 2NH 3 (g) + 10H 2 O(l) The product phases are aqueous solution, a gas and a liquid and the reactants are both solids. The reactants are more ordered compared to the products. Gases have high entropies because the particles are well separated in space, so there are many more microstates possible. In general a substance dissolved in water with have more disorder compared to a solid phase. In solution ions are hydrated, and are able to distribute throughout the solution. There are 13 moles of product compared to 3 moles of reactants, so there are many more substances that the atoms can be distributed between. When there are more moles of products there are larger arrangements/microstates possible. So + S + S

2 both the phase change and the number of particles point to a more disordered products compared to reactants. d) H 2 (g) O 2(g) H 2 O(l) or (g) The products phase is a liquid and a gas and the reactants are a both gases. So the reactants are more disordered compared to the products. Gases have high entropies because the particles are well separated in space, so there are many more microstates possible. Liquids are much more ordered as a condensed phase. There are fewer positions particles can occupy in the liquid phase compared to the gaseous phase. There are equal numbers of product particles and reactants. So the phase change points to a more ordered products compared to reactants. e) CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O(l) The products phase is a liquid and a gas and the reactants are a both gases. So the reactants are more disordered compared to the products. Gases have high entropies because the particles are well separated in space, so there are many more microstates possible. Liquids are much more ordered as a condensed phase. There are fewer positions particles can occupy in the liquid phase compared to the gaseous phase. There are equal numbers of product particles and reactants. So the phase change points to a more ordered products compared to reactants. f) Al(s) Br 2(l) AlBr 3 (s) The products phase is solid and the reactants are a solid and a liquid. So the reactants are less ordered compared to the products. Liquids are more disordered compared to solids as a condensed phase. In the liquid phase particles are able to move very close to each other, and occupy more positions compared to solids where the particles are static and cannot move. Also there is a wider range of energies for liquids compared to solids. Also there are fewer numbers of product particles compared to the reactants. When there are fewer moles of products there are fewer arrangements/microstates possible. So both the phase change and the number of particles point to a more ordered products compared to reactants. 3. A table of absolute entropies (S ) for selected substances is at the end of this DCI. Identify differences between S and H f as thermodynamic values. The entropy values are positive, while the enthalpy of formation values are positive and negative. The entropy values for the solids are the lowest and the entropy values for gases are the highest. For enthalpy of formations the same substance in different phases the trend is to become more positive from solid, to liquid to gas.

3 4. Write the mathematical equation that relates the standard entropy change in a chemical reaction to the absolute entropy of the reactants and products. 5. Calculate the change in entropy ( S rxn ) for the chemical reactions in question 2. a) H 2 O(l) H 2 O(g) S is positive S rxn = S (H 2 O(l)) S (H 2 O(s)) S rxn = 189 J mol -1 K J mol -1 K -1 = +119 J mol -1 K -1 b) 2Mg(s) + O 2 (g) 2MgO(s) S is negative S rxn = 2S (MgO(s)) [2S (Mg(s)) + S (O 2 (g))] S rxn = J mol -1 K -1 [2 33 J mol -1 K J mol -1 K -1 ] = 217 J mol -1 K -1 c) Ba(OH) 2. 8H 2 O(s) + 2NH 4 Cl(s) BaCl 2 (aq) + 2NH 3 (g) + 10H 2 O(l) S is positive S rxn = [S (BaCl 2 (aq)) + 2S (NH 3 (g)) + 10S (H 2 O(l))] [S (Ba(OH) 2. 8H 2 O(s)) 2S (NH 4 Cl(g))] S rxn = 123 J mol -1 K J mol -1 K J mol -1 K -1 [427 J mol -1 K J mol -1 K -1 ] = +592 J mol -1 K -1 d) H 2 (g) O 2(g) H 2 O(l) S is negative S rxn = 164 J mol -1 K -1 e) CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O(l) S is negative S rxn = 242 J mol -1 K -1 f) Al(s) Br 2(l) AlBr 3 (s) S is negative S rxn = 72.6 J mol -1 K -1

4 6. The natural tendency for spontaneous chemical reactions is to increase entropy. Is the entropy an absolute predictor of spontaneity? Defend your answer. The entropy of a chemical reaction is not an absolute predictor of the spontaneity of a chemical reaction. In Q5 note that all reactions are spontaneous, however there are some reactions with a negative S and some reactions with a positive S. 7. Predict whether the entropy of the system increases, remains constant or decreases when the following processes occur. Explain your reasoning. a. Ice melts at 0 C. H 2 O(s) H 2 O(l) Liquids are more disordered compared to solids as a condensed phase. In the liquid phase particles are able to move very close to each other, and occupy more positions compared to solids where the particles are static and cannot move. Also there are a wider range of energies for liquids compared to solids. S is positive. b. A precipitate forms in aqueous solution. Ag + (aq) + Cl (aq) AgCl(s) Ions dissolved in water are mobile, therefore they can occupy many more positions compared to the ions in the solid phase. In the solid phase ions are static, so there is effectively one positional microstate. The products are less random compared to the reactants and S is negative. c. A solid dissolves in water. C 6 H 12 O 6 (s) C 6 H 12 O 6 (aq) A covalent solid like glucose dissolves in water the molecules are more mobile and can move around in the solution. In the solid phase the molecules of glucose are static, there is only one positional microstate compared to the many positional microstates available to a hydrated glucose molecule. S is positive. d. A gas condenses to a liquid. N 2 (g) N 2 (l) gases are mostly empty space and the gas particles can occupy any of the available positions. In the liquid phase, while the molecules are mobile, the phase is condensed so there is considerably less empty space so there are many fewer positional microstates. S is negative.

5 Substance H f Substance H f and State (kj/mol) and State (kj/mol) C(s) (graphite) 0 HCl(g) C(s) (diamond) 2 HBr(g) CO(g) HI(g) 26.5 CO 2 (g) I 2 (g) CH 4 (g) 75 O 2 (g) 0 CH 3 OH(g) -201 O(g) 249 CH 3 OH(l) -239 O 3 (g) 143 H 2 CO(g) -116 CCl 4 (l) N 2 (g) 0 HCOOH(g) -363 NH 3 (g) -46 HCN(g) NH 3 (aq) -80 CS 2 (g) NH + 4 (aq) -132 CS 2 (l) 89.7 NH 4 Cl(s) C 2 H 2(g) 227 N 2 H 4 (l) 50.6 C 2 H 4 (g) 52 NO(g) CH 3 CHO(g) -166 NO 2 (g) C 2 H 5 OH(l) -278 N 2 O(g) 82.0 C 2 H 5 O 2 N(g) -533 N 2 O 4 (g) 9.16 C 2 H 6 (g) N 2 O 4 (l) 20 C 3 H 6 (g) 20.9 HNO 3 (aq) C 3 H 8 (g) -104 HNO 3 (l) C 4 H 10 (g) -126 NH 4 ClO 4 (s) -295 C 8 H 18 (l) -208 CH 2 = CHCN(l) 152 CH 3 COOH(l) -484 S 2 Cl 2 (g) -18 C 6 H 12 O 6 (s) SO 2 (g) H 2 S(g) Cl 2 (g) 0 SOCl 2 (g) -213 Cl 2 (aq) -23 Cl - (aq) SiCl 4 (g) -657 SiO 2 (s) SiF 4 (g) H 2 (g) 0 H(g) 217 Ba(OH) 2 8H 2 O(s) H + (aq) 0 BaCl 2 (aq) -872 OH - (aq) -230 AlBr 3 (s) -526 H 2 O(l) -286 H 2 O(g) -242 ZnS(s) -206

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