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Chapter 17: Problem 17

Use Table \(17.1\) to calculate \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\) (b) \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)\) (c) \(\mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) (d) \(2 \mathrm{NaCl}(s)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NaF}(s)+\mathrm{Cl}_{2}(g)\)

Short Answer

Expert verified
Question: Calculate the standard entropy change (\(\Delta S^{\circ}\)) for the following reactions: (a) CO(g) + 2H2(g) -> CH3OH(l) (b) N2(g) + O2(g) -> 2 NO(g) (c) BaCO3(s) -> BaO(s) + CO2(g) (d) 2 NaCl(s) + F2(g) -> 2 NaF(s) + Cl2(g) Provide your answers in J/mol·K. Answer: (a) \(\Delta S^{\circ} = -331\: J\: mol^{-1} K^{-1}\) (b) \(\Delta S^{\circ} = 25.4\: J\: mol^{-1} K^{-1}\) (c) \(\Delta S^{\circ} = 155.7\: J\: mol^{-1} K^{-1}\) (d) \(\Delta S^{\circ} = -60.2\: J\: mol^{-1} K^{-1}\)

Step by step solution

01

(a) Calculate \(\Delta S^{\circ}\) for the given reaction.

Reaction (a): $\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)$ Follow these steps to calculate \(\Delta S^{\circ}\): 1. Find the standard entropies for the reactants and products in Table 17.1: $S^{\circ}_{CO} = 197.6\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{H2} = 130.6\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{CH3OH} = 126.8\: J\: mol^{-1} K^{-1}$ 2. Apply the formula to calculate \(\Delta S^{\circ}\): \(\Delta S^{\circ} = S^{\circ}_{CH3OH} - (S^{\circ}_{CO} + 2S^{\circ}_{H2}) = 126.8 - (197.6 + 2(130.6))\) 3. Calculate the result: \(\Delta S^{\circ} = -331\: J\: mol^{-1} K^{-1}\)
02

(b) Calculate \(\Delta S^{\circ}\) for the given reaction.

Reaction (b): \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)\) 1. Find the standard entropies for the reactants and products in Table 17.1: $S^{\circ}_{N2} = 191.5\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{O2} = 205.0\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{NO} = 210.7\: J\: mol^{-1} K^{-1}$ 2. Apply the formula to calculate \(\Delta S^{\circ}\): \(\Delta S^{\circ} = 2S^{\circ}_{NO} - (S^{\circ}_{N2} + S^{\circ}_{O2}) = 2(210.7) - (191.5 + 205.0)\) 3. Calculate the result: \(\Delta S^{\circ} = 25.4\: J\: mol^{-1} K^{-1}\)
03

(c) Calculate \(\Delta S^{\circ}\) for the given reaction.

Reaction (c): \(\mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) 1. Find the standard entropies for the reactants and products in Table 17.1: $S^{\circ}_{BaCO3} = 112.2\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{BaO} = 54.3\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{CO2} = 213.6\: J\: mol^{-1} K^{-1}$ 2. Apply the formula to calculate \(\Delta S^{\circ}\): \(\Delta S^{\circ} = (S^{\circ}_{BaO} + S^{\circ}_{CO2}) - S^{\circ}_{BaCO3} = (54.3 + 213.6) - 112.2\) 3. Calculate the result: \(\Delta S^{\circ} = 155.7\: J\: mol^{-1} K^{-1}\)
04

(d) Calculate \(\Delta S^{\circ}\) for the given reaction.

Reaction (d): \(2 \mathrm{NaCl}(s)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NaF}(s)+\mathrm{Cl}_{2}(g)\) 1. Find the standard entropies for the reactants and products in Table 17.1: $S^{\circ}_{NaCl} = 72.1\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{F2} = 202.7\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{NaF} = 51.4\: J\: mol^{-1} K^{-1} \\ S^{\circ}_{Cl2} = 223.0\: J\: mol^{-1} K^{-1}$ 2. Apply the formula to calculate \(\Delta S^{\circ}\): \(\Delta S^{\circ} = (2S^{\circ}_{NaF} + S^{\circ}_{Cl2}) - (2S^{\circ}_{NaCl} + S^{\circ}_{F2}) = (2(51.4) + 223.0) - (2(72.1) + 202.7)\) 3. Calculate the result: \(\Delta S^{\circ} = -60.2\: J\: mol^{-1} K^{-1}\) The standard entropies for the given reactions are: (a) \(\Delta S^{\circ} = -331\: J\: mol^{-1} K^{-1}\) (b) \(\Delta S^{\circ} = 25.4\: J\: mol^{-1} K^{-1}\) (c) \(\Delta S^{\circ} = 155.7\: J\: mol^{-1} K^{-1}\) (d) \(\Delta S^{\circ} = -60.2\: J\: mol^{-1} K^{-1}\)

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Most popular questions from this chapter

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\) (b) \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(g)\) (c) \(\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)\)

Show by calculation whether the reaction $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(a q) \quad \Delta G^{\circ}=+27.2 \mathrm{~kJ} $$ is spontaneous at \(25^{\circ} \mathrm{C}\) (a) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=0.85 M_{;}\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=0.15 \mathrm{M}\). (b) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=2.0 \times 10^{-3} \mathrm{M} ;\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=1.0 \mathrm{M}\).

At \(1200 \mathrm{~K}\), an equilibrium mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) gases contains 98.31 mol percent CO and some solid carbon. The total pressure of the mixture is \(1.00 \mathrm{~atm}\). For the system $$ \mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightleftharpoons 2 \mathrm{CO}(g) $$ calculate (a) \(P_{\mathrm{Co}}\) and \(P_{\mathrm{CO}_{2}}\) (b) \(K\) (c) \(\Delta G^{\circ}\) at \(1200 \mathrm{~K}\)

On the basis of your experience, predict which of the following reactions are spontaneous. (a) \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) (b) \(\mathrm{NaCl}(s) \longrightarrow \mathrm{NaCl}(l)\) at \(25^{\circ} \mathrm{C}\) (c) \(2 \mathrm{NaCl}(s) \longrightarrow 2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g)\) (d) \(\mathrm{CO}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{O}_{2}(g)\)

Two possible ways of producing iron from iron ore are (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\frac{3}{2} \mathrm{C}(s) \longrightarrow 2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{CO}_{2}(g)\) (b) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) Which of these reactions proceeds spontaneously at the lower temperature?
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