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Chapter 19: Problem 59

Using data from Appendix \(\mathrm{C}\), calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at $298 \mathrm{~K}$ under standard conditions. (a) \(2 \mathrm{Zn}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)\) (b) \(2 \mathrm{NaBr}(s) \longrightarrow 2 \mathrm{Na}(g)+\mathrm{Br}_{2}(g)\) (c) $\mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)+\mathrm{H}_{2}(g)$

Short Answer

Expert verified
For the given reactions, we calculated the Gibbs free energy changes (ΔG°) as follows: (a) ΔG° = -665.9 kJ/mol, reaction is spontaneous. (b) ΔG° = 483.4 kJ/mol, reaction is not spontaneous. (c) ΔG° = 36.12 kJ/mol, reaction is not spontaneous. Only reaction (a) is spontaneous at 298 K under standard conditions.

Step by step solution

01

Calculate ΔH° for each reaction

Calculate the enthalpy change (ΔH°) for each reaction by subtracting the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products. Use the values from Appendix C. (a) ΔH° = [2 × (-348.0)] - [2 × 0 + 0] = -696.0 kJ/mol (b) ΔH° = [2 × 0 + 0] - [2 × (-362.1)] = 724.2 kJ/mol (c) ΔH° = [(-234.8) + 0] - [(-200.7) + (-50.45)] = 16.35 kJ/mol
02

Calculate ΔS° for each reaction

Calculate the entropy change (ΔS°) for each reaction by subtracting the sum of the standard entropies of the reactants from the sum of the standard entropies of the products. Use the values from Appendix C. (a) ΔS° = [2 × (43.6)] - [2 × (41.6) + 205.1] = 187.2 - 288.3 = -101.1 J/mol·K (b) ΔS° = [2 × (154.3) + 245.5] - [2 × (102.8)] = 808.1 J/mol·K (c) ΔS° = [(65.63) + 130.7] - [(188.8) + (74.87)] = -66.34 J/mol·K
03

Calculate ΔG° for each reaction

Calculate the Gibbs free energy change (ΔG°) for each reaction using the relationship: ΔG° = ΔH° - TΔS°. We are given the temperature T = 298 K. (a) ΔG° = -696.0 kJ/mol - 298 K × (-101.1 J/mol·K) / 1000 = -696.0 + 30.11 = -665.9 kJ/mol (b) ΔG° = 724.2 kJ/mol - 298 K × 808.1 J/mol·K / 1000 = 724.2 - 240.8 = 483.4 kJ/mol (c) ΔG° = 16.35 kJ/mol - 298 K × (-66.34 J/mol·K) / 1000 = 16.35 + 19.77 = 36.12 kJ/mol
04

Determine the spontaneity of the reactions

A reaction is spontaneous under the given conditions if ΔG° < 0. (a) ΔG° = -665.9 kJ/mol < 0, so the reaction is spontaneous. (b) ΔG° = 483.4 kJ/mol > 0, so the reaction is not spontaneous. (c) ΔG° = 36.12 kJ/mol > 0, so the reaction is not spontaneous. So, only reaction (a) is spontaneous at 298 K under standard conditions.

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Most popular questions from this chapter

In chemical kinetics, the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. Predict whether the entropy of activation for a bimolecular process is usually positive or negative.

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathbf{b})\) How much heat is produced in burning \(1 \mathrm{~mol}\) of $\mathrm{C}_{2} \mathrm{H}_{2}$ under standard conditions if both reactants and products are brought to \(298 \mathrm{~K} ?\) (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

The element sodium (Na) melts at \(97.8^{\circ} \mathrm{C},\) and its molar enthalpy of fusion is $\Delta H_{\text {fus }}=2.60 \mathrm{~kJ} / \mathrm{mol}$. (a) When molten sodium solidifies to \(\mathrm{Na}(\mathrm{s})\), is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when \(50.0 \mathrm{~g}\) of \(\mathrm{Na}(l)\) solidifies at \(97.8^{\circ} \mathrm{C}\).

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Using \(S^{\circ}\) values from Appendix \(\mathrm{C}\), calculate $\Delta S^{\circ}$ values for the following reactions. In each case, account for the sign of \(\Delta S\). (a) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{Cl}^{-}(a q)$ (b) $\mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$ (c) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ (d) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
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