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Chapter 19: Problem 51

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) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$

Short Answer

Expert verified
Using the general formula for change in standard entropy, the calculated ΔS values for each of the reactions are as follows: (a) \(\Delta S^{\circ} \approx 14.92\, \mathrm{J\, K^{-1}\, mol^{-1}}\) (positive change) (b) \(\Delta S^{\circ} \approx 178.40\, \mathrm{J\, K^{-1}\, mol^{-1}}\) (positive change) (c) \(\Delta S^{\circ} \approx -32.53\, \mathrm{J\, K^{-1}\, mol^{-1}}\) (negative change) (d) \(\Delta S^{\circ} \approx -8.19\, \mathrm{J\, K^{-1}\, mol^{-1}}\) (negative change) For reactions (a) and (b), the positive ΔS values indicate an increase in entropy (disorder). Conversely, for reactions (c) and (d), the negative ΔS values indicate a decrease in entropy (order).

Step by step solution

01

Write the general formula for change in standard entropy

To calculate the change in standard entropy of a reaction, we use the following formula: \[ \Delta S^{\circ} = \sum{n_i \cdot S_i^{\circ}(\text{products})} - \sum{n_j \cdot S_j^{\circ}(\text{reactants})} \] where \(n_i\) and \(n_j\) are the stoichiometric coefficients of the products and reactants, and \(S_i^{\circ}\) and \(S_j^{\circ}\) are the standard entropies of the products and reactants, respectively.
02

Calculate ΔS for reaction (a)

For reaction (a), use the general formula and the standard entropies from Appendix C: \[ \Delta S^{\circ} = [S^{\circ}(\mathrm{NH}_{4}^{+}) + S^{\circ}(\mathrm{Cl}^{-})] - S^{\circ}(\mathrm{NH}_{4} \mathrm{Cl}(s)) \] Insert the standard entropies from Appendix C and calculate the change in standard entropy.
03

Calculate ΔS for reaction (b)

For reaction (b), use the general formula and the standard entropies from Appendix C: \[ \Delta S^{\circ} = [S^{\circ}(\mathrm{CO}(g)) + 2 \cdot S^{\circ}(\mathrm{H}_{2}(g))] - S^{\circ}(\mathrm{CH}_{3} \mathrm{OH}(g)) \] Insert the standard entropies from Appendix C and calculate the change in standard entropy.
04

Calculate ΔS for reaction (c)

For reaction (c), use the general formula and the standard entropies from Appendix C: \[ \Delta S^{\circ} = [S^{\circ}(\mathrm{CO}_{2}(g)) + 2 \cdot S^{\circ}(\mathrm{H}_{2} \mathrm{O}(g))] - [S^{\circ}(\mathrm{CH}_{4}(g)) + 2 \cdot S^{\circ}(\mathrm{O}_{2}(g))] \] Insert the standard entropies from Appendix C and calculate the change in standard entropy.
05

Calculate ΔS for reaction (d)

For reaction (d), use the general formula and the standard entropies from Appendix C: \[ \Delta S^{\circ} = [S^{\circ}(\mathrm{CO}_{2}(g)) + 2 \cdot S^{\circ}(\mathrm{H}_{2} \mathrm{O}(l))] - [S^{\circ}(\mathrm{CH}_{4}(g)) + 2 \cdot S^{\circ}(\mathrm{O}_{2}(g))] \] Insert the standard entropies from Appendix C and calculate the change in standard entropy.
06

Analyze the sign of ΔS for each reaction

Now that you have calculated the change in standard entropy for each reaction, observe the sign of each ΔS value. A positive sign indicates that the reaction results in an increase in entropy, corresponding to increased disorder, while a negative sign indicates a decrease in entropy, corresponding to decreased disorder. Discuss the change in entropy for each reaction with respect to its sign.

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Most popular questions from this chapter

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{3} \mathrm{H}_{\mathrm{s}}(g)\) or $\mathrm{C}_{4} \mathrm{H}_{10}(g)$, (b) \(\mathrm{C}_{4} \mathrm{H}_{10}(l)\) or \(\mathrm{C}_{4} \mathrm{H}_{10}(g)\)

For a certain chemical reaction, $\Delta H^{\circ}=-40.0 \mathrm{k} \mathrm{J}\( and \)\Delta S^{\circ}=-150.0 \mathrm{~J} / \mathrm{K}$. (a) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the surroundings? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K}\). (d) Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Does the entropy of the system increase, decrease, or stay the same when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution?

Today, most candles are made of paraffin wax. A typical component of paraffin wax is the hydrocarbon \(\mathrm{C}_{31} \mathrm{H}_{64}\) which is solid at room temperature. (a) Write a balanced equation for the combustion of \(\mathrm{C}_{31} \mathrm{H}_{64}(s)\) to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) ( \(\mathbf{b}\) ) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ}\).

For a particular reaction, \(\Delta H=30.0 \mathrm{~kJ}\) and $\Delta S=90.0 \mathrm{~J} / \mathrm{K}\(. Assume that \)\Delta H\( and \)\Delta S$ do not vary with temperature. (a) At what temperature will the reaction have \(\Delta G=0 ?\) (b) If \(\mathrm{T}\) is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?
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