反應性1.4—熵與自發性（高級程度增修內容）：練習題

The standard molar entropies for the following species at 298 K are:
\(S^\ominus[\text{H}_2(g)] = 131\text{ J K}^{-1}\text{mol}^{-1}\)
\(S^\ominus[\text{O}_2(g)] = 205\text{ J K}^{-1}\text{mol}^{-1}\)
\(S^\ominus[\text{H}_2\text{O}(l)] = 70\text{ J K}^{-1}\text{mol}^{-1}\)
What is the standard entropy change, \(\Delta S^\ominus\), in \(\text{J K}^{-1}\text{mol}^{-1}\), for the reaction:
\(2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l)\)?

The standard Gibbs free energy of formation, \(\Delta G_f^{\circ}\), for \(CO_2(g)\) is \(-394\) \(kJ \cdot mol^{-1}\) and for \(CO(g)\) is \(-137\) \(kJ \cdot mol^{-1}\). Calculate \(\Delta G^{\circ}\) for the reaction:
\(2CO(g) + O_2(g) \rightarrow 2CO_2(g)\)

Consider the thermal decomposition of calcium carbonate:
\(\text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g)\)
Which statement correctly describes the entropy change, \(\Delta S\), for this reaction?

A reaction has an enthalpy change of \(\Delta H = -120\text{ kJ mol}^{-1}\) and an entropy change of \(\Delta S = -300\text{ J K}^{-1}\text{mol}^{-1}\). What is the Gibbs free energy change, \(\Delta G\), at 400 K?

The enthalpy of vaporization of a liquid is \(35.0\) \(kJ \cdot mol^{-1}\) and its boiling point is \(350\) K. What is the entropy change of vaporization, \(\Delta S_{vap}^{\circ}\), for this liquid at its boiling point?

A specific chemical reaction has an enthalpy change \( ΔHထ = +178 \, kJ \, mol^{-1} \) and an entropy change \( ΔSထ = +161 \, J \, K^{-1} \, mol^{-1} \). Determine the minimum temperature in Kelvin at which this reaction becomes spontaneous.

Predict the sign of the entropy change (ΔSထ) for the vaporization of bromine:
\( Br_2(l) \rightarrow Br_2(g) \)
Justify your answer by comparing the degrees of freedom and the distribution of microstates in the two physical states.

Calculate the standard entropy change (ΔSထ) for the reaction:
\( N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \)
Given the following standard entropy values:
\( Sထ(N_2) = 191.6 \, J \, K^{-1} \, mol^{-1} \)
\( Sထ(H_2) = 130.7 \, J \, K^{-1} \, mol^{-1} \)
\( Sထ(NH_3) = 192.5 \, J \, K^{-1} \, mol^{-1} \)

Consider the reaction: \(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\). At 298 K, \(\Delta H^{\ominus} = -92.2\text{ kJ}\) and \(\Delta S^{\ominus} = -198.7\text{ J K}^{-1}\).
(a) Calculate \(\Delta G^{\ominus}\) for this reaction at 298 K.
(b) Determine the temperature above which the reaction becomes non-spontaneous.
(c) In the Haber process, the reaction is performed at approximately 700 K. Discuss why this temperature is chosen by considering both the spontaneity of the reaction and the rate of reaction.

The decomposition of calcium carbonate is represented by the following equation:
\(CaCO_3(s) \rightarrow CaO(s) + CO_2(g)\)

The standard enthalpy change, \(\Delta H^{\circ}\), is \(+178.3\text{ kJ mol}^{-1}\) and the standard entropy change, \(\Delta S^{\circ}\), is \(+160.4\text{ J K}^{-1}\text{ mol}^{-1}\).

(a) Calculate the standard Gibbs free energy change (\(\Delta G^{\circ}\)) for this reaction at \(298\text{ K}\).
(b) Determine the temperature (in \(^{\circ}C\)) above which the reaction becomes spontaneous.
(c) Explain the sign of \(\Delta S^{\circ}\) by referring to the states of the reactants and products.