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Chapter 17: Problem 18

Calculate \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) : (a) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow\) $$ 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ See Appendix 2 for thermodynamic data.

Short Answer

Expert verified
The calculations would provide standard Gibbs free energy \(\Delta G^{\circ}\) for each of the given reactions. The actual numerical values cannot be provided without the thermodynamic data from Appendix 2. Please refer to the Appendix 2 to perform the above calculations for each reaction.

Step by step solution

01

Calculate \(\Delta H^{\circ}\)

The \(\Delta H^{\circ}\) for each reaction can be calculated using the given standard enthalpies of formation from Appendix 2. The \(\Delta H^{\circ}\) for a reaction is determined 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. Fo each given reaction, check the standard enthalpies of formation \(ΔH_f^°\) of the reactants and products from the data in Appendix 2. Then calculate \(\Delta H^{\circ}\) as following: \(\Delta H^{\circ} = \Sigma \Delta H_f^{\circ} \text{ (products)} - \Sigma \Delta H_f^{\circ} \text{ (reactants)}\)
02

Calculate \(\Delta S^{\circ}\)

Similarly, the \(\Delta S^{\circ}\) for each reaction can be calculated. The \(\Delta S^{\circ}\) for a reaction is determined by subtracting the sum of standard entropies of the reactants from the sum of standard entropies of the products. Fo each given reaction, check the standard entropies \(S^°\) of the reactants and products from the data in Appendix 2. Then calculate \(\Delta S^{\circ}\) as following: \(\Delta S^{\circ} = \Sigma S^{\circ} \text{ (products)} - \Sigma S^{\circ} \text{ (reactants)}\)
03

Calculate \(\Delta G^{\circ}\)

Once \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are calculated for each reaction, use these values to calculate \(\Delta G^{\circ}\) using the formula \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\). Here, \(T\) is the absolute temperature and in this case, it is 25°C, which is equal to 298.15 K. Note, the temperature value must be converted to Kelvin (K) before performing the calculation because the SI unit for temperature in thermodynamics is K. Therefore, for each reaction: \(\Delta G^{\circ} = \Delta H^{\circ} - 298.15 \Delta S^{\circ}\)

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Most popular questions from this chapter

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) dissolves spontaneously and endothermically in water. What can you deduce about the sign of \(\Delta S\) for the solution process?

State the second law of thermodynamics in words and express it mathematically.

Explain the difference between \(\Delta G\) and \(\Delta G^{\circ} .\)

As an approximation, we can assume that proteins exist either in the native (or physiologically functioning) state and the denatured state: $$ \text { native } \rightleftharpoons \text { denatured } $$ The standard molar enthalpy and entropy of the denaturation of a certain protein are \(512 \mathrm{~kJ} / \mathrm{mol}\) and \(1.60 \mathrm{~kJ} / \mathrm{K} \cdot \mathrm{mol},\) respectively. Comment on the signs and magnitudes of these quantities, and calculate the temperature at which the process favors the denatured state.

In each of the following reactions, there is one species for which the standard entropy value is not listed in Appendix \(2 .\) Determine the \(S^{\circ}\) for that species. (a) The \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reaction \(\mathrm{Na}(s) \longrightarrow \mathrm{Na}(l)\) is \(48.64 \mathrm{~J} / \mathrm{K}\) mol. (b) The \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reaction \(2 \mathrm{~S}\) (monoclinic) \(+\) \(\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{S}_{2} \mathrm{Cl}_{2}(g)\) is \(43.4 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} .\) (c) The \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reaction \(\mathrm{FeCl}_{2}(s) \longrightarrow \mathrm{Fe}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q)\) is \(-118.3 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\)
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