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Chapter 19: Problem 24

Use data from Appendix D to determine values of \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})\) (b) \(2 \mathrm{SO}_{3}(\mathrm{g}) \longrightarrow 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) (c) \(\mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{H}^{+}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

Short Answer

Expert verified
The solution involves converting temperature from Celsius to Kelvin, utilizing Appendix D to derive \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) values and substituting them in the given formula to calculate \(\Delta G^{\circ}\). As we don't have Appendix D's data to get exact figures; the answer may vary.

Step by step solution

01

Convert temperature to Kelvin

Given the temperature is \(25^{\circ}\) Celsius, we need to convert it to Kelvin for the calculations: T = \(25 + 273.15 = 298.15 K\)
02

Determine \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each reaction

For each reaction, we need to determine the standard enthalpy change (\(\Delta H^{\circ}\)) and the standard entropy change (\(\Delta S^{\circ}\)) using the tables in Appendix D. Remember that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for a reaction can be found by subtracting the sum of the \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) values of the reactants from those of the products.
03

Calculate \(\Delta G^{\circ}\) for each reaction

Use the determined values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) to calculate \(\Delta G^{\circ}\) by substituting them into the formula \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\). Once the calculations are performed correctly for all four reactions, values of \(\Delta G^{\circ}\) for each reaction are obtained.

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Most popular questions from this chapter

Titanium is obtained by the reduction of \(\mathrm{TiCl}_{4}(1)\) which in turn is produced from the mineral rutile \(\left(\mathrm{TiO}_{2}\right)\) (a) With data from Appendix D, determine \(\Delta G^{\circ}\) at 298 K for this reaction. $$\mathrm{TiO}_{2}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{TiCl}_{4}(1)+\mathrm{O}_{2}(\mathrm{g})$$ (b) Show that the conversion of \(\mathrm{TiO}_{2}(\mathrm{s})\) to \(\mathrm{TiCl}_{4}(1)\) with reactants and products in their standard states, is spontaneous at \(298 \mathrm{K}\) if the reaction in (a) is coupled with the reaction $$2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})$$

For the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) \(K_{\mathrm{c}}=2.8 \times 10^{2}\) at \(1000 \mathrm{K}\) (a) What is \(\Delta G^{\circ}\) at \(1000 \mathrm{K} ?\left[\text { Hint: What is } \mathrm{K}_{\mathrm{p}} ?\right]\) (b) If \(0.40 \mathrm{mol} \mathrm{SO}_{2}, 0.18 \mathrm{mol} \mathrm{O}_{2},\) and \(0.72 \mathrm{mol} \mathrm{SO}_{3}\) are mixed in a 2.50 L flask at \(1000 \mathrm{K}\), in what direction will a net reaction occur?

Explain briefly why (a) the change in entropy in a system is not always a suitable criterion for spontaneous change; (b) \(\Delta G^{\circ}\) is so important in dealing with the question of spontaneous change, even though the conditions employed in a reaction are very often nonstandard.

At room temperature and normal atmospheric pressure, is the entropy of the universe positive, negative, or zero for the transition of carbon dioxide solid to liquid?

The following data are given for the two solid forms of \(\mathrm{HgI}_{2}\) at \(298 \mathrm{K}\). $$\begin{array}{llll} \hline & \Delta H_{f}^{\circ} & \Delta G_{f,}^{\circ} & S^{\circ} \\ & \text { kJ mol }^{-1} & \text {kJ mol }^{-1} & \text {J mol }^{-1} \text {K }^{-1} \\ \hline \mathrm{HgI}_{2} \text { (red) } & -105.4 & -101.7 & 180 \\ \mathrm{Hg} \mathrm{I}_{2} \text { (yellow) } & -102.9 & (?) & (?) \\ \hline \end{array}$$ Estimate values for the two missing entries. To do this, assume that for the transition \(\mathrm{HgI}_{2}(\mathrm{red}) \longrightarrow\) \(\mathrm{HgI}_{2}(\text { yellow }),\) the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) at \(25^{\circ} \mathrm{C}\) have the same values that they do at the equilibrium temperature of \(127^{\circ} \mathrm{C}\).
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