Chapter 19: Problem 3
What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?
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Chapter 19: Problem 3
What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?
These are the key concepts you need to understand to accurately answer the question.
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For each pair of substances, choose the one that you expect to have the higher standard molar entropy \(\left(S^{\circ}\right)\) at \(25^{\circ} \mathrm{C} .\) Explain your choices. a. \(\mathrm{CO}(g) ; \mathrm{CO}_{2}(g)\) b. \(\mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)\) c. \(\operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)\) d. \(\mathrm{CH}_{4}(g) ; \mathrm{SiH}_{4}(g)\) e. \(\mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g)\) f. \(\operatorname{NaBr}(s) ; \operatorname{NaBr}(a q)\)
Given the values of \(\Delta H_{\mathrm{rxn}},\) and \(T,\) determine \(\Delta S_{\mathrm{rxn}},\) and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) b. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=855 \mathrm{~K}\) c. \(\Delta H_{\mathrm{rxn}}^{\circ}=+95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}\) d. \(\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+157 \mathrm{~J} / \mathrm{K} ; T=398 \mathrm{~K}\)
Determine \(\Delta G^{\circ}\) for the reaction: $$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)$$ Use the following reactions with known \(\Delta G_{\mathrm{rxn}}^{\circ}\) values: $2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$$$ \Delta G_{\mathrm{rxn}}^{\circ}=-742.2 \mathrm{~kJ} $$$\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)$$$\Delta G_{\mathrm{rxn}}^{\circ}=-257.2 \mathrm{~kJ}$$
Rank each set of substances in order of increasing standard molar entropy \(\left(S^{\circ}\right)\). Explain your reasoning. a. \(\mathrm{NH}_{3}(g) ; \operatorname{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \operatorname{He}(g)\) b. \(\mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(l) ; \mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)\)
Calculate the free energy change for this reaction at \(25^{\circ} \mathrm{C}\). Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) $$ \begin{array}{c} 2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-1269.8 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-364.6 \mathrm{~J} / \mathrm{K} \end{array} $$
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