Chemistry: The Molecular Science (5th Edition)

Published by Cengage Learning
ISBN 10: 1285199049
ISBN 13: 978-1-28519-904-7

Chapter 16 - Thermodynamics: Directionality of Chemical Reactions - Problem Solving Practice 16.5 - Page 712: a


-29.09 kJ/mol

Work Step by Step

$\Delta _{r}H^{\circ}=\Sigma n_{p}\Delta _{f}H^{\circ}(products)-\Sigma n_{r}\Delta _{f}H^{\circ}(reactants)$ $=[\Delta_{f}H^{\circ}(CH_{3}OH,l)]-[\Delta _{f}H^{\circ}(CO,g)+2\Delta _{f}H^{\circ}(H_{2},g)]$ $=(-238.66\,kJ/mol)-[(-110.525\,kJ/mol)+2(0)]$ $=-128.14\,kJ/mol$ $\Delta _{r}S^{\circ}=\Sigma n_{p}S^{\circ}(products)-\Sigma n_{r}S^{\circ}(reactants)$ $=[S^{\circ}(CH_{3}OH,l)]-[S^{\circ}(CO,g)+2S^{\circ}(H_{2},g)]$ $=(126.8\,JK^{-1}mol^{-1})-[(197.674\,JK^{-1}mol^{-1})+2(130.684\,JK^{-1}mol^{-1})]$ $=-332.2\,JK^{-1}mol^{-1}$ $\Delta _{r}G^{\circ}=\Delta _{r}H^{\circ}-T\Delta _{r}S^{\circ}$ $=(-128.14\,kJ/mol)-(298.15\,K)(-0.3322\,kJK^{-1}mol^{-1})$ $=-29.09\,kJ/mol$ $\Delta _{r}G^{\circ}$ is negative verifying that the reaction is product-favored.
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