Chemistry: A Molecular Approach (3rd Edition)

Published by Prentice Hall
ISBN 10: 0321809246
ISBN 13: 978-0-32180-924-7

Chapter 17 - Sections 17.1-17.9 - Exercises - Problems by Topic - Page 853: 34c

Answer

$\Delta S_{sys}$ is negative. $\Delta S_{surr}$ is positive. The reaction is spontaneous at low temperatures.

Work Step by Step

The number of moles of gas decreases from 3 to 2 and therefore entropy of the system decreases. $\Delta S _{sys}$ is negative. Given that $\Delta H^{\circ}_{rxn}=-483.6\,kJ$, we have $\Delta S_{surr}=\frac{-\Delta H_{sys}}{T}\gt0$ If the reaction is spontaneous, $\Delta G\lt0$ $\implies \Delta H_{sys}-T\Delta S_{sys}\lt0$ Since both $\Delta H_{sys}$ and $\Delta S_{sys}$ are negative, $T$ should be small for $\Delta G$ to be negative.
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