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Problem 88

$\mathrm{H}_{2}$ reacts with the halogens $\left(…

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Problem 87

Ethene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ can be halogenated by the reaction:
$$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g)$$
where $\mathrm{X}_{2}$ can be $\mathrm{Cl}_{2}, \mathrm{Br}_{2},$ or $\mathrm{I}_{2} .$ Use the thermodynamic data given to calculate $\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ},$ and $K_{\mathrm{p}}$ for the halogenation reaction by each of the three halogens at $25^{\circ} \mathrm{C}$ . Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

Answer

CHLORINE: $\Delta H^{\circ}=-182.1 \mathrm{kJ}, \Delta S^{\circ}=-134.4 \mathrm{J} / \mathrm{K}, \Delta G^{\circ}=-142.0 \mathrm{kJ}$
and $K_{p}=7.94 \times 10^{24}$
BROMINE: $\Delta H^{\circ}=-45.0 \mathrm{kJ}, \Delta S^{\circ}=-134.2 \mathrm{J} / \mathrm{K}, \Delta G^{\circ}=-5.0 \mathrm{kJ},$ and
$K_{p}=7.5$
IODINE: $\Delta H^{\circ}=-48.3 \mathrm{kJ}, \Delta S^{\circ}=-132.2 \mathrm{J} / \mathrm{K}, \Delta G^{\circ}=-8.9 \mathrm{kJ},$ and
$K_{p}=37$
See explanation.


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