For a given reaction, if $\Delta H = 35.5 ext{ kJ/mol}$ and $\Delta S = 83.6 ext{ J/K}\cdot ext{mol}$, at

Question

For a given reaction, if $\Delta H = 35.5 	ext{ kJ/mol}$ and $\Delta S = 83.6 	ext{ J/K}\cdot	ext{mol}$, at what temperature is the reaction spontaneous? (Assume $\Delta H$ and $\Delta S$ remain constant with temperature.)

Accepted Answer

For a reaction to be spontaneous, the change in Gibbs free energy ($\Delta G$) must be negative ($\Delta G < 0$). We know that, $\Delta G = \Delta H - T\Delta S$ For $\Delta G < 0$, $\Delta H - T\Delta S < 0 \implies T > \frac{\Delta H}{\Delta S}$ Given: $\Delta H = 35.5 ext{ kJ/mol} = 35500 ext{ J/mol}$ $\Delta S = 83.6 ext{ J/K}\cdot ext{mol}$ Substituting the values: $T > \frac{35500}{83.6} ext{ K}$ $T > 424.64 ext{ K}$ Thus, the reaction is spontaneous at temperatures greater than $425 ext{ K}$ (i.e., $T > 425 ext{ K}$) .

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