Which set of thermodynamic conditions indicates that a reaction is favourable and spontaneous?

$T\Delta S > \Delta H$, $\Delta H = +\text{ve}$, $\Delta S = +\text{ve}$
$T\Delta S > \Delta H$, $\Delta H = +\text{ve}$, $\Delta S = -\text{ve}$
$T\Delta S = \Delta H$, $\Delta H = -\text{ve}$, $\Delta S = +\text{ve}$
$T\Delta S = \Delta H$, $\Delta H = -\text{ve}$, $\Delta S = -\text{ve}$

Correct answer: $T\Delta S = \Delta H$, $\Delta H = -\text{ve}$, $\Delta S = +\text{ve}$

Solution

A reaction is spontaneous when $\Delta G=\Delta H-T\Delta S<0$. The combination $\Delta H<0$ and $\Delta S>0$ makes $\Delta G$ negative for any temperature, so it is the strongest condition for spontaneity among the options.

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