Answer
Reaction A:
$\Delta G = +1560 J/mol$
$\Delta G = positive$, so reaction is non spontaneous.
At $T > 77^{\circ}C$ $\Delta G < 0$, the reaction will be spontaneous.
Reaction B:
$\Delta G = - 31874 J/mol$
$\Delta G = negative$, so reaction is spontaneous.
Work Step by Step
For a spontaneous reaction ΔG should be negative, that is $\Delta G < 0$.
$\Delta G = \Delta H - T \Delta S$
Reaction A:
$\Delta H = 10.5 kJ/mol = 10500 J/mol$, $\Delta S = 30 J/K mol$,
$T = 25^{\circ}C = 298 K$
$\Delta G = 10500 J/mol – (298 K \times 30 J/K mol )$
$\Delta G = 10500 J/mol – 8940 J/mol = +1560 J/mol$
$\Delta G = positive$, so the reaction is non spontaneous.
If $\Delta G = 0$
$\Delta H = T \Delta S$
Then ,$ T = ΔH\div ΔS$
$T = (10500 J/mol) \div(30 J/K mol) = 350 K = 77^{\circ}C$
At 350 K or $77^{\circ}C$ $\Delta G = 0$
Then at $T > 77^{\circ}C$ $\Delta G < 0$, so the reaction will be spontaneous.
Reaction B:
$\Delta H = 1.8 kJ/mol = 1800 J/mol$, $\Delta S = -113 J/K mol$,
$ T = 25^{\circ}C = 298 K$
$\Delta G = 1800 J/mol – (298 K \times -113 J/K mol )$
$\Delta G = 1800 J/mol – 33674 J/mol = - 31874 J/mol$
$\Delta G = negative$, so the reaction is spontaneous.
