Browse Questions

$CO(g) + \frac{1}{2} O _2 \longrightarrow CO_2$, $\Delta H$ and $\Delta S$ for the reaction are -283 kJ and -87 $JK^{-1}$. It was intended to carry out this reaction at 1000, 1500, 3000 and 3500 K. At which of these temperatures would this reaction be thermodynamically spontaneous?

(a) 1500 and 3500 K
(b) 3000 and 3500 K
(c) 1000, 1500 and 3000 K
(d) 1500, 3000 and 3500 K

Answer: 1000, 1500 and 3000 K
For the reaction to be spontaneous : $\Delta G < 0$
$\Delta G = \Delta H - T\Delta S$
$\Delta G = -283 \times 10^3 J - T(-87 Jk^{-1})$
Since, $\Delta G < 0$
$\Longrightarrow-283 \times 10^3 J + T \times 87 Jk^{-1} < 0$
$\Longrightarrow T \times 87 Jk^{-1} < 283 \times 10^3 J$
$\Longrightarrow T < \frac{283 \times 10^3}{87} K$
$\Longrightarrow T< 3252.8 K$
$\therefore$ reaction is spontaneous at 1000, 1500 and 3000 K.