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The values of $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ for the reaction, $\mathrm{C}$ (graphite) $+\mathrm{CO}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}(\mathrm{g})$ are $170 \mathrm{~kJ}$ and $170 \mathrm{JK}^{-1}$ respectively. This reaction will be spontaneous at -
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Verified Answer
The correct answer is:
$1110 \mathrm{~K}$
For a spontaneous reaction
$$
\Delta \mathrm{G}=-\mathrm{ve}
$$
Or ar eq. $\Delta \mathrm{G}=0$
$$
\begin{aligned}
\Delta \mathrm{H} & =\mathrm{T} \Delta \mathrm{S} \\
\mathrm{T} & =\frac{\Delta \mathrm{H}}{\Delta \mathrm{S}} \\
& =\frac{170 \times 10^3}{170} \\
& =1000 \mathrm{~K}
\end{aligned}
$$
$$
\Delta \mathrm{G}=-\mathrm{ve}
$$
Or ar eq. $\Delta \mathrm{G}=0$
$$
\begin{aligned}
\Delta \mathrm{H} & =\mathrm{T} \Delta \mathrm{S} \\
\mathrm{T} & =\frac{\Delta \mathrm{H}}{\Delta \mathrm{S}} \\
& =\frac{170 \times 10^3}{170} \\
& =1000 \mathrm{~K}
\end{aligned}
$$
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