For the following reaction $\mathrm{Fe}_{2} \mathrm{O}_{3(\mathrm{~s})}+3 \mathrm{CO}_{(\mathrm{g})}…
For the following reaction
$\mathrm{Fe}_{2} \mathrm{O}_{3(\mathrm{~s})}+3 \mathrm{CO}_{(\mathrm{g})} \longrightarrow 2 \mathrm{Fe}_{(\mathrm{s})}+3 \mathrm{CO}_{2(\mathrm{~g})} \Delta \mathrm{H}^{\circ}=-29 \cdot 8 \mathrm{~kJ}$
and $\Delta \mathrm{S}^{\circ}=15 \mathrm{JK}^{-1}$. What is the value of $\Delta \mathrm{S}_{\text {(total) }}$ at $298 \mathrm{~K}$ ?
29.8 J
$100 \cdot 0 \mathrm{~J}$
$298 \cdot 0 \mathrm{~J}$
$115 \cdot 0 \mathrm{~J}$
Solution
Since the reaction is exothermic, system loses heat to surrounding. Hence the entropy of the surrounding increases.
$\begin{aligned}
\quad \Delta \mathrm{H}_{\text {surr }} &=+29.8 \mathrm{~kJ}=29800 \mathrm{~J} \\
\therefore \Delta \mathrm{S}_{\text {sur }} &=\frac{\Delta \mathrm{H}_{\text {sur }}}{\mathrm{T}}=\frac{29800}{298}=100 \mathrm{JK}^{-1} \\
\therefore \quad \Delta \mathrm{S}_{\text {Total }} &=\Delta \mathrm{S}_{\text {sys }}+\Delta \mathrm{S}_{\text {surr }}=15+100=115 \mathrm{JK}^{-1}
\end{aligned}$