What is the value of $\Delta \mathrm{S}_{(\text {total })}$ for following reaction at $300 \mathrm{~K}$…

What is the value of $\Delta \mathrm{S}_{(\text {total })}$ for following reaction at $300 \mathrm{~K}$ $\mathrm{Fe}_{2} \mathrm{O}_{3(\mathrm{~s})}+3 \mathrm{CO}_{(\mathrm{g})} \longrightarrow 2 \mathrm{Fe}_{(\mathrm{s})}+3 \mathrm{CO}_{2(\mathrm{~g})} \Delta \mathrm{H}^{\circ}=-25 \mathrm{~kJ}, \Delta \mathrm{S}^{\circ}=15 \mathrm{JK}^{-1}$
  1. $68 \cdot 2 \mathrm{JK}^{-1}$
  2. $98 \cdot 3 \mathrm{JK}^{-1}$
  3. $8 \cdot 32 \mathrm{JK}^{-1}$
  4. $-10 \cdot 0 \mathrm{JK}^{-1}$

Solution

The reaction the exothermic, $\begin{aligned} \therefore \Delta H_{\text {sur }} &=+25 \mathrm{~kJ}=25000 \mathrm{~J} \\ \therefore \Delta S_{\text {sur }} &=\frac{\Delta H_{\text {arr }}}{T}=\frac{25000 \mathrm{~J}}{300 \mathrm{~K}}=83.33 \mathrm{JK}^{-1} \\ \Delta S_{\text {ton } 1} &=\Delta S_{\text {sys }}+\Delta S_{\text {surr }} \\ &=15 \mathrm{JK}^{-1}+83.33 \mathrm{JK}^{-1} \\ \therefore \Delta S_{\text {tow }} &=98.33 \mathrm{~J} \mathrm{~K}^{-1} \end{aligned}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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