The values of $\Delta H$ and $\Delta S$ for the reaction, $\mathrm{C}_{\text {(graphite)…

The values of $\Delta H$ and $\Delta S$ for the reaction, $\mathrm{C}_{\text {(graphite) }}+\mathrm{CO}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}(\mathrm{g})$ are $170 \mathrm{~kJ}$ and $170 \mathrm{JK}^{-1}$, respectively. This reaction will be spontaneous at
  1. $710 \mathrm{~K}$
  2. $910 \mathrm{~K}$
  3. $1110 \mathrm{~K}$
  4. $510 \mathrm{~K}$

Solution

Key Idea For spontaneous process, $\Delta \mathrm{G} < 0$ $\begin{aligned} & \Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S} \\ & \text { Given, } \Delta \mathrm{H}=170 \mathrm{~kJ}=170 \times 10^3 \mathrm{~J} \\ & \Delta \mathrm{S}=170 \mathrm{JK}^{-1} \\ & \mathrm{~T}=\text { ? } \\ & \Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S} \\ & 0 < 170 \times 10^3-\mathrm{T} \times 170 \\ & \mathrm{~T} > 1000 \\ & \therefore \quad \mathrm{T}=1110 \mathrm{~K} \\ & \end{aligned}$

Asked in: NEET 2009 (Screening)

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