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AP EAMCET · Chemistry · Thermodynamics (C)

If the standard enthalpy change \(\left(\Delta_{\mathrm{r}} \mathrm{H}^\theta\right)\) for a certain reaction at \(298 \mathrm{~K}\) and constant pressure is \(-1860 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\), the standard entropy change \(\left(\Delta_{\text {sys }} \mathrm{s}^\theta\right)\) of the same reaction is \(-550 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\), which one of the following statements is correct?

  1. A \(\left(\Delta_{\text {sys }} S^\theta\right)+\Delta_{\text {surr }} S^\theta=-7692 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), the reaction is spontaneous
  2. B \(\left(\Delta_{\text {sys }} \mathrm{S}^\theta\right)+\Delta_{\text {surr }} \mathrm{S}^\theta=-5692 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), the reaction is non-spontaneous
  3. C \(\left(\Delta_{\text {sys }} \mathrm{S}^\theta\right)+\Delta_{\text {surr }} \mathrm{S}^\theta=+5692 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), the reaction is spontaneous
  4. D \(\left(\Delta_{\text {sys }} S^\theta\right)+\Delta_{\text {surr }} S^\theta=+7692 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), the reaction is non-spontaneous
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Correct Answer

(C) \(\left(\Delta_{\text {sys }} \mathrm{S}^\theta\right)+\Delta_{\text {surr }} \mathrm{S}^\theta=+5692 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\), the reaction is spontaneous

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\[ \begin{aligned} & \text { } \Delta \mathrm{G}^{\circ}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{s}^{\circ} \\ & =\left(-1860 \times 10^3\right)-298(-550) \\ & =-1696.1 \mathrm{~kJ} \mathrm{Mol}^{-1} \end{aligned} \] Thus, the reaction is Spontaneous as…
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