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A plot of In \(\mathrm{k}\) against \(\frac{1}{\mathrm{~T}}\) (abscissa) is expected to be a straight line with intercept on ordinate axis equal to
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The correct answer is:
\(\frac{\Delta \mathrm{S}^{\circ}}{\mathrm{R}}\)
Hints: \(\Delta \mathrm{G}^{\circ}=-\mathrm{RT} \operatorname{InK}\)
or, \(\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}=-\mathrm{RT} \operatorname{InK}\)
or, \(\operatorname{InK}=\frac{-\Delta \mathrm{H}^{\circ}}{\mathrm{RT}}+\frac{\Delta \mathrm{S}^{\circ}}{\mathrm{R}}\) comparing with \(\mathrm{y}=\mathrm{m} \cdot \mathrm{x}+\mathrm{c}\)
\(\therefore \mathrm{y}\) intercept is \(\frac{\Delta \mathrm{S}^{\circ}}{\mathrm{R}}\)
or, \(\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{S}^{\circ}=-\mathrm{RT} \operatorname{InK}\)
or, \(\operatorname{InK}=\frac{-\Delta \mathrm{H}^{\circ}}{\mathrm{RT}}+\frac{\Delta \mathrm{S}^{\circ}}{\mathrm{R}}\) comparing with \(\mathrm{y}=\mathrm{m} \cdot \mathrm{x}+\mathrm{c}\)
\(\therefore \mathrm{y}\) intercept is \(\frac{\Delta \mathrm{S}^{\circ}}{\mathrm{R}}\)
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