The equilibrium constant of the reaction A(g)⇌B(g)+C(g) is related to its ΔH∘and ΔS∘ at temperature T  by the expression

# The equilibrium constant of the reaction $\mathrm{A}\left(\mathrm{g}\right)⇌\mathrm{B}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{g}\right)$ is related to its ${\mathrm{\Delta H}}^{\circ }$and ${\mathrm{\Delta S}}^{\circ }$ at temperature T  by the expression

1. A

$\begin{array}{r}\mathrm{\Delta }{H}^{\circ }-T\mathrm{\Delta }{S}^{\circ }=+RT\mathrm{ln}{K}_{p}^{\circ }\end{array}$

2. B

$\begin{array}{r}\mathrm{\Delta }H-T\mathrm{\Delta }{S}^{\circ }=-RT\mathrm{ln}{K}_{p}\end{array}$

3. C

$\begin{array}{r}\mathrm{\Delta }{H}^{\circ }=-RT\mathrm{ln}{K}_{p}^{\circ }\end{array}$

4. D

$\begin{array}{r}\mathrm{\Delta }{H}^{\circ }+T\mathrm{\Delta }{S}^{\circ }=-RT\mathrm{ln}{K}_{p}\end{array}$

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### Solution:

For a reaction at equilibrium ${\mathrm{\Delta G}}^{\circ }=-\mathrm{RTln}{\mathrm{K}}_{\mathrm{p}}$  where  