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

Δ H ∘ − T Δ S ∘ = + R T ln ⁡ K p ∘

Δ H ∘ − T Δ S ∘ = + R T ln ⁡ K p ∘

Δ H − T Δ S ∘ = − R T ln ⁡ K p

Δ H ∘ − T Δ S ∘ = + R T ln ⁡ K p ∘

Δ H ∘ = − R T ln ⁡ K p ∘

Δ H ∘ + T Δ S ∘ = − R T ln ⁡ K p

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The equilibrium constant of the reaction $A (g) ⇌ B (g) + C (g)$ is related to its ${ΔH}^{\circ}$ and ${ΔS}^{\circ}$ at temperature T by the expression

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$\begin{aligned} Δ H - T Δ S^{\circ} = - R T \ln K_{p} \end{aligned}$

$\begin{aligned} Δ H^{\circ} - T Δ S^{\circ} = + R T \ln K_{p}^{\circ} \end{aligned}$

$\begin{aligned} Δ H^{\circ} = - R T \ln K_{p}^{\circ} \end{aligned}$

$\begin{aligned} Δ H^{\circ} + T Δ S^{\circ} = - R T \ln K_{p} \end{aligned}$

answer is B.

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For a reaction at equilibrium ${ΔG}^{\circ} = - RTln K_{p}$ where

${ΔG}^{\circ} = {ΔH}^{\circ} - {TΔS}^{\circ} ∆ H - T ∆ S ° = - {RTlnK}_{p}$

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