Chemistry - Chemical Equilibrium Question with Solution | TestHub

$$\begin{array}{c}\text{Van’t}\text{Hoff}\text{equation:}\text{(dln}{\text{K}}_{\text{P}}\text{)/dT}\text{=}\text{(}\Delta {\text{H)/RT}}^{\text{2}}\text{Integrating}\text{between}{\text{T}}_{\text{1}}\text{and}{\text{T}}_{\text{2}}\text{:}{\text{lnK}}_{\text{P2}}\\ {\text{/K}}_{\text{P1}}\text{=}\text{(}\Delta {\text{H)/R(1/T}}_{\text{1}}\text{-}{\text{1/T}}_{\text{2}}\text{)}\\ {\text{1/T}}_{\text{1}}\text{-}{\text{1/T}}_{\text{2}}\text{=}{\text{(T}}_{\text{2}}\text{-}{\text{T}}_{\text{1}}{\text{)/T}}_{\text{1}}{\text{T}}_{\text{2}}\\ {\text{logK}}_{\text{P2}}{\text{/K}}_{\text{P1}}\text{=}\text{(}\Delta {\text{H)/2.303R[(T}}_{\text{2}}\text{-}{\text{T}}_{\text{1}}{\text{)/T}}_{\text{1}}{\text{T}}_{\text{2}}\text{],}\text{so}\text{(b)}\text{is}\text{correct}\text{and}\text{(a)}\text{has}\text{the}\\ \text{wrong}\text{sign}\\ \text{The}\text{same}\text{derivation}\text{with}\Delta \text{U}\text{for}{\text{K}}_{\text{C}}\text{gives}\text{(c),}\text{so}\text{(d)}\text{is}\text{incorrect}\\ \text{The}\text{correct}\text{options}\text{are}\text{(b)}\text{and}\text{(c).}\end{array}$$