Chemistry - Chemical Equilibrium Question with Solution | TestHub

$$\begin{array}{c}{\text{Cl}}_{\text{2}}\text{is}\text{formed}\text{only}\text{by}\text{dissociation}\text{of}{\text{PCl}}_{\text{5}}\text{:}{\text{PCl}}_{\text{5}}\text{=}\text{1}\text{-}\text{0.004}\text{=}\text{0.996}\text{mol,}{\text{PCl}}_{\text{3}}\\ \text{=}\text{1.004}\text{mol,}{\text{Cl}}_{\text{2}}\text{=}\text{0.004}\text{mol}{\text{K}}_{\text{C}}\text{=}{\text{[PCl}}_{\text{3}}{\text{][Cl}}_{\text{2}}{\text{]/[PCl}}_{\text{5}}\text{]}\text{=}\\ \text{(1.004/10)(0.004/10)/(0.996/10)}\\ {\text{K}}_{\text{C}}\text{=}\text{4.03}\times {\text{10}}^{\text{-4}}\approx \text{0.0004}\text{M,}\text{so}\text{(a)}\text{is}\text{correct}\\ \text{For}\text{the}\text{reverse}\text{reaction}{\text{K}}_{\text{P}}\text{=}{\text{1/[K}}_{\text{C}}\text{(RT)]}\text{=}\text{1/[0.0004}\times \text{0.082}\times \text{400],}\text{not}\text{0.0004}\\ \times \text{(0.082}\times \text{400),}\text{so}\text{(b)}\text{is}\text{wrong}\\ \Delta \text{G}\text{=}\text{0}\text{at}\text{every}\text{equilibrium,}\text{old}\text{or}\text{new,}\text{so}\text{(c)}\text{is}\text{wrong}\\ \text{Doubling}{\text{PCl}}_{\text{3}}\text{and}\text{halving}{\text{Cl}}_{\text{2}}\text{leaves}\text{the}\text{product}{\text{[PCl}}_{\text{3}}{\text{][Cl}}_{\text{2}}\text{]}\text{unchanged}\\ \text{So}\text{Q}\text{=}{\text{K}}_{\text{C}}\text{still}\text{and}\text{the}\text{system}\text{stays}\text{at}\text{equilibrium,}\text{and}{\text{P}}_{\text{PCl5}}\text{is}\text{unchanged,}\text{so}\\ \text{(d)}\text{is}\text{correct}\\ \text{The}\text{correct}\text{statements}\text{are}\text{(a)}\text{and}\text{(d).}\end{array}$$