Chemistry - Chemical Equilibrium Question with Solution | TestHub

$$\begin{array}{c}\text{Take}\text{initial}\text{moles}\text{A}\text{=}\text{1,}\text{B}\text{=}\text{2,}\text{D}\text{=}\text{3}\text{in}\text{volume}\text{V}\text{(total}\text{6}\text{units)}\text{Total}\text{moles}\\ \text{at}\text{first}\text{equilibrium}\text{=}\text{(5/6)(6)}\text{=}\text{5,}\text{and}\text{each}\text{unit}\text{of}\text{extent}\text{lowers}\text{moles}\text{by}\text{2,}\\ \text{so}\text{extent}\text{=}\text{0.5}\\ \text{First}\text{equilibrium:}\text{A}\text{=}\text{0.5,}\text{B}\text{=}\text{1,}\text{C}\text{=}\text{0.5,}\text{D}\text{=}\text{3}\\ {\text{K}}_{\text{c}}\text{=}{\text{n}}_{\text{C}}{\text{V}}^{\text{2}}{\text{/(n}}_{\text{A}}{\text{n}}_{\text{B}}^{\text{2}}\text{)}\text{=}{\text{(0.5)V}}^{\text{2}}{\text{/[(0.5)(1)}}^{\text{2}}\text{]}\text{=}{\text{V}}^{\text{2}}\\ \text{Let}\text{the}\text{total}\text{extent}\text{of}\text{the}\text{first}\text{reaction}\text{be}\text{u}\text{and}\text{that}\text{of}\text{the}\text{second}\text{be}\text{y}\\ {\text{n}}_{\text{A}}\text{=}\text{1}\text{-}\text{u,}{\text{n}}_{\text{B}}\text{=}\text{2}\text{-}\text{2u,}{\text{n}}_{\text{C}}\text{=}\text{u}\text{-}\text{2y,}{\text{n}}_{\text{D}}\text{=}\text{3}\text{-}\text{y,}{\text{n}}_{\text{F}}\text{=}\text{2y}\\ \text{Total}\text{moles}\text{=}\text{6}\text{-}\text{2u}\text{-}\text{y}\\ \text{At}\text{volume}\text{V/2:}{\text{K}}_{\text{c}}\text{=}{\text{n}}_{\text{C}}{\text{(V/2)}}^{\text{2}}{\text{/(n}}_{\text{A}}{\text{n}}_{\text{B}}^{\text{2}}\text{)}\text{=}{\text{V}}^{\text{2}}\text{,}\text{so}{\text{n}}_{\text{C}}{\text{/(n}}_{\text{A}}{\text{n}}_{\text{B}}^{\text{2}}\text{)}\text{=}\text{4}\\ \text{With}{\text{n}}_{\text{A}}\text{=}{\text{n}}_{\text{C}}\text{:}{\text{n}}_{\text{B}}^{\text{2}}\text{=}\text{1/4,}\text{so}\text{2}\text{-}\text{2u}\text{=}\text{0.5}\text{and}\text{u}\text{=}\text{0.75}\\ \text{1}\text{-}\text{u}\text{=}\text{u}\text{-}\text{2y}\text{gives}\text{0.25}\text{=}\text{0.75}\text{-}\text{2y,}\text{so}\text{y}\text{=}\text{0.25}\\ \text{Total}\text{moles}\text{at}\text{second}\text{equilibrium}\text{=}\text{6}\text{-}\text{1.5}\text{-}\text{0.25}\text{=}\text{4.25}\\ \text{Pressure}\text{ratio}\text{=}\text{(4.25/(V/2))/(5/V)}\text{=}\text{8.5/5}\text{=}\text{1.7}\\ \text{1.7}\text{=}\text{x/100,}\text{so}\text{x}\text{=}\text{170,}\text{written}\text{as}\text{0170}\end{array}$$