Chemistry - Chemical Equilibrium Question with Solution | TestHub

$$\begin{array}{c}{\text{K}}_{\text{P}}\text{=}{\text{P}}_{\text{A6}}{\text{/P}}_{\text{A2}}^{\text{3}}\text{=}{\text{0.2/P}}_{\text{A2}}^{\text{3}}\text{=}\text{1.6}{\text{P}}_{\text{A2}}^{\text{3}}\text{=}\text{0.125,}\text{so}{\text{P}}_{\text{A2}}\text{=}\text{0.5}\text{atm}\\ \text{Let}\text{the}\text{initial}\text{pressures}\text{(no}\text{reaction)}\text{be}{\text{A}}_{\text{2}}\text{=}\text{2p}\text{and}\text{C}\text{=}\text{p}\\ \text{Total}\text{moles}\text{of}\text{gas}\text{reduce}\text{only}\text{through}\text{reactions,}\text{so}\text{total}\text{pressure}\text{=}\text{0.5}\text{+}\text{0.2}\\ \text{+}{\text{P}}_{\text{C}}\text{+}{\text{P}}_{\text{A2C}}\\ {\text{P}}_{\text{C}}\text{+}{\text{P}}_{\text{A2C}}\text{=}\text{p}\text{(C}\text{is}\text{conserved}\text{between}\text{free}\text{C}\text{and}{\text{A}}_{\text{2}}\text{C)}\\ \text{0.7}\text{+}\text{p}\text{=}\text{1.4,}\text{so}\text{p}\text{=}\text{0.7}\text{atm}\\ {\text{A}}_{\text{2}}\text{balance:}\text{2(0.7)}\text{=}\text{0.5}\text{+}\text{3(0.2)}\text{+}{\text{P}}_{\text{A2C}}\text{,}\text{so}{\text{P}}_{\text{A2C}}\text{=}\text{0.3}\text{atm}\\ {\text{P}}_{\text{C}}\text{=}\text{0.7}\text{-}\text{0.3}\text{=}\text{0.4}\text{atm}\\ \text{x}\text{=}\text{0.3/[(0.5)(0.4)]}\text{=}\text{1.5}\\ \text{4x}\text{=}\text{6}\end{array}$$