# How to calculate the relationship between the pressures of zinc, carbon monoxide, and carbon dioxide based on mole balance?

Zinc oxide is reduced at a constant temperature in a closed reactor using $$\ce{ZnO(s)}$$ and $$\ce{C(s)}$$ as the only starting materials. The following reactions are assumed to be at thermodynamic equilibrium. \begin{align} \ce{ZnO(s) + C(s) &-> Zn(g) + CO(g)}\\ \ce{2CO(g) &-> CO2(g) + C(s)} \end{align}

Assume ideal gas behaviour. Based on mole balance, the relationship applicable to the system at equilibrium is: \begin{align} \tag{A} P_{\ce{Zn}} &= P_{\ce{CO}} + 2P_{\ce{CO2}}\\ \tag{B} P_{\ce{Zn}} &= 2P_{\ce{CO}} + P_{\ce{CO2}}\\ \tag{C} P_{\ce{Zn}} &= P_{\ce{CO}} + P_{\ce{CO2}}\\ \tag{D} P_{\ce{Zn}} &= 0.5P_{\ce{CO}} + 2P_{\ce{CO2}} \end{align}

In this problem seeing that none of the given options consisted of $$\ce{C(s)}$$, so in order to get rid of that I just added the two equations and arrived at the equation $$\ce{ZnO(s) + CO(g) = Zn(g) + CO2(g)}.$$ Now just sort of comparing with the options I find that $$\ce{CO(g)}$$ and $$\ce{CO2(g)}$$ are on the opposite sides. It sort of gives me the intuition that may be the pressure term should have had a minus. Anyway I know that I have gone horribly wrong somewhere with regard to my concepts. Please tell me how to solve the problem henceforth.