The equation for the Kp is the multiplication of the products exponentiated by its stoichiometric coefficients divided by the same for the reactants.
In this case, we have a single product, NO₂ (g), with stoichiometry 2, and a single reactant, N₂O₄ (g), with stoichiometry 1. So, the equation for Kp, is:
[tex]K_p=\frac{(p_{NO_{2}})^2}{(p_{N_{2}O_{4}})^1}[/tex]Since we know that the equilibrium was reached where:
[tex]p_{NO_2}=3(p_{N_2O_4})^{\frac{1}{2}}[/tex]So, we can substitute that into the Kp equation to get:
[tex]K_p=\frac{(p_{NO_2})^2}{(p_{N_2O_4})^1}=\frac{(3(p_{N_2O_4})^{\frac{1}{2}}_{})^2}{p_{N_2O_4}^{}}=\frac{3^2(p_{N_2O_4})^{\frac{1}{2}\cdot2}}{p_{N_2O_4}^{}}=\frac{9p_{N_2O_4}}{p_{N_2O_4}}=9[/tex]So, the Kp for this temperature must be 9.
