3.1.10 Equilibrium Constant Kp

Build Kp from equilibrium partial pressures of gaseous species, with each pressure raised to its stoichiometric coefficient. Only gases appear in the expression.

For aA(g) + bB(g) ⇌ cC(g), Kp = p(C)^c/[p(A)^a p(B)^b]. Keep the equation as written because changing coefficients changes the corresponding form and numerical value of Kp.

Kp uses equilibrium partial pressures at a fixed temperature. If you are given amounts and total pressure, calculate equilibrium moles first, then mole fractions, then partial pressures.

Do not substitute total pressure where the expression needs a component pressure. Each p term belongs to one gas species in the equilibrium mixture.

For a gas mixture, xᵢ = nᵢ/n(total) and pᵢ = xᵢp(total). The component partial pressures should add back to the total pressure, which gives you a useful numerical check.

I usually write p(component) = mole fraction × total pressure on the page before substituting. It prevents the common slip of putting total pressure into every Kp term.

Write Kp from gaseous equilibrium species only. Use partial-pressure symbols; concentration brackets belong to Kc, and raise each partial pressure to the coefficient in the balanced equation.

Check state symbols before you include a species. Pure solids and liquids do not appear in a Kp expression.

For a quantitative Kp problem, use the reaction stoichiometry to find equilibrium moles, total the gas moles, convert to mole fractions and partial pressures, then substitute into Kp.

Keep that chain visible on paper. Jumping straight from moles to Kp is where total pressure or mole fraction is most often used in place of a partial pressure.

If you increase total pressure, first compare the gaseous mole numbers on the two sides. The equilibrium shifts towards the side with fewer moles of gas; if the gaseous mole totals are equal, pressure does not shift the position.

Temperature is different: raising T favours the endothermic direction. State the direction first, then translate it into the change in yield or composition the question asks about.

When a question asks what changes the numerical value of Kp, again it is temperature. Heating increases Kp when the forward reaction is endothermic and decreases it when the forward reaction is exothermic.

Changing total pressure can shift the equilibrium composition, but after re-equilibration the same Kp applies if the temperature has not changed.

A catalyst speeds both the forward and reverse reactions, so the system reaches equilibrium sooner. It does not alter equilibrium partial pressures or Kp at the same temperature.

Keep kinetics and equilibrium thermodynamics separate: “faster equilibrium” is a time statement, not a claim that the equilibrium contains more product.