Kp Calculator | Equilibrium Constant

Kc (equilibrium constant in concentration) uses molar concentrations (mol/L) for the equilibrium expression, while Kp (equilibrium constant in pressure) uses partial pressures (atm or bar). For the reaction aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / [A]^a[B]^b and Kp = (P_C)^c(P_D)^d / (P_A)^a(P_B)^b. Both measure the position of equilibrium but use different units.

The relationship is Kp = Kc(RT)^(Δn), where R = 0.082057 L·atm/(mol·K), T is temperature in Kelvin, and Δn = (moles gaseous products) - (moles gaseous reactants). If Δn = 0, then Kp = Kc. If Δn > 0 (more gas molecules on product side), Kp > Kc at typical temperatures. If Δn < 0, Kp < Kc.

Δn is the change in the number of moles of gas between products and reactants: Δn = Σ(n_gas, products) - Σ(n_gas, reactants). For example, in N₂ + 3H₂ ⇌ 2NH₃: Δn = 2 - (1 + 3) = -2. For N₂O₄ ⇌ 2NO₂: Δn = 2 - 1 = 1. This term accounts for the difference between concentration and pressure-based equilibrium expressions.

Both constants are used because different experimental conditions favor different measures. For reactions in solution, Kc is more practical. For gas-phase reactions at varying temperatures and pressures, Kp is more appropriate. Some problems specify which form to use, and converting between them is essential when given one form but needing the other for calculations.

When Δn = 0, the number of gas molecules is the same on both sides of the reaction. In this case, Kp = Kc because (RT)^0 = 1. Examples: H₂ + I₂ ⇌ 2HI (Δn = 0), N₂ + O₂ ⇌ 2NO (Δn = 0). For these reactions, you can use either constant interchangeably without conversion.

Both Kp and Kc change with temperature, but not by simple scaling. According to the van't Hoff equation, ln(K₂/K₁) = -ΔH°/R × (1/T₂ - 1/T₁). For endothermic reactions (ΔH° > 0), increasing temperature increases K. For exothermic reactions (ΔH° < 0), increasing temperature decreases K. The relationship between Kp and Kc also involves temperature through the RT term.