Kp vs. Kc: Two Ways to Express Equilibrium
Reversible reactions reach a balance where forward and backward reactions proceed at equal rates. You can quantify this equilibrium position using either concentration-based or pressure-based equilibrium constants.
- Kc uses molar concentrations of all species present.
- Kp uses only the partial pressures of gaseous species.
For heterogeneous systems (those containing solids or liquids), Kp is often the better choice because pure solids and liquids do not contribute meaningfully to the equilibrium expression. Gases, by contrast, directly influence Kp through their partial pressures. The choice of which to use depends on your reaction medium and available data.
Converting Kc to Kp
The relationship between Kc and Kp hinges on temperature and the change in the number of moles of gas.
Kp = Kc × (R × T)^Δn
Kp— Equilibrium constant in terms of partial pressure (unitless)Kc— Equilibrium constant in terms of molar concentration (unitless)R— Universal gas constant (0.0821 L·atm/(K·mol), 8.314 J/(K·mol), or 0.08314 L·bar/(K·mol) depending on pressure units)T— Absolute temperature in KelvinΔn— Change in moles of gas: (moles of gaseous products) − (moles of gaseous reactants)
Calculating Kp from Partial Pressures
When partial pressures of all gaseous species are known, you can calculate Kp directly without needing Kc.
For a reaction:
a A(g) + b B(g) ⇌ c C(g) + d D(g)
The expression is:
Kp = (P_C^c × P_D^d) / (P_A^a × P_B^b)
where P denotes partial pressure and the exponents are stoichiometric coefficients. Remember: only gases appear in Kp. Solids, liquids, and pure solvents are omitted because their activities are defined as unity. In heterogeneous equilibria, this can dramatically simplify your calculation.
Common Pitfalls When Using Kp
Several mistakes commonly occur when working with pressure equilibria.
- Forgetting to exclude non-gaseous species — A frequent error is including solids or liquids in the Kp expression. For the reaction 2H₂(g) + O₂(g) ⇌ 2H₂O(l), water is a liquid and does not appear in Kp. Only include gases and aqueous ions if the reaction occurs in solution.
- Mixing pressure units without adjusting R — The gas constant R varies with pressure units: use 0.0821 L·atm/(K·mol) for atmospheres, 8.314 J/(K·mol) for SI units, or 0.08314 L·bar/(K·mol) for bars. Mismatching units will produce wildly incorrect results.
- Neglecting the Δn exponent — When converting Kc to Kp, the exponent (R × T)^Δn is crucial. If Δn is zero, Kp = Kc regardless of temperature. If Δn is negative (more moles of reactants than products), higher temperatures favour the reactants.
- Using Celsius instead of Kelvin for temperature — Temperature must always be in Kelvin. A reaction at 25°C is 298 K, not 25 K. This error propagates through the (R × T)^Δn term and skews results by orders of magnitude.
Practical Applications and Interpretation
Kp values reveal whether a reaction is product-favoured or reactant-favoured at a given temperature:
- Kp ≫ 1: Products dominate at equilibrium; the reaction proceeds far to the right.
- Kp ≪ 1: Reactants dominate; little product forms.
- Kp ≈ 1: Significant amounts of both reactants and products coexist.
Engineers designing industrial reactors use Kp to estimate conversion rates and decide on optimal pressure and temperature. Geochemists apply Kp to mineral equilibria in geological systems. In every case, understanding Kp allows prediction of the equilibrium composition without running the reaction.