Kp (equilibrium)
Kp is the equilibrium constant expressed in terms of the partial pressures of gaseous reactants and products, each raised to the power of their stoichiometric coefficients. It is used exclusively for reactions involving gases and is related to Kc through the ideal gas equation, with the conversion factor depending on the change in moles of gas in the reaction. Kp is particularly useful in industrial gas-phase reactions such as the Haber process and the Contact process.
Key Formula
Kp = Kc × (RT)^Δng
LaTeX: K_p = K_c (RT)^{\Delta n_g}
| Symbol | Meaning | Unit |
|---|---|---|
| Kp | Equilibrium constant in terms of partial pressures | dimensionless (or atm^Δng) |
| Kc | Equilibrium constant in terms of molar concentrations | dimensionless (or (mol/L)^Δng) |
| R | Ideal gas constant (0.08206 L·atm/mol·K) | L·atm/mol·K |
| T | Absolute temperature | K |
| Δng | Change in moles of gas = (moles gaseous products) − (moles gaseous reactants) | dimensionless |
Worked Example
Problem
For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), Kc = 0.500 at 400 °C. Calculate Kp at the same temperature.
Solution
Step 1 – Find Δng: Δng = moles gaseous products − moles gaseous reactants = 2 − (1 + 3) = 2 − 4 = −2. Step 2 – T = 400 + 273.15 = 673.15 K. Step 3 – RT = 0.08206 × 673.15 = 55.23 L·atm/mol. Step 4 – (RT)^Δng = (55.23)^(−2) = 1 ÷ (55.23)² = 1 ÷ 3050.4 = 3.278 × 10⁻⁴. Step 5 – Kp = Kc × (RT)^Δng = 0.500 × 3.278 × 10⁻⁴ = 1.639 × 10⁻⁴.
Answer
Kp = 1.64 × 10⁻⁴ atm⁻²
Kp vs Kc: Key Comparisons
| Feature | Kc | Kp | Notes |
|---|---|---|---|
| Variable used | Molar concentration [mol/L] | Partial pressure [atm or Pa] | Different units of measurement |
| Applies to | All phases (aq, g, heterogeneous) | Gases only | Kp undefined for pure solids/liquids |
| Relationship | Kp = Kc(RT)^Δng | Kc = Kp/(RT)^Δng | Linked via ideal gas law |
| Equal when | Δng = 0 | Δng = 0 | Equal moles of gas on both sides |
| Example (Δng=0) | H₂ + I₂ ⇌ 2HI | Kp = Kc | No conversion needed |
| Example (Δng≠0) | N₂ + 3H₂ ⇌ 2NH₃ | Kp ≠ Kc | Δng = −2, so Kp < Kc |
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Related Terms
Kc (equilibrium)
Kc is the equilibrium constant expressed in terms of molar concentrations (mol/L) of reactants and products at equilibrium. Each concentration is raised to the power of its stoichiometric coefficient, and pure solids and pure liquids are excluded from the expression because their concentrations are constant. Kc is temperature-dependent and is the most commonly used form of the equilibrium constant in solution-phase and heterogeneous equilibria.
Equilibrium Constant
The equilibrium constant (K) is a dimensionless number that expresses the ratio of the concentrations (or partial pressures) of products to reactants, each raised to the power of their stoichiometric coefficients, for a reversible reaction at equilibrium at a given temperature. A large K (K >> 1) indicates the equilibrium favours products, while a small K (K << 1) indicates reactants predominate. K changes with temperature but is independent of initial concentrations, catalysts, or pressure (for Kc).
Le Chatelier's Principle
Le Chatelier's Principle states that if an external stress is applied to a system at equilibrium, the system will shift in the direction that partially counteracts the applied stress and re-establishes equilibrium. Stresses include changes in concentration, pressure, volume, or temperature. This principle is fundamental to industrial process optimisation — for example, the Haber process for ammonia synthesis uses elevated pressure to favour product formation.
The subscript "p" in Kp stands for "pressure" (from Latin "pressura"), distinguishing it from Kc. The use of partial pressures in equilibrium expressions follows directly from van't Hoff's thermodynamic treatment of ideal gases in the 1880s.