Home›Calculators›Chemistry›Kp Calculator

Kp Calculator

Chemistry

Calculate the equilibrium constant Kp from partial pressures of reactants and products. Convert between Kc and Kp using the relationship Kp = Kc × (RT)^Δn.

0.5 atm
atm
2
0.2 atm
atm
1
298 K
K
1

Kp

1.25
Kc (from Kp)
0.051
log Kp
0.097

This calculator computes your Kp, Kc (from Kp), log Kp from the values you enter.

Inputs
Product Partial Pressure (atm)Product Stoichiometric CoefficientReactant Partial Pressure (atm)Reactant Stoichiometric CoefficientTemperatureΔn (moles gas: products − reactants)
Outputs
KpKc (from Kp)log Kp

What is a Kp?

The Kp Calculator computes the equilibrium constant in terms of partial pressures (Kp) from the equilibrium partial pressures and stoichiometric coefficients of one product species and one reactant species in a gas-phase reversible reaction. It also converts Kp to the concentration-based equilibrium constant Kc using the relationship Kp = Kc × (RT)^Δn, where Δn is the change in moles of gas and R = 0.08206 L·atm/(mol·K).

For reactions where all species are gases, equilibrium can be expressed equivalently in terms of concentrations (Kc) or partial pressures (Kp). The two forms are related through temperature and Δn — the change in total moles of gas from reactants to products. When Δn = 0 (equal moles of gas on both sides), Kp and Kc are numerically identical. When Δn is positive (more moles of gas produced), Kp > Kc; when negative (fewer moles of gas produced), Kp < Kc.

Partial pressures are measured directly in many high-pressure industrial reactions and gas-phase equilibrium experiments, making Kp the natural equilibrium expression for these systems. The Haber process (ammonia synthesis), the Contact process (sulfuric acid manufacture), and petroleum refining all involve gas-phase equilibria where Kp characterises the equilibrium composition under operating pressure conditions.

The Equilibrium Constant Calculator covers the concentration-based Kc; the Reaction Quotient Calculator evaluates Qc for non-equilibrium mixtures. Together with this Kp Calculator, they provide the complete set of gas-phase equilibrium tools.

How to use this Kp calculator

  1. Write the balanced equation for your gas-phase reaction. Count Δn = (total moles of gaseous product coefficients) − (total moles of gaseous reactant coefficients). Exclude pure solids and liquids.
  2. Measure or identify the equilibrium partial pressures of the product and reactant species in atm.
  3. Enter the product partial pressure in atm in the Product Partial Pressure field and its stoichiometric coefficient in Product Stoichiometric Coefficient.
  4. Enter the reactant partial pressure and coefficient in the corresponding fields.
  5. Enter the temperature in Kelvin in the Temperature field.
  6. Enter Δn in the Δn field. For N₂ + 3H₂ ⇌ 2NH₃, Δn = 2 − 4 = −2.
  7. Read Kp and Kc (from Kp). Use the Reaction Quotient Calculator with Kc to evaluate any non-equilibrium mixture for this reaction.

Formula & Methodology

Kp expression (single product, single reactant):

Kp = (P_product)^nP / (P_reactant)^nR

Kp to Kc conversion:

Kp = Kc × (RT)^Δn Kc = Kp / (RT)^Δn

Where: R = 0.08206 L·atm/(mol·K), T in Kelvin, Δn = Δ(moles of gas)

Worked example — decomposition of PCl₅:

Balanced equation: PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), Δn = (1 + 1) − 1 = +1, T = 523 K (250°C)

Equilibrium partial pressures measured: P(PCl₅) = 0.15 atm, P(PCl₃) = 0.35 atm, P(Cl₂) = 0.35 atm

Step 1 — Calculate Kp: Kp = (P_PCl₃ × P_Cl₂) / P_PCl₅    = (0.35 × 0.35) / 0.15    = 0.1225 / 0.15    = 0.817 atm    (or dimensionless if pressures normalised to 1 atm standard)  Step 2 — Convert to Kc: RT = 0.08206 × 523 = 42.92 L·atm/mol Kc = Kp / (RT)^Δn = 0.817 / (42.92)^1 = 0.0190 mol/L  log Kp = log(0.817) = −0.088

Kp = 0.817 (close to 1) indicates a moderate equilibrium — neither strongly product-favoured nor reactant-favoured. At 250°C, significant amounts of both PCl₅ and its dissociation products coexist at equilibrium, consistent with the known moderate thermal stability of PCl₅.

Frequently Asked Questions

Kp is the equilibrium constant expressed in terms of partial pressures of gaseous reactants and products, rather than molar concentrations. For a gas-phase reaction aA + bB ⇌ cC + dD, Kp = (P_C^c × P_D^d) / (P_A^a × P_B^b), where P_X is the partial pressure of species X at equilibrium (in atm or Pa). Kp is used when the reaction involves gases and the measurement of equilibrium partial pressures is more convenient than measuring concentrations directly.
Kp and Kc are related by Kp = Kc × (RT)^Δn, where R is 0.08206 L·atm/(mol·K), T is the absolute temperature in Kelvin, and Δn is the change in moles of gas (sum of gaseous product coefficients minus sum of gaseous reactant coefficients from the balanced equation). This calculator inverts this to give Kc = Kp / (RT)^Δn. When Δn = 0 (no change in moles of gas), Kp = Kc and partial pressures and concentrations give the same equilibrium constant value.
Δn is the change in total moles of gas in the reaction: Δn = (moles of gaseous products) − (moles of gaseous reactants). For N₂ + 3H₂ → 2NH₃, Δn = 2 − (1 + 3) = −2. For PCl₅ → PCl₃ + Cl₂, Δn = (1 + 1) − 1 = +1. Pure solids and liquids do not count toward Δn — only gas-phase species matter. When Δn is positive, Kp > Kc; when Δn is negative, Kp < Kc; when Δn = 0, Kp = Kc.
The partial pressure of a gas in a mixture is the pressure that gas would exert if it alone occupied the same volume at the same temperature. It equals the total pressure multiplied by the mole fraction of that gas: P_A = x_A × P_total. Partial pressures are measured using pressure transducers for the total pressure, combined with gas composition analysis (GC, mass spectrometry) to determine mole fractions. For ideal gases, PV = nRT, so partial pressure is proportional to concentration: P_A = [A] × RT.
Use Kp when your experimental data consists of partial pressures rather than concentrations — common in high-pressure gas-phase reactions (industrial synthesis, catalytic combustion, high-pressure kinetics). Use Kc when you measure concentrations directly (solution chemistry, analytical chemistry, biochemistry). For reactions in solution, Kp is not applicable. For reactions involving both gases and solutes, Kc is more practical. Either form is valid for gas-phase reactions as long as you apply the correct R value and conversion formula.
In the formal thermodynamic definition, Kp is dimensionless — partial pressures are divided by the standard pressure (1 atm or 10⁵ Pa) to make them dimensionless before taking ratios. In practice, when all pressures are in atm and the standard pressure is 1 atm, the numerical values are unchanged and Kp appears unitless. However, some older texts and problems quote Kp with units of atm^Δn. The calculator uses pressures in atm to match the standard R = 0.08206 L·atm/(mol·K) in the Kp–Kc conversion.
Enter the equilibrium partial pressure of the product in atm and its stoichiometric coefficient. Enter the equilibrium partial pressure of the reactant in atm and its coefficient. Enter the temperature in Kelvin and Δn (moles of gaseous products minus moles of gaseous reactants). The calculator returns Kp, the corresponding Kc, and log Kp.
For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), Kp at 25°C is approximately 6.0 × 10⁵ atm⁻² — large and product-favoured at room temperature. At 400–500°C (the industrial operating temperature), Kp drops to 10⁻⁴–10⁻³, making equilibrium less favourable. The industrial process operates at 150–300 atm to shift equilibrium toward ammonia (Le Chatelier) and uses an iron catalyst to achieve adequate reaction rates despite the lower temperature. Understanding Kp and Kc is central to designing this reaction, which produces the nitrogen fertilisers that feed approximately half the world's population, including India.
No — Kp (like Kc) is a constant at fixed temperature. Adding inert gas at constant volume does not change partial pressures of reactants or products, so Kp and equilibrium positions are unchanged. Increasing total pressure at constant volume by compressing the system does change partial pressures — if Δn ≠ 0, this shifts the equilibrium position (more product for Δn < 0), but Kp itself does not change. Only a temperature change alters Kp.
ΔG° = −RT ln(Kp) when Kp is expressed in terms of dimensionless activities (pressures in atm / standard pressure 1 atm). This is the same relationship as for Kc: ΔG° = −RT ln(Kc). Since Kp = Kc × (RT)^Δn, the ΔG° values from the two equilibrium constants differ by −RT × Δn × ln(RT), reflecting the choice of standard state. The [Gibbs Free Energy Calculator](/gibbs-free-energy-calculator/) computes ΔG° from Kc, and the relationships above let you inter-convert.