Calculate Kp: Equilibrium Constant Formula and Example

Kp is the equilibrium constant expressed using the partial pressures of gaseous reactants and products. To calculate it, enter each gas’s equilibrium partial pressure and its stoichiometric coefficient; the calculator returns Kp as a dimensionless value for the balanced reaction you specify.

Formula

For a general gaseous equilibrium, aA + bB ⇌ cC + dD, the equilibrium constant in terms of partial pressures is:

Kp = (pC^c × pD^d) / (pA^a × pB^b)

Here, pA, pB, pC, and pD are the equilibrium partial pressures of the gases, and a, b, c, and d are their coefficients in the balanced chemical equation. Pure solids and pure liquids are omitted. The calculator uses a simplified reaction with one product and one reactant: Kp = p_product^m / p_reactantⁿ. Enter pressures in the same unit; pressure ratios cancel, leaving Kp dimensionless when defined using standard-state-normalized pressures.

Worked Example

Using the calculator’s defaults, the simplified equilibrium has a product pressure of 2 bar, a reactant pressure of 1 bar, and coefficients m = 2 and n = 1:

1. Raise the product pressure to its coefficient: 2² = 4.
2. Raise the reactant pressure to its coefficient: 1¹ = 1.
3. Divide the product term by the reactant term: Kp = 4 / 1 = 4.

The calculator displays Kp = 4.0000. This is a simple arithmetic illustration, not a claim that these pressures describe a particular real reaction.

What Kp Means

Kp describes the equilibrium composition of a gaseous reaction using partial pressures. It is calculated from equilibrium values—not starting pressures or pressures measured while the reaction is still changing. A larger Kp generally corresponds to products being favored relative to reactants at equilibrium under the specified conditions; a smaller Kp generally corresponds to reactants being favored. The value alone does not tell how quickly equilibrium is reached.

For example, for N₂(g) + 3H₂(g) ⇌ 2NH₃(g), the expression is Kp = p_NH3² / (p_N2 × p_H2³). The coefficients become exponents. Do not include a pure solid or pure liquid in the expression, because its activity is treated as constant.

How to Calculate Kp Correctly

• Balance the chemical equation first. Changing coefficients changes the equilibrium-constant expression.
• Identify which substances are gases and omit pure solids and liquids.
• Use equilibrium partial pressures for every gas included. For a gas mixture, a component’s partial pressure can be obtained from its mole fraction multiplied by total pressure, when the mixture behaves ideally.
• Raise each pressure to the power given by its balanced-equation coefficient, multiply terms on each side, then divide the product-side terms by the reactant-side terms.
• Keep pressure units consistent. You may use bar, pascals, atmospheres, or another pressure unit, but use the same unit throughout a calculation.

For measurements in US customary units, pressure might be stated in pounds per square inch (psi); in metric contexts it is often given in pascals or bar. Convert all pressures to one common unit before substituting them. The result is independent of the chosen common unit when the total gas stoichiometric coefficients on each side are equal. More generally, a thermodynamic equilibrium constant is defined using dimensionless pressure ratios relative to a standard pressure; this avoids treating a dimensional pressure expression as a truly dimensionless constant.

Kp, Kc, and Reaction Changes

Kc is the corresponding equilibrium constant expressed using concentrations, commonly mol/L. For ideal gases, the relationship is Kp = Kc(RT)^Δn, where R is the gas constant in units consistent with the chosen pressure and concentration units, T is absolute temperature in kelvin, and Δn is the total stoichiometric coefficient of gaseous products minus that of gaseous reactants. Solids and liquids do not contribute to Δn.

If Δn = 0, Kp and Kc have the same numerical value under consistent conventions. If Δn is not zero, they generally differ. A temperature is needed to convert between them, so this calculator does not convert Kc to Kp. It calculates Kp directly from supplied equilibrium pressures.

Reversing a reaction makes the new equilibrium constant the reciprocal of the original. Multiplying every equation coefficient by a factor q raises the equilibrium constant to the power q. These are useful checks when comparing reported values, but they do not replace calculating from the exact balanced equation in question.

Common Mistakes and Limits

• Using starting values: Kp is evaluated with equilibrium partial pressures, not initial conditions.
• Using coefficients as multipliers: They are exponents in the expression, not factors multiplied by pressure.
• Including condensed substances: Pure solids and liquids are left out of the equilibrium expression.
• Mixing pressure units: Convert all entries to a shared unit first, especially when raising pressures to powers.
• Overinterpreting the result: Kp indicates equilibrium composition, not reaction speed or the time needed to reach equilibrium.

The calculator handles one product and one reactant; for a reaction with multiple gases on either side, multiply all corresponding pressure terms using their own exponents. In precise thermodynamics, gas activities or fugacities may be needed instead of raw partial pressures when gases are non-ideal. Equilibrium constants also depend on temperature, so a value should be associated with the temperature at which the equilibrium data apply. Rounding intermediate values can shift the final result, particularly when pressures are raised to large powers; retain available precision until the final step.

Frequently Asked Questions

What is the formula for Kp?
Kp is the product of equilibrium gas partial pressures, each raised to its balanced-equation coefficient, divided by the equivalent product for gaseous reactants. Omit pure solids and liquids.

Can Kp be less than 1?
Yes. A positive Kp below 1 generally indicates that reactants are favored in the equilibrium composition under the stated conditions. It does not mean the reaction cannot form products.

Do I need to enter temperature to calculate Kp?
Not if you already have the equilibrium partial pressures: substitute them directly into the expression. Temperature is needed for relationships such as converting Kc to Kp, and the equilibrium constant itself changes with temperature.

Does Kp have units?
Thermodynamic Kp is dimensionless because it is defined using pressure relative to a standard pressure. A raw pressure expression may appear to carry units when Δn is not zero; state the convention and units used when reporting such a calculation.

Why is my calculated Kp different from a reference value?
Check the balanced equation, temperature, equilibrium rather than initial pressures, pressure units, and whether the reference uses Kp, Kc, or a different standard-state convention. Reversing or rescaling the reaction also changes the reported constant.

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in a | Product partial pressure | bar | 2 | 0
in b | Reactant partial pressure | bar | 1 | 0
in m | Product coefficient | - | 2 | 0
in n | Reactant coefficient | - | 1 | 0
out kp | Kp | - | a^m / b^n | 4