Last updated: July 3, 2026
Kp Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Kp calculator converts Kc to the gas-pressure equilibrium constant using Kp = Kc × (RT)^Δn. Enter Kc, the change in gaseous moles from the balanced reaction, and temperature in kelvin. Δn = 0 makes Kp equal Kc; negative Δn divides by RT powers.
Kp equals Kc times R T raised to delta n, where delta n is gaseous product moles minus gaseous reactant moles and temperature is in kelvin.
Key Takeaways
- Kp converts equilibrium constants into gas partial-pressure form.
- Use Kp = Kc × (RT)^Δn with R = 0.082057 L·atm/(mol·K).
- Δn equals gaseous product coefficients minus gaseous reactant coefficients.
- Temperature must be entered in kelvin, not Celsius.
- Kp equals Kc when Δn is zero because the RT factor becomes one.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Kp = Kc × (R × T)^Δn
Where:
- Kp=Pressure equilibrium constant(dimensionless or pressure powers)
- Kc=Concentration equilibrium constant(dimensionless or concentration powers)
- R=Ideal gas constant(0.082057 L·atm/(mol·K))
- T=Absolute temperature(K)
- Δn=Moles of gaseous products minus moles of gaseous reactants(dimensionless)
Worked Examples
No change in gas moles
When Δn is zero, the RT factor is raised to zero and equals one.
- 1Write the conversion: Kp = Kc × (RT)^Δn.
- 2Substitute values: Kp = 4 × (0.082057 × 298.15)^0.
- 3Any nonzero value to the zero power is 1, so Kp = 4 × 1 = 4.
One extra mole of gas products
A positive Δn multiplies Kc by one power of RT.
- 1Compute RT = 0.082057 × 300 = 24.617.
- 2Apply Δn = 1: Kp = 0.5 × 24.617^1.
- 3Multiply to get Kp = 12.3085, which rounds to 12.31.
Ammonia synthesis has Δn = −2
For N₂ + 3H₂ ⇌ 2NH₃, gaseous products minus reactants is 2 − 4 = −2.
- 1Compute RT = 0.082057 × 500 = 41.029.
- 2Apply Δn = −2: Kp = 100 × 41.029^-2.
- 3Square RT: 41.029² ≈ 1683.4, so Kp ≈ 100 ÷ 1683.4 = 0.0594.
Introduction
The Kp calculator converts a concentration equilibrium constant, Kc, into a pressure equilibrium constant, Kp, for gas-phase reactions. The conversion uses Kp = Kc × (RT)^Δn, where Δn is the net change in moles of gaseous species. Use it after finding Kc with the equilibrium constant calculator and when comparing gas pressures from the partial pressure calculator. The relationship follows the ideal-gas connection between concentration and pressure described in IUPAC terminology and standard equilibrium treatments.
What is Kp?
Kp is the equilibrium constant written in terms of gas partial pressures rather than molar concentrations. For a balanced gaseous reaction, each partial pressure term is raised to its stoichiometric coefficient, products are multiplied in the numerator, and reactants are multiplied in the denominator. Kp is most useful when equilibrium data are measured as pressures or when gases dominate the reaction mixture.
Kp uses gas partial pressures, commonly in atm or bar depending on convention.
Kc uses concentrations, commonly mol/L.
The two constants are equal only when Δn = 0 under the ideal-gas conversion.
Pure solids and pure liquids do not appear in either equilibrium expression.
Kp and Kc conversion formula
The conversion is Kp = Kc × (RT)^Δn. R is 0.082057 L·atm/(mol·K) in this calculator, T is absolute temperature in kelvin, and Δn equals the sum of gaseous product coefficients minus the sum of gaseous reactant coefficients. The exponent means Δn controls how strongly temperature and the gas constant scale the result.
Use kelvin, not Celsius. For example, 25 °C is 298.15 K.
How to find Δn
Balance the reaction first, then count only species that are gases. Add the coefficients of gaseous products and subtract the coefficients of gaseous reactants. For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), products have 2 moles of gas and reactants have 4, so Δn = 2 − 4 = −2. If a reaction includes aqueous ions, solids, or liquids, do not include them in Δn for this Kp-Kc gas conversion.
How to calculate Kp step by step
First, obtain Kc at the same temperature, often from measured equilibrium concentrations or from a table. Second, determine Δn from the balanced gas equation. Third, multiply R by T. Fourth, raise RT to Δn, remembering that a negative Δn means a reciprocal. Finally, multiply by Kc. If you need molar concentrations before calculating Kc, use the molarity calculator or concentration calculator.
Balance the equation.
Count gaseous products and reactants for Δn.
Convert temperature to kelvin.
Compute Kp = Kc × (RT)^Δn.
Interpreting the result
Like Kc, a large Kp indicates product-favored equilibrium in pressure terms, while a small Kp indicates reactant-favored equilibrium. Because the conversion contains RT, Kp and Kc can differ greatly when Δn is not zero. A positive Δn multiplies by powers of RT; a negative Δn divides by powers of RT. Thermodynamic equilibrium constants are formally based on activities, but Kp and Kc are practical classroom and laboratory forms for ideal or dilute systems.
Always pair a reported Kp with its temperature, because equilibrium constants are temperature-specific.
Quick Δn patterns
The table shows common gas-mole patterns and how the RT factor changes Kc.
| Gas reaction pattern | Δn | Conversion factor |
|---|---|---|
| A(g) ⇌ B(g) | 0 | Kp = Kc |
| A(g) ⇌ 2B(g) | +1 | Kp = Kc × RT |
| 2A(g) ⇌ B(g) | −1 | Kp = Kc / RT |
| N₂(g)+3H₂(g)⇌2NH₃(g) | −2 | Kp = Kc / (RT)² |
Assumptions and limitations
The formula comes from substituting the ideal gas law into concentration and pressure equilibrium expressions. It works best for ideal gases and introductory equilibrium calculations. At high pressure, low temperature, or strongly nonideal conditions, fugacity-based thermodynamic constants are more rigorous. For background data and terminology, consult the NIST Chemistry WebBook and the LibreTexts chemical equilibrium chapters.
Quick Reference Card
Kp Conversion — Quick Reference
Quick reference • Kp Calculator
Kp = Kc × (RT)^Δn; R = 0.082057 L·atm/(mol·K)Valid range: Kc ≥ 0, T > 0 K, and Δn can be negative, zero, or positive for gas equilibria.
Common Values
⚠ Watch Out
- •Convert Celsius to kelvin before calculating.
- •Count only gaseous species when finding Δn.
- •Use Kc measured or calculated at the same temperature as Kp.
- •The formula assumes ideal-gas behavior and may need fugacity corrections at high pressure.
- •Do not include pure solids, pure liquids, or solvents in Δn.
Pro Tips
- →Write gas states beside the balanced equation before counting Δn.
- →If Δn is negative, rewrite the factor as division by (RT)^|Δn| to avoid sign mistakes.
- →Report Kp with the temperature because equilibrium constants are temperature-specific.
- →Use enough significant figures for R and T before rounding the final Kp.
- →Compare Kp trends with partial pressures to check whether products or reactants are favored.
FAQs
What is the formula for Kp from Kc?
The conversion is Kp = Kc × (RT)^Δn, where R = 0.082057 L·atm/(mol·K), T is temperature in kelvin, and Δn is gaseous product moles minus gaseous reactant moles.
What does Δn mean in the Kp equation?
Δn is the sum of stoichiometric coefficients for gaseous products minus the sum for gaseous reactants. Count gases only; omit solids, liquids, and aqueous species.
When are Kp and Kc equal?
Kp and Kc are equal under this conversion when Δn = 0, because (RT)^0 = 1.
Can Δn be negative?
Yes. A negative Δn means fewer gas moles are present on the product side, so the RT term is in the denominator. For ammonia synthesis, Δn = −2.
Why must temperature be in kelvin?
The ideal gas relationship uses absolute temperature. Celsius values must be converted by adding 273.15 before applying Kp = Kc × (RT)^Δn.
Does this calculator work for non-gas reactions?
The Kp-Kc conversion is for gas-phase species. If no gases are involved, Kp is usually not the relevant form; use Kc or an activity-based equilibrium constant instead.