Kp Calculator
Enter Kc (or Kp), the change in moles of gas, and temperature to convert between pressure-based and concentration-based equilibrium constants.
🌡️ What is Kp?
Kp is the equilibrium constant for a gas-phase reaction expressed in terms of partial pressures rather than molar concentrations. It measures exactly the same underlying chemical equilibrium as Kc, just using a different, equally valid set of units, pressures in atmospheres instead of concentrations in moles per liter.
Kp shows up throughout gas-phase equilibrium chemistry: industrial processes like the Haber-Bosch ammonia synthesis and the Contact process for sulfuric acid are routinely analyzed and optimized using Kp, since pressure is usually the variable engineers control directly. Atmospheric and combustion chemistry also favor Kp, since pressure is the naturally measured quantity in those systems. Textbook problems frequently give data in one form and ask for the other, making Kp-to-Kc conversion one of the most common calculation types in an equilibrium chapter.
A common point of confusion is forgetting that the conversion factor, (RT) raised to the power of delta n, depends on both temperature and the specific reaction's stoichiometry (through delta n), not on any universal constant. Two different reactions at the same temperature can have completely different Kp-to-Kc ratios, and the same reaction at two different temperatures also converts differently.
This calculator handles both conversion directions, Kc to Kp and Kp to Kc, and shows a chart of how the converted value shifts as temperature changes, making the temperature dependence of the relationship, not just the equilibrium itself, visible at a glance.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — PCl5 decomposition, Kc to Kp
PCl5(g) ⇌ PCl3(g) + Cl2(g), Δn = 2 − 1 = 1. Kc = 0.045 at T = 500 K.
Example 2 — N2O4/NO2 equilibrium, Kp to Kc
N2O4(g) ⇌ 2NO2(g), Δn = 2 − 1 = 1. Kp = 0.5 at T = 298 K.
Example 3 — H2 + I2 equilibrium, Δn = 0
H2(g) + I2(g) ⇌ 2HI(g), Δn = 2 − (1+1) = 0. Kc = 54.3 at T = 698 K.
❓ Frequently Asked Questions
🔗 Related Calculators
What is the difference between Kp and Kc?
Kc is the equilibrium constant expressed using molar concentrations of each species, mol/L. Kp is the equilibrium constant expressed using partial pressures of gaseous species, typically in atmospheres. Both describe the same equilibrium, just measured with different quantities, and they are related through the ideal gas law.
What is the formula relating Kp and Kc?
Kp = Kc times (RT) raised to the power of delta n, where R is the gas constant (0.082057 L atm per mol K), T is the absolute temperature in Kelvin, and delta n is the change in moles of gas, moles of gaseous products minus moles of gaseous reactants, in the balanced equation.
How do I calculate delta n for the Kp formula?
Delta n equals the total stoichiometric coefficients of gaseous products minus the total stoichiometric coefficients of gaseous reactants, counting only species labeled (g). For example, in N2(g) + 3H2(g) rightleftharpoons 2NH3(g), delta n = 2 minus (1+3) = -2. Solids, liquids, and aqueous species are never counted.
When are Kp and Kc equal to each other?
Kp equals Kc exactly whenever delta n = 0, meaning the reaction has the same number of moles of gas on both sides. In that special case, (RT) raised to the power of 0 equals 1 regardless of temperature, so the conversion factor disappears entirely and the two constants are numerically identical at any temperature.
Why does temperature matter in the Kp to Kc conversion?
Temperature enters the conversion formula directly through the (RT) term, so even at a fixed delta n, the numeric relationship between Kp and Kc shifts as temperature changes. This is separate from the fact that Kc and Kp themselves are also each individually temperature-dependent, since equilibrium position itself shifts with temperature per Le Chatelier's principle.
What value of the gas constant R does this calculator use?
This calculator uses R = 0.082057 L atm per mol K, the standard value for use with pressure in atmospheres, volume in liters, and temperature in Kelvin. Some textbooks round this to 0.0821, which can introduce a small rounding difference of well under 1% compared to this calculator's more precise value.
Can Kp or Kc be negative?
No, an equilibrium constant is always a positive number (or exactly zero only in the theoretical limiting case of a reaction that does not proceed at all). If a calculation produces a negative Kp or Kc, one of the input values was entered incorrectly, most likely a negative concentration or pressure was used somewhere upstream.
What units does Kp have?
Like Kc, Kp is formally unitless under the strict IUPAC definition, which uses dimensionless activities. In practice, when Kp is computed directly from partial pressures in atmospheres (as this calculator does, consistent with its value of R), it is often informally reported with implied pressure units raised to the power of delta n.
How do I find delta n if I don't know which species are gases?
Check each species' physical state in the balanced equation, usually noted as (g) for gas, (l) for liquid, (s) for solid, or (aq) for aqueous (dissolved in water). Only species marked (g) count toward delta n, everything else is excluded from both the Kp/Kc conversion and from the equilibrium expression itself.
Why is my converted Kp value extremely small or extremely large?
This is expected behavior, not an error, whenever delta n has a large magnitude. Because Kp = Kc times (RT) raised to the delta n power, and RT is typically a two-digit number, even a modest delta n of 2 or 3 can multiply or divide Kc by a factor of several hundred to several thousand, producing a Kp value that looks very different in magnitude from Kc.