What this calculator does
Kp and Kc describe the same equilibrium in different units, and converting between them needs only the change in moles of gas. Kp equals Kc multiplied by RT raised to the power of that change.
When the moles of gas are equal on both sides, the exponent is zero, the factor is exactly 1 and the two constants are identical. That is worth checking first, because it saves the calculation entirely for a great many reactions, including all those with no gases at all.
The formula
The conversion factor is RT raised to the power of delta n, where delta n is the moles of gaseous product minus the moles of gaseous reactant, read from the balanced equation. R is 0.0820574 L·atm/(mol·K) so that pressures come out in atmospheres. Only gases count toward delta n; solids and liquids are excluded.
| Term | Meaning |
|---|---|
| Kc | Equilibrium constant expressed in concentrations. |
| Kp | Equilibrium constant expressed in partial pressures. |
| Δn | Moles of gaseous products minus moles of gaseous reactants. |
| RT | About 24.465 L·atm/mol at 298.15 K, which is the size of the conversion factor per unit of Δn. |
The inputs explained
| Field | What to enter |
|---|---|
| Convert | Direction of conversion. |
| Known constant (Kc or Kp) | The known constant. |
| Temperature (K) | Temperature in kelvin. |
| Δn (mol gas products − mol gas reactants) | Change in moles of gas. Count only gaseous species from the balanced equation. |
When to use it
Comparing literature values
Sources quote whichever constant suits their measurement method, and comparison requires converting to a common basis.
Switching between gas and solution work
Concentration is natural for solution equilibria and pressure for gas-phase ones.
Checking a reaction quotient
Q must be computed on the same basis as the K it is compared against.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much does Δn change the constant?
The same equilibrium constant with different gas mole changes.
| Δn | Kp | (R·T)^Δn factor | R·T |
|---|---|---|---|
| Δn = -2 | 0.00250603 | 0.00167069 | 24.465 L·atm/mol |
| Δn = -1 | 0.06131104 | 0.04087403 | 24.465 L·atm/mol |
| Δn = 0 | 1.5 | 1 | 24.465 L·atm/mol |
| Δn = 1 | 36.69812071 | 24.46541381 | 24.465 L·atm/mol |
| Δn = 2 | 897.8347093 | 598.5564729 | 24.465 L·atm/mol |
Questions
When are Kp and Kc equal?
Whenever the moles of gas are the same on both sides of the balanced equation, making Δn zero. This includes every reaction with no gaseous species at all, and gas reactions such as H₂ + I₂ ⇌ 2HI where two moles become two moles.
Which species count toward Δn?
Gases only. Solids and pure liquids do not appear in equilibrium expressions and are excluded from the count. Aqueous species do not count either, since they belong to concentration-based expressions rather than pressure ones.
Which value of R should I use?
0.0820574 L·atm/(mol·K) if you want pressures in atmospheres, which is what this calculator uses. Using 8.314 J/(mol·K) gives pressures in pascals and a numerically very different answer. The R must match the pressure units you intend.
Are equilibrium constants unitless?
Strictly yes, because they are defined using activities relative to a standard state. In practice they are usually computed from concentrations or pressures directly, which makes the numerical value depend on the units chosen. This is why the conversion is needed at all.
For the current state of a reaction, see the reaction quotient calculator. For partial pressures in a mixture, see the partial pressure calculator.