Equilibrium Constant Calculator
Convert between Kc and Kp, find K from a Gibbs energy, and work out how much gas dissociates.
What it does
An equilibrium constant is the number that says where a reversible reaction settles. It is built from the concentrations, or the partial pressures, of everything in the equation, each raised to the power of its coefficient, and it stays the same as long as the temperature does not change. The OpenStax chemistry text sets out the expressions and the conversions between them.
There are two forms of the same constant. Kc uses molar concentrations, Kp uses partial pressures in atmospheres, and the two are linked by the temperature and by the change in the number of moles of gas across the reaction. A reaction that makes more gas than it consumes has a positive change, and then Kp is larger than Kc.
The thermodynamic route starts from free energy. The standard reaction Gibbs energy and the equilibrium constant are tied together by dG = -RT ln K, so a strongly negative dG means a large constant and a reaction that runs forwards on its own. This is the number a thermochemistry table gives you, and it is the way to get K when nobody has measured it.
The last form here is the classic dissociation problem, where a single gas breaks into two and you want to know how much of it breaks up. The answer depends on the total pressure, because a higher pressure pushes the reaction back towards the side with fewer moles of gas.
One warning applies to everything on this page: a constant belongs to a temperature. The same reaction at a different temperature has a different constant, and the Kc and the temperature you use together have to match.
How to use
- Choose which of the four results you want.
- Fill in the fields for that result.
- For Kp from Kc, enter the change in moles of gas, counting only the gases.
- For K from a Gibbs energy, use the standard reaction value, not a value at some other composition.
- Read the result and the working, which show the numbers that went into it.
Formula
- Kc
- Equilibrium constant built from molar concentrations.
- Kp
- Equilibrium constant built from partial pressures in atmospheres.
- delta n
- Change in moles of gas across the reaction.
- dG
- Standard reaction Gibbs energy in kJ per mole.
- alpha
- Fraction of the original gas that dissociates.
Pure solids and pure liquids do not appear in either expression, because their activities do not change. The dimensionless thermodynamic constant is built from activities rather than bare pressures, and the classroom expressions used here fix the pressure and concentration reference conventions, which is what the OpenStax and Purdue presentations do as well. The dissociation result is for a reaction that starts as pure A and involves no inert gas.
Worked example
Example: Kc of 0.113 at 323 K for N2O4 giving 2 NO2
Defaults: Kp from Kc, Kc of 0.113, a change of one mole of gas and a temperature of 323 K.
- Delta n: 2 moles of NO2 minus 1 mole of N2O4 = 1.
- R T: 0.08206 x 323 = 26.50538 L atm per mole.
- Kp = 0.113 x 26.50538 = 2.9951.
- The same constant read the other way would be Kc = 2.9951 / 26.50538 = 0.113.
- The tool shows Kp = 2.9951, Kc = 0.1130 and the working with delta n and the temperature.
Reference table
| Temperature | R T | Kp for delta n of 1 | Kp for delta n of -1 |
|---|---|---|---|
| 273 K | 22.40 | 2.531 | 0.00504 |
| 298 K | 24.45 | 2.763 | 0.00462 |
| 323 K | 26.51 | 2.995 | 0.00426 |
| 350 K | 28.72 | 3.245 | 0.00393 |
Limits
- Uses the classroom expressions for Kc and Kp rather than dimensionless activities.
- The dissociation result covers a reaction that starts as pure A with no inert gas present.
- Gives no help with a non ideal gas or a solution that is not dilute.
- Every result is tied to the temperature entered, so a constant from a table has to match.
Common mistakes
- Counting solids and liquids in the change in moles of gas, which changes the exponent.
- Using Kc at one temperature with a Kp conversion at another.
- Forgetting that the change in moles of gas can be negative, which makes Kp smaller than Kc.
- Using the Gibbs energy of a mixture instead of the standard reaction value, which cannot give K on its own.
- Treating the equilibrium constant as the fraction of product at equilibrium, which it is not.
Try it yourself
Quick checks. Answers sit tucked under each question.
What is Kp for Kc of 0.113 at 323 K when the change in moles of gas is 1?
Kp = 0.113 x (0.08206 x 323) = 2.9951.
What constant does a standard Gibbs energy of -10.0 kJ/mol give at 298 K?
ln K = 10,000 / (8.314 x 298) = 4.0362, so K = 56.611.
A gas mixture at equilibrium has pA of 0.50 atm and pB of 0.20 atm, with coefficients of 1 and 2. What is Kp?
Kp = 0.20 squared / 0.50 = 0.08, so the constant is 0.08000.
Questions
What is an equilibrium constant?
A number built from the concentrations or partial pressures at equilibrium that stays constant as long as the temperature does. It says where the reaction settles, not how fast it gets there.
What is the difference between Kc and Kp?
Kc uses molar concentrations and Kp uses partial pressures. They describe the same equilibrium and are linked by Kp = Kc (RT) raised to the change in moles of gas.
Does the constant change with pressure?
No. Changing the pressure moves the composition of the mixture but leaves the constant alone, as long as the temperature is unchanged.
How do I get K from a table of free energies?
Use dG = -RT ln K with the standard reaction Gibbs energy, which is the difference between the products and the reactants. The calculator does the conversion from kJ per mole to joules and the natural logarithm.
What does a large K mean?
That products are favoured. A K well above 1 means the reaction runs forwards on its own, and a K near 1 means the mixture is about half and half.
Why does pressure change the fraction dissociated?
Because the reaction that breaks one molecule into two makes more gas, and a higher pressure pushes the mixture back towards the side with fewer moles. That is Le Chatelier's principle in the dissociation problem.
Sources
- OpenStax Chemistry 2e: 13.2, equilibrium constants
- OpenStax Chemistry 2e: 16.4, free energy and the equilibrium constant
- Purdue University chemistry: converting Kc to Kp