# Kp Calculator

Created by Julia Żuławińska
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Nov 22, 2021

The Kp calculator is a tool that will convert the equilibrium constant, Kc, to Kp - the equilibrium constant in terms of partial pressure. In the following article we will explain what is Kp, as well as providing you with the Kp equation. You will also find out how to calculate Kp from Kc (or Kc from Kp).

## What is Kp, and how is it different from Kc?

In some chemical reactions, the change is not permanent - the products can sometimes form the reactants. If both the forward and backward reactions occur simultaneously, then it is known as a reversible reaction. In such cases, you can calculate the equilibrium constant by using the molar concentration (Kc) of the chemicals, or by using their partial pressure (Kp). In both cases, the equations are fairly similar. For the reaction:

a*A + b*B ⇌ c*C + d*D,

the equilibrium constant in terms of concentration is:

Kc = ([C]c * [D]d) / ([B]b * [A]a),

where

• [A] and [B] are the molar concentrations of the reactants
• [C] and [D] are the molar concentrations of the products

The equilibrium constant formula in terms of partial pressure is:

Kp = (Pcc * Pdd) / (Pbb * Paa),
where, analogously

• Pa and Pb are partial pressures of the reactants
• Pc and Pd are partial pressures of the products

## How to calculate Kp from Kc?

The relationship between Kp and Kc is:

Kp = Kc * (R * T) Δn, where

• Kp is the equilibrium constant in terms of pressure.
• Kc is the equilibrium constant in terms of molarity.
• R is the gas constant.
• T is the temperature.
• Δn is the change in the number of moles:

Δn = mol of gaseous products - mol of gaseous reactants

To save time, start calculations with the change in the number of moles. If it's zero (Δn = 0) then Kc equals Kp. If not, read the last paragraph of this article, use the correct units, and find the answer in less than a few minutes (or seconds if you use our Kp calculator ;) ).

## Let's calculate the value of Kp for a reaction!

The most important thing to remember when calculating the equilibrium constant in terms of pressure is to only take into account components in the gas phase. For example, the Kp of the following heterogenous reaction:

2H2(g) + O2(g) ⇌ 2H2O(s)

is equal to:

Kp = 1 / (PH22 * PO2)

So, instead of using the pressure of water you just need to input 1. You might be wondering, what if there aren't exactly two reactants, or two products? Then, similarly to the above Kp equation, divide the pressures of the products by the pressures of the reactants, just like we did in the following example:

H2O(g) + C(s) ⇌ H2(g) + CO(g)

Kp = (PH2 * PCO) / PH2O

Keep in mind to always double-check the units! They should always be the same!

## How to convert between Kp and Kc?

The conversion between Kc and Kp might be tricky. The equilibrium constant is a unitless number, but give some thought to the gas constant unit. It indicates if the equilibrium constant for partial pressures is calculated in terms of bars, atmospheres, or Pascals. We've prepared a table with the most common pressure units and their corresponding gas constants:

Pressure unit Gas constant value Gas constant unit
atm 0.082 057 46(14) L * atm / K * mol
kPa 8.314 462 1(75) L * kPa / K * mol
bar 0.083 144 621(75) L * bar / K * mol
Torr 62.363 67(11) L * Torr / K * mol
mmHg 62.363 67(11) L * mmHg / K * mol

Now, let's have a look at this reversible reaction:

N2(g) + 3H2(g) ⇌ 2NH3(g)

How do we find the equilibrium constant Kp in terms of pressure, in atmospheres, if at 298 K the equilibrium constant Kc is 2.27 * 10-2?

R = 0.082 057 46(14) L * atm / K * mol

1. Then, determine the change in moles:

Δn = 2 - (3 + 1) = -2

1. Finally, calculate the value of Kp for the equation:

Kp = 2.27 * 10-2 * (0.0820574614 * 298)-2 = 3.796 * 10-5

Now you know the equilibrium constant for an example of the Haber process, and how to calculate Kp! But if you don't feel like doing all that math on your own, you can always put our Kp calculator to good use!

Can't get enough of chemistry? Check out the Avogadro's number calculator next!

Julia Żuławińska
I want to:
convert between Kₚ and K꜀
Kₚ = K꜀ * (R * T)^(Δn)
Equilibrium constant (K꜀)
Equilibrium constant for partial pressures in:
atm
Temperature (T)
K
Number of moles of products (n)
mol
Number of moles of reactants (n₀)
mol
Equilibrium constant (Kₚ)
How to find Kc?
Use the equilibrium constant calculator to calculate equilibrium constant (Kc) of a reaction in terms of molar concentration.
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