# Kp Calculator

Created by Julia Żuławińska
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 05, 2023

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).

To understand the progression of a reversible reaction, in the case the reaction is not at the equilibrium yet, you should use the reaction quotient. In each case, the equations are fairly similar. For the reaction:

$\footnotesize a\cdot A + b \cdot B \rightleftharpoons c \cdot C + d \cdot D$,

the equilibrium constant in terms of concentration is:

$\small K_c = \frac{[C]^c \space\cdot \space [D]^d}{[B]^b \space\cdot\space [A]^a}$,

where

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

The equilibrium constant formula in terms of partial pressure is:

$\small K_p = \frac{{P_c}^c \space\cdot \space{P_d}^d}{{P_b}^b \space\cdot\space {P_a}^a}$,

where, analogously

• $\footnotesize P_a$ and $\footnotesize P_b$ are partial pressures of the reactants
• $\footnotesize P_c$ and $\footnotesize P_d$ are partial pressures of the products

## How to calculate Kp from Kc?

The relationship between Kp and Kc is:

$\footnotesize K_p = K_c \cdot (R \cdot T)^{\Delta n}$, where

• $\footnotesize K_p$ is the equilibrium constant in terms of pressure.
• $\footnotesize K_c$ is the equilibrium constant in terms of molarity.
• $\footnotesize R$ is the gas constant.
• $\footnotesize T$ is the temperature.
• $\footnotesize \Delta n$ is the change in the number of moles:

$\footnotesize \Delta n = \text{mol of gaseous products} - \text{mol of gaseous reactants}$

To save time, start calculations with the change in the number of moles. If it's zero ($\footnotesize \Delta n = 0$) 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:

$\footnotesize 2H_{2(g)} + O_{2(g)} \rightleftharpoons 2H_2O_{(s)}$

is equal to:

$\small K_p = \frac{1}{{P_{H_2}}^2 \space \cdot \space P_{O_2}}$

So, instead of using the pressure of water you just need to input $\footnotesize 1$. 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:

$\footnotesize H_2O_{(g)} + C_{(s)} \rightleftharpoons H_{2(g)} + CO_{(g)}$

$\small K_p = \frac{P_{H_2} \space \cdot \space P_{CO}}{P_{H_2O}}$

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)

$\small \frac{L \cdot atm}{k \cdot mol}$

kPa

8.314 462 1(75)

$\small \frac{L \cdot kPa}{k \cdot mol}$

bar

0.083 144 621(75)

$\small \frac{L \cdot bar}{k \cdot mol}$

Torr

62.363 67(11)

$\small \frac{L \cdot Torr}{k \cdot mol}$

mmHg

62.363 67(11)

$\small \frac{L \cdot mmHg}{k \cdot mol}$

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

$\footnotesize N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

How do we find the equilibrium constant Kp in terms of pressure, in atmospheres, if at $\footnotesize 298 K$ the equilibrium constant Kc is $\footnotesize 2.27 \cdot 10^{-2}$?

$\footnotesize R = 0.082 \space 057 \space 46(14) \frac{L \cdot atm}{K \cdot mol}$

2. Then, determine the change in moles:

$\footnotesize \Delta n = 2 - (3+1) = -2$

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

$\footnotesize K_p = 2.27 \cdot 10^{-2} \cdot (0.0820574614 \cdot 298)^{-2} = 3.796 \cdot 10^{-5}$

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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