_{c}) of a reaction in terms of molar concentration.

# Kp Calculator

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

To learn more about equilibrium constant K_{c}, go to the equilibrium constant calculator.

## What is K_{p}, and how is it different from K_{c}?

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 (K_{c}) of the chemicals, or by using their partial pressure (K_{p}). 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:

`K`

,_{c} = ([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:

`K`

,
where, analogously_{p} = (P_{c}^{c} * P_{d}^{d}) / (P_{b}^{b} * P_{a}^{a})

- P
_{a}and P_{b}are partial pressures of the reactants - P
_{c}and P_{d}are partial pressures of the products

## How to calculate K_{p} from K_{c}?

The relationship between K_{p} and K_{c} is:

`K`

, where_{p} = K_{c} * (R * T)^{ Δn}

`K`

is the equilibrium constant in terms of pressure._{p}`K`

is the equilibrium constant in terms of molarity._{c}`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 K_{c} equals K_{p}. 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 K_{p} calculator ;) ).

## Let's calculate the value of K_{p} 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 K_{p} of the following heterogenous reaction:

`2H`

_{2(g)} + O_{2(g)} ⇌ 2H_{2}O_{(s)}

is equal to:

`K`

_{p} = 1 / (P_{H2}^{2} * P_{O2})

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 K_{p} equation, divide the pressures of the products by the pressures of the reactants, just like we did in the following example:

`H`

_{2}O_{(g)} + C_{(s)} ⇌ H_{2(g)} + CO_{(g)}

`K`

_{p} = (P_{H2} * P_{CO}) / P_{H2O}

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

## How to convert between K_{p} and K_{c}?

The conversion between K_{c} and K_{p} 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:

`N`

_{2(g)} + 3H_{2(g)} ⇌ 2NH_{3(g)}

How do we find the equilibrium constant K_{p} in terms of pressure, in atmospheres, if at **298** K the equilibrium constant K_{c} is **2.27 * 10 ^{-2}**?

- Start with establishing the value of the gas constant:

`R = `

**0.082 057 46(14)** ^{L * atm} / _{K * mol}

- Then, determine the change in moles:

`Δn = 2 - (3 + 1) = `

**-2**

- Finally, calculate the value of K
_{p}for the equation:

`K`

_{p} = 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 K_{p}! But if you don't feel like doing all that math on your own, you can always put our K_{p} calculator to good use!

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