 # Relation Between Kp And Kc

## Kp And Kc

Kp And Kc are the equilibrium constant of an ideal gaseous mixture. Kp is equilibrium constant used when equilibrium concentrations are expressed in atmospheric pressure and Kc is equilibrium constant used when equilibrium concentrations are expressed in molarity.

For many general chemical reactions aA + bB ⇋ cC + dD

Where a mole of reactant A

b mole of reactant B

c mole of product C

d mole of product D

Consider an example

2A(g)+B(g) ⇋ 2C(g) All in the gas phase.

The Kp is given by-

$K_{p}= \frac{P_{C}^{2}}{P_{A}^{2}P_{B}}$ ———(1)

### Ideal Gas Equation

Each of these ideal gas molecules behaves similarly. So for each of them,

PV = nRT

On rearranging we get-

$P=\frac{n}{V}RT$

Substituting these in equation (1)

$\Rightarrow K_{p}=\frac{\left [ C \right ]^{2}\left ( RT \right )^{2}}{\left [ A \right ]^{2}\left ( RT \right )^{2}\left [ B \right ]\left ( RT \right )}$ $\Rightarrow K_{p}=\frac{\left [ C \right ]^{2}}{\left [ A \right ]^{2}\left [ B \right ]}\times \frac{\left ( RT \right )^{2}}{\left ( RT \right )^{2}\left ( RT \right )}$

On canceling like terms and substituting $K_{c}=\frac{\left [ C \right ]^{2}}{\left [ A \right ]^{2}\left [ B \right ]}$ we get-

$\Rightarrow K_{p}=\frac{K_{c}}{RT}$

Or

$K_{p}=K_{c}\left ( RT \right )^{-1}$

In general,

 $K_{p}=K_{c}\left ( RT \right )^{\Delta n}$

Where, Δn represents the change in the number of moles of gas molecules. [That is Δn = product – reactant in moles only for gas molecules]

When the change in the number of moles of gas molecules is zero, that is Δn = 0

⇒ Kp=Kc

In general, for any chemical reactions of gas molecules the relation between Kp And Kc is-

 $K_{p}=K_{c}\left ( RT \right )^{\Delta n}$ $K_{c}=K_{p}\left ( RT \right )^{-\Delta n}$

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