# Understanding Relation between Kp and Kc

Kc and Kp are the equilibrium constants for a given gaseous chemical reaction based on the concentration in the chemical reaction or the partial pressures of the elements in the chemical reaction respectively. The equilibrium constants can be satisfied for the reactions that are reversible at a given temperature, and as the term equilibrium states balance, it denotes that the rate of the forward reaction at that point of time equals the rate of backward reaction at a given temperature.

The relation between Kp and Kc is given by: Kp = Kc[RT]Δng, which is discussed further in the article.

## What is Kc?

The equilibrium constant of concentration (Kc) of a chemical reaction at the equilibrium state is the ratio of the concentration of the products to the concentration of the reactants, where each term is raised to their stoichiometric coefficients.

Kc can be calculated based on the given formula for a given chemical reaction:

aA + bB  cC + dD

## What is Kp?

The equilibrium constant of partial pressures (Kp) is determined by the partial pressures of the reactants and the products in the chemical reaction. Kp is the ratio of product of the partial pressures of the products raised to their stoichiometric coefficients to the product of the partial pressures of the reactants raised to their stoichiometric coefficients.

As Kp is the ratio of partial pressure, it is unitless.

Kp for the given reaction can be found out using the given formula:

aA + bB ⇔ cC

Where,

Px represents the partial pressure of the given product or the reactant.

# Relation between Kp and Kc?

Kp and Kc are the equilibrium constants for the given chemical reaction as we saw in the above discussion, let us now derive an expression relating both the terms as it is helpful in certain cases where the values for the constants is given and the partial pressure or the chemical composition of the element involved in the reaction is to be figured out.

To derive the relation, let us suppose a reversible reaction as follows:

aA + bB cC + dD

Kp for the given equation can be given as: Kp = Pcc PddPaa Pbb ……………(a)

Kc for the given equation can be given as: [C]c [D]d[A]a [B]b ……………..(b)

However, for the ideal gas, the equation is given as follows:

PV = nRT

P = nVRT ………..(1)

In eqn (1), n/V can be substituted by the concentrations of the individual elements in the given equation.

Therefore, eqn (1), now becomes:

P = CRT, where C is the concentration.

Now, concentrations for the individual elements can be replaced as:

Pa = ART

Pb = BRT

Pc = CRT

Pd = DRT

Replacing the values in the eqn(a), we will get

Kp = Cc (RT)C  Dd (RT)dAa (RT)a Bb (RT)b

Kp = Cc  Dd (RT)c + dAa Bb (RT)a + b

Kp = Cc  Dd (RT)(c + d) – (a + b)Aa Bb

Kp = Cc  Dd (RT)ΔngAa Bb

Now, as we know, Kc = [C]c [D]d[A]a [B]b from the given eqn(b)

Hence, Kp = Kc (RT)Δng

Where, n is the difference between the number of moles of the products and reactants in the given chemical equation.

## Characteristics of Equilibrium Constants

• The equilibrium constant for a given chemical reaction at a given temperature is constant.
• For any chemical reaction, the value of the equilibrium constant value may vary for different temperatures at which the reaction is carried out.
• Any changes in the values of the concentration or the partial pressures, the values for the equilibrium constants may change favouring either forward or backward reactions.
• A catalyst may favour the rate of reaction in the forward or the backward direction, but the value for the equilibrium constant may not be altered.
• If any chemical reaction is multiplied by a number, the value of the equilibrium constant is equal to the power of the same number.
• Equilibrium constants are used to find out the direction of the reaction.

## Factors affecting Equilibrium Constant

Various factors affect the value of the equilibrium constant, such as:

• Change in the concentration of the reactants or the products
• Change in pressure
• Change in the temperature of the reaction
• Adding an inert gas in the chemical reaction