How to find Keq? - Equilibrium constant

The symbol K_eq represents the equilibrium constant. K_eq helps in understanding the behavior of a chemical reaction at equilibrium under varying concentration, temperature, and pressure conditions.

What is K_eq?

In chemistry, a reversible reaction is one that takes place in both forward as well as backward directions simultaneously.

aA + bB ⇌ cC + dD

Dynamic equilibrium is a state of balance achieved when the rate of forward reaction becomes equal to the rate of backward reaction.

K_eq helps in predicting quantitatively to what extent the reaction proceeds in the forward or reverse direction.

In this article, we will teach you how to calculate K_eq, what the different types of equilibrium constants are and when to use which one, using some examples.

So for all this valuable information, continue reading!

What are the different types of K_eq?

For the reversible reaction aA + bB ⇌ cC + dD, where a moles of A react with b moles of B to produce c moles of C and d moles of D, the equilibrium constant (K_eq) can be expressed as:

Where,

• [A] = Molar concentration of reactant A at equilibrium (Units: mol/dm³ or mol/L)
• [B] = Molar concentration of reactant B at equilibrium (Units: mol/dm³ or mol/L)
• [C] = Molar concentration of reactant C at equilibrium (Units: mol/dm³ or mol/L)
• [D] = Molar concentration of reactant D at equilibrium (Units: mol/dm³ or mol/L)

As per equation (i), K_eq is defined as the ratio of the product of the molar concentration of products to the product of the molar concentration of reactants.

All the reactant and product concentrations are raised to the number of moles of each in the balanced chemical equation.

The equilibrium constant (K_eq) expressed in terms of molar concentrations is denoted as K_c.

K_c represents the relative amount of reactants and products at equilibrium.  

The units of K_c are subjective. It depends upon the total number of reactants and products participating in the reversible chemical reaction.

For example, let’s see how we can express K_eq for the reaction given below and what are its units.

• If K_eq > 1: Forward reaction (Reactants → Products) is favored.
• If K_eq < 1: Backward reaction (Products → Reactants) is favored.
• If K_eq = 1: The reaction stays at equilibrium (Reactants ⇌ Products)
• If K_eq → ∞: The reaction becomes irreversible

If gaseous reactants and/or products are involved in a chemical reaction, the equilibrium constant (K_eq) can be expressed in terms of partial pressures. In this case, K_eq is denoted as K_p.

For the reversible reaction aA _(g) + bB _(g) ⇌ cC _(g) + dD _(g)

……equation (ii)

Where;

• P_A = Partial pressure of A (Units: Pa or atm)
• P_B = Partial pressure of B (Units: Pa or atm)
• P_C = Partial pressure of C (Units: Pa or atm)
• P_D = Partial pressure of D (Units: Pa or atm)

Partial pressure is defined as the pressure exerted (force/area) by one of the gases in a gaseous mixture.

However, you must keep in mind that equation (ii) is only applicable to gaseous components in the chemical reaction.

For example,

PCl_{5 (g)} ⇌ PCl_{3 (g)} + Cl_{2 (g)}

For the above reaction, the K_p expression is:

K_{eq} = K_p = \frac{P_{\mathrm{PCl_3}} \times P_{\mathrm{Cl_2}}}{{P_{\mathrm{PCl_5}}}}

Contrarily,

C_(s) + H₂O _(g) ⇌ H_{2 (g)} + CO _(g)

In this case, carbon (C) is not a gaseous component, so it is omitted in the K_p expression. The K_p expression thus reduces to:

K_{eq} = K_p = \frac{{P_{\mathrm{H_2}}}^{1} \cdot {P_{\mathrm{CO}}}^{1}}{{P_{\mathrm{H_2O}}}^{1}}

Similarly, the units of K_p are variable, depending upon the total number of gaseous components involved and their mole ratio.

K_p is related to K_c by equation (iii).

K_p = K_c (RT) ^∆n…Equation (iii)

Where;

• K_p = K_eq in terms of partial pressures
• K_c = K_eq in terms of molar concentrations
• R = Ideal gas constant (R= 8.314 J/K.mol)
• T = Absolute temperature
• ∆n = Difference in the number of moles from the reactant to the product side

If ∆n = 0, then two equilibrium constants become equal, i.e., K_p = K_c.

How to calculate K_eq? – Examples  

K_eq can be calculated using any of the equations (i), (ii), or (iii) depending upon the information provided in the question statement.

Let us see how through the examples given below.

FAQ