Expressions for equilibrium constant (K_c)

Take the following reversible reaction: A + 2B ? C + 3D

It is possible for the rate expression for the forward reaction to be written as:

rate = k_f [A][B]²

In which:

• k_f = rate constant for the forward reaction

It is possible for the rate expression for the reverse reaction to be written as:

rate = k_r [C][D]³

In which:

• k_r = rate constant for the reverse reaction

When equilibrium is reached, the forward and reverse reactions are equal to one another:

k_f [A][B]² = k_r [C][D]³

You can rearrange this to give:

k_f / k_r = ([C][D]³) / ([A][B]²)

At a constant temperature it follows that the term k_f / k_r is constant at this temperature. Therefore, this term is usually represented simply as constant K_c: the equilibrium constant of the reaction.

K_c = ([C][D]³) / ([A][B]²)

Units for equilibrium constants (K_c)

The number of species involved dictates the units of the equilibrium constant. To calculate the units you need to multiply out the units of concentration and cancel as appropriate. The units of the equilibrium constant depend on the reaction and the way in which the reaction is written.

Example 1: H₂(g) + I₂(g) ? 2HI(g)

K_c = [HI]² / ([H₂][I₂])

There are no units.

Example 2: Pl₅(g) ? PCl₃(g) + Cl₂(g)

K_c = ([PCl₃][Cl₂]) / [PCl₅]

The units are moldm^-3.

Example 3: consider the equilibrium 2SO₂(g) + O₂(g) ? 2SO₃(g)

K¹_c = [SO₃]² / ([SO₂]²[O₂]) units mol^-1dm³

However, if you write the equation another way: SO2(g) +