Understanding the relationship between Kc and Kp

We can derive a value for the equilibrium constant in a gaseous equilibrium system either using partial pressures, Kp, or concentrations ,Kc, which means the two must be related.

N2O4(g) ⇌ 2NO2(g)

The number of moles of a gas can be calculated in two ways:

  1. Number of moles = concentration x volume

nNO2 = [NO2(g)] x V

nN2O4 = [N2O4(g)] x V

  1. Using the ideal gas equation (PV = nRT)

PNO2 V = nNO2 RT

PN2O4 V = nN2O4 RT

We can combine these two methods for each gas:

PNO2 V = [NO2(g)] x V x RT

PN2O4 V = [N2O4(g)] x V x RT

In each equation, the volume, V, cancels out on each side.

PNO2 = [NO2(g)] x RT

PN2O4 = [N2O4(g)] x RT

The equilibrium expressions, Kp and Kc, for this system are:

But we could also write the gaseous equilibrium expression as:

Which leaves us with …