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:
- Number of moles = concentration x volume
nNO2 = [NO2(g)] x V
nN2O4 = [N2O4(g)] x V
- 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 …