Equilibrium Calculations – Calculating a Missing Equilibrium Concentration

When the equilibrium constant and all but one equilibrium concentration are provided, the other equilibrium concentration(s) may be calculated by solving the K expression algebraically.

A computation of this sort is illustrated in the next example exercise:

Calculation of a Missing Equilibrium Concentration

Nitrogen oxides are air pollutants produced by the reaction of nitrogen and oxygen at high temperatures. At 2000 °C, the value of the Kc for the reaction, N2(g)+O2(g)2NO(g) is 4.1×104. Calculate the equilibrium concentration of NO(g) in air at 1 atm pressure and 2000 °C. The equilibrium concentrations of N2 and O2 at this pressure and temperature are 0.036 M and 0.0089 M, respectively.

Solution
Substitute the provided quantities into the equilibrium constant expression and solve for [NO]:

Kc=[NO]2[N2][O2][NO]2=Kc[N2][O2][NO]=Kc[N2][O2][NO]=(4.1×104)(0.036)(0.0089)[NO]=1.31×107[NO]=3.6×104M

Thus [NO] is 3.6×104 mol/L at equilibrium under these conditions.

To confirm this result, it may be used along with the provided equilibrium concentrations to calculate a value for K: Kc=[NO]2[N2][O2]Kc=(3.6×104)2(0.036)(0.0089)Kc=4.0×104

This result is consistent with the provided value for K within nominal uncertainty, differing by just 1 in the least significant digit’s place.

Check Your Learning

The equilibrium constant Kc for the reaction of nitrogen and hydrogen to produce ammonia at a certain temperature is 6.00×102. Calculate the equilibrium concentration of ammonia if the equilibrium concentrations of nitrogen and hydrogen are 4.26 M and 2.09 M, respectively.

Answer

First, write the reaction described in the question: N2+3H22NH3 Use this reaction to determine the formula for KC and solve as above: KC=[NH3]2[N2][H2]36.00×102=[NH3]2[4.26M][2.09M]3[NH3]2=2.333456[NH3]=1.527566[NH3]=1.53M