CHM 1046
General Chemistry II
Dr. Michael Blaber

Chemical Equilibrium

Calculating Equilibrium Constants

The Haber process revisited:

Haber and his coworkers were concerned with figuring out what the value of the equilibrium constant, Kc, was at different temperatures.

Haber did experiments where he started with various mixtures of N2, H2 and NH3 and allowed them to come to equilibrium at various temperatures

In one experiment a mixture of H2, N2 and NH3 was allowed to reach equilibrium conditions at 472°C. The concentration of gases at equilibrium was analyzed and found to contain 0.1207M H2, 0.0402M N2 and 0.00272M NH3. What value did Haber come up with for the equilibrium constant, Kc?

Kc = (0.00272)2/(0.0402)(0.1207)3

Kc = 0.105

(equilibrium lies to the left, not much ammonia will be present at equilibrium conditions)

Often we do not know (or are not easily able to determine) the concentration of all products and reactants at equilibrium

The steps in this method are as follows:

  1. List the known initial and equilibrium concentrations of all reactants and products involved in the equilibrium
  2. For those reactants or products, for which both the initial and equilibrium concentrations are known, calculate the change in concentration that occurs as the system reaches equilibrium
  3. Use the stoichiometry of the reaction to calculate the predicted changes in concentration for all the other reactants and products in the equilibrium
  4. From the initial concentrations, and the changes in concentration, calculate the equilibrium concentrations (and Kc)

 

In one of Haber's experiments, 0.025 mol of H2(g) and 0.010 mol of N2(g) are combined in a 2L vessel at 472°C. The mixture is allowed to come to equilibrium and the concentration of NH3(g) is observed to be 3.18 x 10-5M. Calculate Kc for the Haber reaction at this temperature. 

1. The known initial and equilibrium concentrations for the different compounds are:

Initial concentrations:

H2(g) is 0.025 mol / 2L = 0.0125M

N2(g) is 0.010 mol / 2L = 0.005M

NH3(g) is 0M initially

Final (equilibrium) concentrations:

H2(g) ?

N2(g) ?

NH3(g) is 3.18 x 10-5M

2. Initial and final concentrations are known only for NH3(g):

D[NH3(g)] = Equilibrium concentration - Initial concentration

D[NH3(g)] = 3.18 x 10-5M - 0M = 3.18 x 10-5M = the amount of ammonia produced in the reaction

3. Stoichiometry of balanced equation:

N2(g) + 3H2(g) -> 2NH3(g), therefore, stoichiometry is:

[N2] 3[H2] 2[NH3]

Thus, if 3.18 x 10-5M of NH3 is being produced,

(3.18 x 10-5M NH3) * (1 N2 / 2 NH3) = 1.59 x 10-5M of N2 must have been consumed

and

(3.18 x 10-5M NH3) * (3 H2 / 2 NH3) = 4.77 x 10-5M of H2 must have been consumed

4. Calculation of concentration of all reactants and products at equilibrium by knowing initial concentrations and how much was consumed:

N2 started with 0.005M, and 1.59 x 10-5M of N2 was consumed, therefore, at equilibrium there was (0.005M - 1.59 x 10-5M) = 4.98 x 10-3M of N2

H2 started with 0.0125M, and 4.77 x 10-5M of H2 was consumed, therefore, at equilibrium there was (0.0125M - 4.77 x 10-5M) = 1.245 x 10-2M of H2

NH3 concentration at equilibrium was given as 3.18 x 10-5M

Kc = [NH3]2/[N2][H2]3 = (3.18 x 10-5)2 / (4.98 x 10-3)(1.245 x 10-2)3

= (1.01 x 10-9) / (4.98 x 10-3)(1.95 x 10-6)

= 0.104

Relating Kc and Kp

For a gas we can express the equilibrium constant in terms of concentration (molarity) or in units of pressure. How are these related?

PV = nRT

P = (n/V)RT

P = MRT

For a gaseous substance, A, the partial pressure of A is equal to the molarity times the gas constant R and temperature T in Kelvin

PA = [A](RT)

Note: P = MRT can be manipulated to solve for R, the gas constant: R =P/MT. This provides an interpretation for the meaning of the gas constant - it is a way to relate the molarity of a gas sample to its pressure and temperature

Kp = Kc(RT)Dn

N2O4(g) ó 2NO2(g)

Dn = (2-1) = 1

Kp = Kc(RT)1 = Kc(RT)

© 2000 Dr. Michael Blaber