Question

At 850. K, the value of the equilibrium constant Kp for the hydrazine synthesis reaction below is 0.2100. If a vessel contains an initial reaction mixture in which [N2] = 0.02000 M, [H2] = 0.03000 M, and [N2H2] = 1.000×10-4 M, what will the [N2H2] be when equilibrium is reached?

Answer 1

Ans. Create an ICE table as shown in figure

Equilibrium constant, Kp = [N2H2] / ([N2] [H2])             - all concentrations at equilibrium.

Putting the values in above equation-

0.21 = (0.0001 + X) / [(0.02 -X) (0.03 -X)] = (0.0001 + X) / (0.0006 – 0.02X – 0.03X + X²)

            Or, 0.21 x (X² – 0.05X + 0.0006) = (0.0001 + X)

            Or, 0.21X² – 0.0105X + 0.000126 = 0.0001 + X

            Or, 0.21X² – 0.0105X + 0.000126 - 0.0001 – X = 0

            Or, 0.21X² – 1.0105X + 0.000026 = 0

Solving the quadratic equation we get,

            X1 = 4.812                 ; X2 = 2.573 x 10^-5

Since, X can’t be greater than initial concertation of reactants, reject X1.

Hence, X = 2.573 x 10^-5

Now,

            [N2H2] at equilibrium = 0.0001 + X = 0.0001 + (2.573 x 10^-5) = 1.26 x 10^-4 M