Question

Making Hydrogen Gas ​Passing steam over hot carbon produces a mixture of carbon monoxide

and hydrogen:

H₂O(g) + C(s) <=> CO(g) + H₂(g)

The value of K_c for the reaction at 1000°C is 3.0 × 10^–2.

a. Calculate the equilibrium partial pressures of the products and reactants if P_H2O = 0.442 atm

   and P_CO = 5.0 atm at the start of the reaction. Assume that the carbon is in excess.

b. Determine the equilibrium partial pressures of the reactants and products after sufficient CO

    and H₂ are added to the equilibrium mixture in part a to initially increase the partial pressures

    of both gases by 0.075 atm.

Answer 1

a. Kc = [CO][H2]/[H2O]

let x be the change at equilibrium

3.0 x 10^-2 = (5 + x)(x)/(0.442 - x)

0.01326 - 3 x 10^-2x = 5x + x^2

x^2 + 5.03x - 0.01326 = 0

x = 2.63 x 10^-3

Thus equilibrium partial pressure for,

[H2O] = 0.442 - 2.63 x 10^-3 = 0.4394 atm

[CO] = 5 + 2.63 x 10^-2 = 5.00263 atm

[H2] = 2.63 x 10^-2 atm

b. with,

[CO] = 5.00263 + 0.075 = 5.07763 atm

[H2] = 2.63 x 10^-3 + 0.075 = 0.007763 atm

Kc = 3 x 10^-2 = (5.00763 - x)(0.007763 - x)/(0.4394 + x)

0.0132 + 3 x 10^-2x = 0.039 - 5.0154x + x^2

x^2 - 5.0454x + 0.0258 = 0

x = 5.12 x 10^-3 atm

Thus equilibrium partial pressure for,

[H2O] = 0.4394 + 5.12 x 10^-3 = 0.4445 atm

[CO] = 5.07763 - 5.12 x 10^-3 = 5.0725 atm

[H2] = 0.007763 - 5.12 x 10^-3 = 2.643 x 10^-3 atm