Question 17.7: Determining Equilibrium Concentrations from Kc Problem In a ......
Determining Equilibrium Concentrations from K_c
Problem In a study of the conversion of methane to other fuels, a chemical engineer mixes gaseous CH_4 and H_2O in a 0.32-L flask at 1200 K. At equilibrium, the flask contains 0.028 mol of CO, 0.084 mol of H_2, and 0.045 mol of CH_4. What is [H_2O] at equilibrium (K_c = 0.26 for this process at 1200 K)?
Plan First, we write the balanced equation and the reaction quotient. We calculate the equilibrium concentrations from the given numbers of moles and the flask volume (0.32 L). Substituting these concentrations into Q_c and setting its value equal to the given K_c (0.26), we solve for the unknown equilibrium concentration, [H_2O].
Solution Writing the balanced equation and reaction quotient:
CH_4(g) + H_2O(g) \xrightleftharpoons[]{} CO(g) + 3H_2(g) Q_c = \frac{[CO][H_2]^3}{[CH_4][H_2O]}
Determining the equilibrium concentrations:
Similarly, [CO] = 0.088 M and [H_2] = 0.26 M.
Calculating [H_2O] at equilibrium: Since Q_c = K_c, rearranging gives
Check Always check by substituting the concentrations into Q_c to confirm that the result is equal to K_c:
Q_c = \frac{[CO][H_2]^3}{[CH_4][H_2O]} = \frac{(0.088)(0.26)^3}{(0.14)(0.042)} = 0.26 = K_c