Question 14.8: Finding Equilibrium Concentrations when You are given the Eq...
Finding Equilibrium Concentrations when You are given the Equilibrium Constant and all but One of the Equilibrium Concentrations of the Reactants and Products
Consider the reaction:
2 COF_{2}(g)\xrightleftharpoons[]{}CO_{2}(g) + CF_{4}(g) K_{c} = 2.00 at 1000 °C
In an equilibrium mixture, the concentration of COF_{2} is 0.255 M and the concentration of CF_{4} is 0.118 M. What is the equilibrium concentration of CO_{2}?
| SORT You are given the equilibrium constant of a chemical reaction, together with the equilibrium concentrations of the reactant and one product. You are asked to find the equilib-rium concentration of the other product. | GIVEN [COF_{2}] = 0.255 M [CF_{4}] = 0.118 M K_{c} = 2.00 FIND [CO_{2}] |
| STRATEGIZE Calculate the concentration of the product by using the given quantities and the expression for K_{c}. | CONCEPTUAL PLAN [COF_{2}] , [CF_{4}], K_{c} → [CO_{2}] . \frac{[CO_{2}][CF_{4}]}{[COF_{2}]^{2}} |
| SOLVE Solve the equilibrium expression for [CO_{2}] and then substitute in the appropriate values to calculate it. | |
[CO_{2}] = K_{c}\frac{[COF_{2}]^{2}}{[CF_{4}]}
[CO_{2}] = 2.00\left(\frac{0.255^{2}}{0.118}\right) = 1.10 M
CHECK Check your answer by substituting the given values of [COF_{2}] and [CF_{4}] as well as the calculated value for [CO_{2}]back into the equilibrium expression.
K_{c} = \frac{[CO_{2}][CF_{4}]}{[COF_{2}]^{2}}
[CO_{2}] was found to be roughly equal to 1. [COF_{2}]² ≈ 0.06 and [CF_{4}] ≈ 0.12. Therefore K_{c} is approximately 2, as given in the problem.