Question 15.8: Finding Equilibrium Concentrations When You Know the Equilib...
Finding Equilibrium Concentrations When You Know the Equilibrium Constant and All but One of the Equilibrium Concentrations of the Reactants and Products
Consider the following reaction:
2 \ COF_2(g) \rightleftharpoons 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 equilibrium concentration of the other product.
GIVEN: [COF_2] = 0.255 M
[CF_4] = 0.118 M
K_c = 2.00
FIND: [CO_2]
STRATEGIZE You can calculate the concentration of the product using the given quantities and the expression for K_c.
CONCEPTUAL PLAN
SOLVE Solve the equilibrium expression for [CO_2] and 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 mentally substituting the given values of [COF_2] and [CF_4] as well as your calculated value for CO_2 back into the equilibrium expression.
K_c=\frac{[CO_2][CF_4]}{[COF_2]^2}
You found [CO_2] 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.