Final answer:
To find the equilibrium concentrations of CO and Cl₂ when COCl₂ dissociates with Kc = 0.08, we set up an ICE table and solve the quadratic equation resulting from the equilibrium constant expression. Both CO and Cl₂ have identical equilibrium concentrations of 0.0894 M.
Step-by-step explanation:
To calculate the equilibrium concentrations of CO and Cl₂ when the equilibrium concentration of COCl₂ is given as 0.10M, and the equilibrium constant (Kc) for the reaction COCl₂(g) ⇌ CO(g) + Cl₂(g) is 0.08 at a certain temperature, we can set up an ICE (Initial, Change, Equilibrium) table.
We're given Kc and the equilibrium concentration of COCl₂, but not the initial concentrations of CO and Cl₂. We can assume that these start at 0 since the COCl₂ is dissociating into them. At equilibrium, the concentration of COCl₂ decreases by some amount x, and the concentrations of CO and Cl₂ each increase by x. Therefore, the equilibrium concentrations of CO and Cl₂ are both x M.
The equilibrium expression for this reaction is:
Kc = [CO][Cl₂] / [COCl₂]
Substituting the known values into this expression, we get:
0.08 = (x)(x) / 0.10
Solving for x, we have:
x² = 0.08 * 0.10
x² = 0.008
x = √0.008
x = 0.0894 M
Since x is the change in concentration for CO and Cl₂, and they were both initially 0 M, the equilibrium concentrations of CO and Cl₂ will both be 0.0894 M.
Using these values, we can now confirm that the change is small enough to be neglected. Since the initial concentration was 0.10M and the change x is around 0.09, which is almost the same as the initial concentration, we can see that this change is not negligible.
That means our assumption of negligible x would lead to an inaccurate result and we need to solve the equilibrium concentrations using the quadratic formula, which confirms x = 0.0894 M as a legitimate solution.