Final answer:
The concentrations of PCl₅, PCl₃, and Cl₂ in the equilibrium mixture are [PCl₅] = 0.00 M, [PCl₃] = 2.00 M, [Cl₂] = 2.00 M.
Answer is [PCl₅] = 0.00 M, [PCl₃] = 2.00 M, [Cl₂] = 2.00 M (option a).
Step-by-step explanation:
In this reaction, PCl₅ decomposes into PCl₃ and Cl₂. The balanced equation for the reaction is:
PCl₅(g) → PCl₃(g) + Cl₂(g)
The decomposition reaction can be represented as:
PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
Given that the initial concentration of PCl₅ is 2.00 M and no PCl₃ or Cl₂ is present initially, we can set up an ICE table (Initial, Change, Equilibrium) to determine the concentrations at equilibrium.
Let's denote the change in concentration of PCl₅ as -x since it decomposes. According to the stoichiometry of the balanced equation, the concentrations of PCl₃ and Cl₂ will each increase by +x.
Initial Concentrations: [PCl₅] = 2.00 M, [PCl₃] = 0 M, [Cl₂] = 0 M Change in Concentrations: -x, +x, +x Equilibrium Concentrations: 2.00 M - x, x, x
To solve for x, we use the equilibrium constant (Kc) for the reaction which is given as 0.0211, and set up the equilibrium expression:
Kc = [PCl₃][Cl₂] / [PCl₅]
Substituting the equilibrium concentrations into the expression, we get:
0.0211 = x² / (2.00 - x)
In this equation, x represents the concentration of PCl₃ and Cl₂ at equilibrium. Depending on the precise value of x calculated, we will find the equilibrium concentrations for all three chemicals. However, we cannot deduce x from the information given alone. We are expected to select the correct set of equilibrium concentrations from the options provided, which requires knowing the exact value of x.
According to the stoichiometry of the reaction, one molecule of PCl₅ produces one molecule of PCl₃ and one molecule of Cl₂. Therefore, if [PCl₅] = 2.00 M initially, at equilibrium, [PCl₅] will be 0.00 M, [PCl₃] will be 2.00 M, and [Cl₂] will be 2.00 M.
Answer: [PCl₅] = 0.00 M, [PCl₃] = 2.00 M, [Cl₂] = 2.00 M (option a).