To tackle your question about the equilibrium constant for the decomposition of phosphorus pentachloride (PCl5), let's break it down step by step. We’ll start with the expression for the equilibrium constant (Kc) and then determine the value for the reverse reaction.
Understanding the Equilibrium Constant Expression
The equilibrium constant expression for a reaction is derived from the concentrations of the products and reactants at equilibrium. For the decomposition of phosphorus pentachloride, the reaction can be written as:
PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)
The equilibrium constant expression (Kc) for this reaction is given by:
Kc Expression
The general form of the equilibrium constant expression is:
Kc = [Products] / [Reactants]
For our specific reaction, this translates to:
Kc = [PCl3][Cl2] / [PCl5]
Here, [PCl3], [Cl2], and [PCl5] represent the molar concentrations of phosphorus trichloride, chlorine gas, and phosphorus pentachloride, respectively, at equilibrium.
Calculating Kc for the Reverse Reaction
Now, let’s consider the reverse reaction, which is the formation of phosphorus pentachloride from its products:
PCl3 (g) + Cl2 (g) ⇌ PCl5 (g)
The equilibrium constant for the reverse reaction, Kc (reverse), is related to the Kc of the forward reaction by the following relationship:
Kc (reverse) = 1 / Kc (forward)
Given that Kc for the forward reaction (decomposition of PCl5) is 8.3 × 10-3, we can calculate Kc for the reverse reaction:
Calculation
Kc (reverse) = 1 / (8.3 × 10-3)
Now, performing the calculation:
Kc (reverse) = 1 / 8.3 × 10-3 ≈ 120.5
Summary of Results
- Kc for the forward reaction (decomposition of PCl5): 8.3 × 10-3
- Kc for the reverse reaction (formation of PCl5): 120.5
This means that at 473 K, the equilibrium constant for the reverse reaction is significantly larger, indicating that at equilibrium, the formation of PCl5 is favored compared to its decomposition under these conditions. This is a common scenario in chemical equilibria, where the direction of the reaction can greatly influence the concentrations of reactants and products.
