1. 2.0 mol of PCl5 were introduced in a vessel of 5.0 L capacity at a particular temperature . At equilibrium PCl5 was found to be 35% dissociated into PCl3 and Cl2 . The value of Kc for the reaction is ?

To find the equilibrium constant \( K_c \) for the dissociation of phosphorus pentachloride (PCl5) into phosphorus trichloride (PCl3) and chlorine gas (Cl2), we first need to understand the reaction and how to set up the equilibrium expression based on the information provided.

The Reaction

The dissociation of PCl5 can be represented by the following balanced chemical equation:

PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)

Initial Conditions

We start with 2.0 moles of PCl5 in a 5.0 L vessel. To find the initial concentration of PCl5, we can use the formula:

Concentration (C) = Moles / Volume

So, the initial concentration of PCl5 is:

C_initial = 2.0 mol / 5.0 L = 0.4 M

Dissociation Information

According to the problem, PCl5 is 35% dissociated at equilibrium. This means that:

Dissociated amount = 0.35 × 2.0 mol = 0.7 mol

Thus, at equilibrium, the moles of each species can be calculated:

• Moles of PCl5 remaining = 2.0 mol - 0.7 mol = 1.3 mol
• Moles of PCl3 formed = 0.7 mol
• Moles of Cl2 formed = 0.7 mol

Equilibrium Concentrations

Now, we convert these moles into concentrations:

• [PCl5] = 1.3 mol / 5.0 L = 0.26 M
• [PCl3] = 0.7 mol / 5.0 L = 0.14 M
• [Cl2] = 0.7 mol / 5.0 L = 0.14 M

Setting Up the Equilibrium Expression

The equilibrium constant \( K_c \) for the reaction is defined as:

Kc = [PCl3][Cl2] / [PCl5]

Substituting the equilibrium concentrations into this expression gives:

Kc = (0.14)(0.14) / (0.26)

Calculating Kc

Now, we perform the calculation:

Kc = 0.0196 / 0.26 ≈ 0.07538

Final Result

Thus, the equilibrium constant \( K_c \) for the dissociation of PCl5 at the given conditions is approximately:

Kc ≈ 0.075

This value indicates the extent to which PCl5 dissociates into PCl3 and Cl2 at equilibrium under the specified conditions. A smaller \( K_c \) value suggests that, at equilibrium, the reaction favors the reactants (PCl5) over the products (PCl3 and Cl2).