Question

One mole PCl₅, is heated in a closed container of one litre capacity. At equilibrium, 20% PCl₅, is not dissociated. What should be the value of K. ?

(A) 32
(B) 3.2
(C)2.4
(D) 42

Answer 1

The equilibrium constant, Kc, for the dissociation of PCl5 when 20% remains undissociated in a closed container is calculated to be 0.05, which does not match any of the provided answer choices.

Step-by-step explanation:

When one mole of PCl5 is heated in a closed container with a volume of one liter and 20% of it remains undissociated at equilibrium, we can determine the equilibrium constant for the dissociation reaction:

PCl5(g) ⇌ PCl3(g) + Cl2(g)

Based on the initial information, we can set up an ICE (Initial, Change, Equilibrium) table and then calculate the value of Kc.

• Initial concentrations: [PCl5] = 1 M, [PCl3] = 0 M, [Cl2] = 0 M
• At equilibrium: [PCl5] = 0.8 M (because 20% is not dissociated), therefore the change is 0.2 M
• At equilibrium: [PCl3] = [Cl2] = 0.2 M (from the stoichiometry of the reaction)

Now, we apply the equilibrium expression for Kc:

Kc = ([PCl3][Cl2]) / [PCl5] = (0.2 * 0.2) / 0.8 = 0.04 / 0.8 = 0.05

The closest matching option to the calculated value 0.05 is not provided in the multiple-choice answers (A) 32, (B) 3.2, (C) 2.4, and (D) 42. There may be a typo or error in the question or the given choices, as the correct value of Kc does not match any of the choices.

Answer 2

For the dissociation of PCl₅, at equilibrium 20% is undissociated and concentrations of PCl₃ and Cl₂ are 0.80 M each. Using the expression Kc = [PCl₃][Cl₂] / [PCl₅] and substituting the concentrations, the value of Kc is calculated to be 3.2. The correct option is (B) 3.2.

Step-by-step explanation:

The question asks to calculate the equilibrium constant, Kc, for the dissociation of PCl₅ in a closed container based on the given information that at equilibrium, 20% of PCl₅ is not dissociated. The balanced chemical equation for the dissociation of PCl₅ is PCl₅ (g) ⇌ PCl₃ (g) + Cl₂ (g).

At the start of the reaction, there is 1 mole of PCl₅ in a 1 L container, so its initial concentration is 1 M. At equilibrium, 20% remains undissociated, which means 0.80 M of PCl₅ has dissociated. Therefore, the concentration of PCl₅ at equilibrium is 0.20 M, and the concentration of products, PCl₃ and Cl₂, will each be 0.80 M since they are formed in a 1:1 ratio.

The equilibrium constant expression Kc for this reaction is:

Kc = [PCl₃][Cl₂] / [PCl₅]

Substituting the equilibrium concentrations in this expression, we get:

Kc = (0.80)(0.80) / (0.20) = 0.64 / 0.20 = 3.2

Therefore, the correct option is (B) 3.2.