Equilibrium constant (Kc) is a measure of the extent to which a reaction proceeds to form products at equilibrium. It is expressed as the ratio of the concentration of products to the concentration of reactants, each raised to their stoichiometric coefficients.

The given reaction is A + 2B → 3C, and the equilibrium constant (Kc) is 2 × 10^(-3). We need to determine the equilibrium partial pressure of gas if the initial pressure of gas A is a atm and B is 2 atm.

To determine the equilibrium partial pressure of gas C, we need to use the equilibrium expression and the stoichiometry of the reaction.

The equilibrium expression for the given reaction can be written as:
Kc = [C]^3 / ([A] × [B]^2)

Since we are given the initial pressures of A and B, we can assume that the initial moles of A and B are equal to their respective partial pressures.

Let the equilibrium partial pressure of gas C be x atm.

1. Write the balanced equation:
A + 2B → 3C

2. Write the equilibrium expression:
Kc = [C]^3 / ([A] × [B]^2)

3. Substitute the initial pressures:
Kc = x^3 / (a × (2)^2)

4. Substitute the given value of Kc:
2 × 10^(-3) = x^3 / (a × 4)

5. Solve for x:
x^3 = (2 × 10^(-3)) × (a × 4)
x^3 = 8 × 10^(-3) × a
x = (8 × 10^(-3) × a)^(1/3)

Therefore, the equilibrium partial pressure of gas C is (8 × 10^(-3) × a)^(1/3) atm.

Explanation:
- We start by writing the balanced equation and the equilibrium expression for the given reaction.
- We substitute the initial pressures of A and B into the equilibrium expression.
- We substitute the given value of Kc into the equation and solve for x, the equilibrium partial pressure of gas C.
- Finally, we simplify the expression for x to obtain the equilibrium partial pressure of gas C in terms of the initial pressure of gas A.

Put the formula Kp=Kc×(RT)^∆n(gas)
R=0.082 & T=298