The equilibrium constant (K) of a chemical reaction is a measure of the extent to which the reaction proceeds towards the products at equilibrium. It is determined by the ratio of the concentrations (or partial pressures) of the products to the concentrations (or partial pressures) of the reactants at equilibrium.

Given reaction: 2HCl ⇌ H2 + Cl2

Equilibrium constant (K) = [H2][Cl2] / [HCl]^2

The given value of the equilibrium constant is 4 × 10^-34 at 25 degrees Celsius.

To find the equilibrium constant for the reaction: 1/2H2 + 1/2Cl2 ⇌ HCl, we need to determine the relationship between the given reaction and the given equilibrium constant.

1. Halving the equation:
By halving the given reaction, we obtain:
HCl = 1/2H2 + 1/2Cl2

2. Taking the square root of the equilibrium constant:
Since the reaction has been halved, we need to take the square root of the given equilibrium constant:
√K = 2 × 10^-17

3. Determining the new equilibrium constant:
The new equilibrium constant for the reaction: 1/2H2 + 1/2Cl2 ⇌ HCl is the square root of the given equilibrium constant.
K' = √K = 2 × 10^-17

Therefore, the equilibrium constant for the reaction 1/2H2 + 1/2Cl2 ⇌ HCl is 2 × 10^-17.

Explanation:
The equilibrium constant is a measure of the position of the equilibrium and provides information about the relative concentrations of reactants and products at equilibrium. In this case, the given equilibrium constant for the reaction 2HCl ⇌ H2 + Cl2 is 4 × 10^-34. By halving the equation and taking the square root of the equilibrium constant, we can determine the equilibrium constant for the reaction 1/2H2 + 1/2Cl2 ⇌ HCl, which is 2 × 10^-17.

By following these steps, you can calculate the equilibrium constant for the given reaction.

Answer is 5*10 power 16