**Given: **T = 500 K,

At equilibrium, [HI] = 0.5 M, [H_{2}] = 0.08 M, [I ] = 0.062 M.

**To find: **Equilibrium constant K_{c}

**Formula: **K = \(\frac{[C]^c [D]^d}{[A]^a [B]^b}\)

**Calculation: **The above equilibrium reaction is given as 2HI_{(g)} ⇌ H_{2(g)} + I_{2(g)}

The expression of K_{c} is

K_{c} at 500 K for the given reaction is 0.0198.