H2(g) + I2(g) <=> 2HI(g) [ H2] = 0.50 mol/dm3 [ I2] = 0.20 mol/dm3 [* HI] = 1.00 mol/dm3 Calculate Kc

The balanced chemical equation is:

$$\text{H}_2\text{(g)} + \text{I}_2\text{(g)} \rightleftharpoons 2\text{HI(g)}$$

The equilibrium constant $K_c$ is expressed as the ratio of the product concentrations raised to their stoichiometric coefficients to the reactant concentrations raised to their stoichiometric coefficients.

$$K_c = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]}$$

Given concentrations at equilibrium are:
$[\text{H}_2] = 0.50 \text{ mol/dm}^3$
$[\text{I}_2] = 0.20 \text{ mol/dm}^3$
$[\text{HI}] = 1.00 \text{ mol/dm}^3$

$$K_c = \frac{(1.00 \text{ mol/dm}^3)^2}{(0.50 \text{ mol/dm}^3)(0.20 \text{ mol/dm}^3)}$$

$$K_c = \frac{1.00 \text{ (mol/dm}^3)^2}{0.10 \text{ (mol/dm}^3)^2}$$ $$K_c = 10.0$$

The value of $K_c$ is $\boxed{\text{10.0}}$.