Ethene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) reacts with halogens \(\left(\mathrm{X}_{2}\right)\) by the following reaction: $$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g) $$ The following figures represent the concentrations at equilibrium at the same temperature when \(\mathrm{X}_{2}\) is \(\mathrm{Cl}_{2}\) (green), \(\mathrm{Br}_{2}\) (brown), and \(\mathrm{I}_{2}\) (purple). List the equilibria from smallest to largest equilibrium constant. [Section 15.3\(]\)

The equilibrium constant (K) for a reaction is the ratio of the concentrations of the products to the reactants at equilibrium, raised to their stoichiometric coefficients. In this case, the reaction is: $$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g)$$ The equilibrium constant (K) for this reaction would be: $$K = \frac{[\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}]}{[\mathrm{C}_{2} \mathrm{H}_{4}][\mathrm{X}_{2}]}$$

The given figures show the concentrations of the reactants and products at equilibrium in each case. We are not given specific numerical values, but we can compare the relative heights of the bars to draw conclusions about the equilibrium constants. In each case, the higher the concentration of the halogen, the larger the equilibrium constant will be. Look at the relative heights of the product bars (\(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}\)) in comparison to the reactant bars (\(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{X}_{2}\)) for each halogen: - For Cl2 (green): The product bar is taller than both reactant bars. - For Br2 (brown): The product bar is shorter than both reactant bars. - For I2 (purple): The product bar is shorter than the C2H4 bar, and about the same height as the I2 bar.

Based on the analysis in step 2, we can order the equilibrium constants as follows: 1. I2 (purple): The product concentration is less when compared to reactant concentrations, and as equilibrium constant is the ratio of product concentration over reactant concentrations, K is smallest in this case. 2. Br2 (brown): The product concentration is more than that of I2 while still being less than the reactant concentrations; so its equilibrium constant lies between that of I2 and Cl2 3. Cl2 (green): The product concentration is the highest with respect to reactant concentrations, thus its equilibrium constant is the largest. So, we can now list the equilibria from smallest to largest equilibrium constant: $$K_\mathrm{I_2} < K_\mathrm{Br_2} < K_\mathrm{Cl_2}$$