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 given chemical reaction is an addition reaction between Ethene (C2H4) and a halogen (X2) to form C2H4X2. The reaction is reversible, which means it reaches equilibrium when the forward and reverse reactions are occurring at the same rate. The equilibrium constant (K) for this reaction can be represented as: \[ K = \frac{[C_{2}H_{4}X_{2}]}{[C_{2}H_{4}][X_{2}]}\] Where [C2H4X2] is the equilibrium concentration of the product and [C2H4] and [X2] are the equilibrium concentrations of the reactants. The larger the equilibrium constant, the more the reaction forms the product. In contrast, a smaller equilibrium constant means that the concentrations of reactants are higher at equilibrium.

The exercise provides us with figures showing the equilibrium concentrations of reactants and products for each halogen (Cl2, Br2, I2). The colors representing the halogens are: - Green: Cl2 - Brown: Br2 - Purple: I2 The figures show the relative concentrations of Ethene (C2H4), the halogens (X2), and the product (C2H4X2) at equilibrium. From the graphs, we can infer the equilibrium constants for each halogen reaction.

Now, using the equilibrium constant formula and the information from the graphs: 1. For Cl2 (green), the graph has a relatively higher concentration of [C2H4] and [Cl2] compared to [C2H4Cl2]. This indicates a smaller K, as the reaction leans more towards the reactants. 2. For Br2 (brown), the graph shows a moderate concentration of [C2H4] and [Br2] and an increased concentration of [C2H4Br2]. So, the equilibrium constant K will be larger than for Cl2. 3. For I2 (purple), the graph has a very small concentration of [C2H4] and [I2] and much larger concentration of [C2H4I2]. The equilibrium constant K for I2 will be the largest among the three halogens. Based on the analysis, the order of equilibrium constants will be: Cl2 (green) < Br2 (brown) < I2 (purple)