Question

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]

Short answer

The equilibria can be ordered from smallest to largest equilibrium constant as follows: \(K_\text{I₂} \lt K_\text{Br₂} \lt K_\text{Cl₂}\) based on the given information about equilibrium concentrations for each reaction with halogens.

Step-by-step solution

Understanding the equilibrium constant

The equilibrium constant (K) for a reaction is the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. In this case, our reaction is: $$ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g) $$ So, the equilibrium constant (K) can be expressed as: $$ K = \frac{[\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}]_{eq}}{[\mathrm{C}_{2} \mathrm{H}_{4}]_{eq}\cdot[\mathrm{X}_{2}]_{eq}} $$ Notice that in this reaction, all species are in gaseous form.

Calculate the equilibrium constant for each halogen

We are given the equilibrium concentrations of reactants and products for each halogen. To calculate the equilibrium constant for each halogen, we can simply plug the concentrations into the K expression and calculate K.

Compare the equilibrium constants

Once we have the equilibrium constants for each halogen, we can order them from smallest to largest as requested in the exercise. For the given information, we can see that the equilibrium concentration for C₂H₄X₂ is highest when reacting with Cl₂, slightly lower when reacting with Br₂, and lowest when reacting with I₂. The equilibrium concentration of the reactants C₂H₄ and X₂ increases in the order Cl₂, Br₂, and I₂. So, we can determine the order of the equilibrium constants without actually calculating the K values. Ordering the equilibrium constants from smallest to largest based on the given information: $$ K_\text{I₂} \lt K_\text{Br₂} \lt K_\text{Cl₂} $$