Question

For the reaction \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\), consider two pos- sibilities: (a) you mix \(0.5\) mol of each reactant, allow the system to come to equilibrium, and then add another mole of \(\mathrm{H}_{2}\) and allow the system to reach equilibrium again, or (b) you mix \(1.5 \mathrm{~mol}\) \(\mathrm{H}_{2}\) and \(0.5 \mathrm{~mol} \mathrm{I}_{2}\) and allow the system to reach equilibrium. Will the final equilibrium mixture be different for the two procedures? Explain.

Short answer

The final equilibrium mixture will not be different for the two procedures. In both cases, the reaction shifts right due to the application of Le Châtelier's principle, leading to the same equilibrium mixture for both procedures.

Step-by-step solution

Write down the chemical equation and Le Châtelier's principle

The given reaction is: \[ H_{2}(g) + I_{2}(g) \rightleftharpoons 2HI(g) \] Le Châtelier's principle states that if a chemical system at equilibrium experiences a change in concentration, temperature, volume, or pressure, the equilibrium will shift in a direction that counteracts the change. Now, let's analyze both procedures.

Analyze Procedure (a)

In this procedure, we first mix 0.5 mol of each reactant and reach equilibrium. Then, we add another mole of H₂ to the system and allow it to reach equilibrium again. When we add another mole of H₂ to the system, the concentration of H₂ increases. According to Le Châtelier's principle, the equilibrium will shift in a direction that reduces the concentration of H₂. In this case, that means the reaction will shift to the right (toward the formation of more HI). Now, let the system reach its new equilibrium again.

Analyze Procedure (b)

In this procedure, we mix 1.5 mol H₂ and 0.5 mol I₂ and allow the system to reach equilibrium. Initially, the concentration of H₂ is higher than in procedure (a) before adding the extra mole. According to Le Châtelier's principle, the equilibrium will shift in a direction that decreases the concentration of H₂. In this case, the reaction will again shift to the right (toward the formation of more HI), and the system will reach equilibrium.

Compare the two procedures

In both procedures (a) and (b), we have the same total amount of H₂ and the same amount of I₂. The reaction shifts right in both cases to reach equilibrium, due to the application of the Le Châtelier's principle. Therefore, the final equilibrium mixture will not be different for the two procedures. So, the final equilibrium mixture will be the same for both procedures (a) and (b).

Key concepts

Le Châtelier's Principle

Le Châtelier's principle is a fundamental idea in chemistry. It helps predict how a system at equilibrium responds to changes. When a system's conditions—such as concentration, temperature, or pressure—are altered, the equilibrium position will shift to counteract these changes. For instance, if you increase the concentration of a reactant, the system will typically shift to reduce that change, usually by forming more products. This principle is a helpful tool to understand how equilibrium systems adjust and how they can be manipulated for desired outcomes. It forms the basis for analyzing the behavior of chemical reactions when they are disturbed.

Equilibrium Mixture

An equilibrium mixture is the combination of reactants and products in a chemical reaction that has reached equilibrium. At this point, the concentrations of the substances remain constant because the rate of the forward reaction equals the rate of the backward reaction. This doesn't mean that the reactants and products are in equal amounts, but that their proportions stabilize over time. Understanding the makeup of an equilibrium mixture is key to predicting the outcome of changing conditions, as it tells us the reaction's current state of balance.

Reaction Shift

A reaction shift occurs when an equilibrium system responds to disturbances as described by Le Châtelier's principle. If a change is imposed—like adding more of a reactant or altering temperature—the equilibrium will adjust. The direction of the shift, either to the right or left, aims to minimize the impact of the imposed change. In our example, if more \(H_2\) is added, the system shifts to the right, producing more \(HI\). This helps to understand how different conditions can control the production of the desired product in industrial and laboratory settings.

Equilibrium Concentration

Equilibrium concentration refers to the amount of reactants and products present when a reaction is at equilibrium. These concentrations are crucial for calculating equilibrium constants, which give insight into the extent of a reaction's progress. By knowing the equilibrium concentrations, we can predict how the system will respond to changes. In scenarios like our exercise, determining these concentrations allows us to see if the adjustments in procedure lead to different outcomes. Equilibrium concentrations remain constant until the system is disturbed, showcasing the dynamic yet stable nature of chemical reactions at equilibrium.