Question

Consider the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g)\) Use forward and reverse rate meters to represent the forward and reverse reaction rates for: (a) The initial equilibrium (b) Moments after you disturb the equilibrium by adding \(\mathrm{PCl}_{5}\) (c) The restored equilibrium (d) Which way did the reaction shift to get from the initial equilibrium, part (a), to the restored equilibrium, part (c)?

Short answer

(a) At the initial equilibrium, both forward and reverse rate meters are equal. (b) After adding more \(\mathrm{PCl}_5\), the reverse rate meter shows a higher rate than the forward rate meter as the reaction tries to reduce the excess product. (c) At the restored equilibrium, both rate meters are once again equal, but at different levels from the initial equilibrium. (d) The reaction shifts in the reverse direction from part (a) to part (c) to reduce the excess \(\mathrm{PCl}_{5}\) and restore equilibrium.

Step-by-step solution

General concept

In an equilibrium, the rate at which a reaction occurs in the forward direction is equal to the rate at which the reverse reaction occurs. This results in no net change in the concentration of the reactants and products over time. <ActionResult#:

(a) Initial Equilibrium

At the initial equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. This means that the forward rate meter and the reverse rate meter will be at the same level, showing equal rates.

(b) Moments after adding PCl5

When we add more \(\mathrm{PCl}_5\) to the reaction, we disturb the equilibrium. In this case, the reverse reaction will have a higher rate than the forward reaction, as the system tries to reduce the excess concentration of the product. The reverse rate meter will show a higher rate than the forward rate meter.

(c) Restored Equilibrium

As the reaction proceeds, the consumption of the excess \(\mathrm{PCl}_5\) will eventually lead to a new equilibrium. At this point, the forward and reverse reaction rates will once again be equal, so the forward and reverse rate meters will show the same level, but these levels might be different from the initial equilibrium.

(d) Shift from initial to restored equilibrium

The reaction shifted in the reverse direction to reach the restored equilibrium, from part (a) to part (c). This is because the addition of more \(\mathrm{PCl}_5\) caused a temporary imbalance, and the reverse reaction worked to consume the extra product and restore the equilibrium. In this process, the concentrations of the reactants (\(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\)) increased and the concentration of the product (\(\mathrm{PCl}_{5}\)) decreased to achieve a new balanced state.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium, stating that when a dynamic equilibrium in a chemical system is disturbed by a change in concentration, pressure, or temperature, the system will adjust to partially counteract that change and restore a new equilibrium. In simple terms, if you add something to the system, it will try to get rid of it, and if you remove something, it will try to replace it.

This principle helps to predict the direction of the equilibrium shift. For the reaction \[ \mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g) \]adding more \(\mathrm{PCl}_{5} \) disturbs the equilibrium, causing the reaction to respond by shifting towards the reactants (\(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\)). This shift occurs through an increase in the reverse reaction rate, consuming the excess \(\mathrm{PCl}_{5}\) to restore balance.

Reaction Rates

Reaction rates refer to the speed at which reactants are converted into products in a chemical reaction. The rate of a reaction is influenced by various factors, such as concentration, temperature, and pressure. In a dynamic equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction.

For the reaction \[ \mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g) \] there is a forward rate (formation of \(\mathrm{PCl}_{5}\)) and a reverse rate (conversion back to \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\)). Initially, these rates are equal. When more \(\mathrm{PCl}_{5}\) is added, the reverse rate becomes temporarily higher. As the system adjusts, both rates equalize again at the new equilibrium.

Equilibrium Shift

An equilibrium shift is the movement of the equilibrium position in response to a change in conditions, such as concentration, pressure, or temperature, according to Le Chatelier's Principle. In our reaction \[ \mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g) \] the addition of \(\mathrm{PCl}_{5}\) causes the equilibrium to shift towards the reactants. This happens because the system tries to minimize the disturbance by reducing the concentration of the added substance.

The reaction shifts in the direction where excess reactants or products are consumed. In this case, the excess \(\mathrm{PCl}_{5}\) is reduced by increasing the reverse reaction rate, thus forming more \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\). Eventually, a new equilibrium is established where the concentrations stabilize at new levels.

Dynamic Equilibrium

Dynamic equilibrium occurs in a reversible chemical reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, concentrations of reactants and products remain constant, not because the reactions have stopped, but because they occur at the same rate in both directions.

In the example of \[ \mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g) \] dynamic equilibrium is disturbed by adding \(\mathrm{PCl}_{5}\). This causes a temporary imbalance, with changes in reaction rates until a new equilibrium is reached. The reaction continues to occur in both directions, but the overall concentrations of \(\mathrm{PCl}_{3}\), \(\mathrm{Cl}_{2}\), and \(\mathrm{PCl}_{5}\) do not change at equilibrium.