Question

Suppose we have an equilibrium mixture of reactants and products for the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g)\) Predict the direction in which the reaction will shift when: (a) Chlorine \(\left(\mathrm{Cl}_{2}\right)\) gas is added. (b) Chlorine gas is removed. (c) \(\mathrm{PCl}_{5}\) is added. (d) \(\mathrm{PCl}_{3}\) is removed. (e) \(\mathrm{H}_{2}\) gas is added. (Assume the \(\mathrm{H}_{2}\) does not react with any reactant or product.)

Short answer

(a) The reaction will shift to the right (forward) when Cl₂ is added. (b) The reaction will shift to the left (backward) when Cl₂ is removed. (c) The reaction will shift to the left (backward) when PCl₅ is added. (d) The reaction will shift to the right (forward) when PCl₃ is removed. (e) There is no shift in the equilibrium when non-reactive H₂ gas is added.

Step-by-step solution

(a) Chlorine (Cl₂) gas is added

Adding Cl₂ gas will increase the concentration of Cl₂ in the system. According to Le Châtelier's principle, the reaction will shift in the direction that minimizes this increase in concentration. In this case, the reaction will shift to the right (forward), consuming some of the added Cl₂ gas and producing more PCl₅.

(b) Chlorine gas is removed

Removing Cl₂ gas will decrease the concentration of Cl₂ in the system. According to Le Châtelier's principle, the reaction will shift in the direction that counteracts this decrease in concentration. In this case, the reaction will shift to the left (backward), decomposing some of the PCl₅ into PCl₃ and Cl₂ to replenish some of the removed Cl₂.

(c) PCl₅ is added

Adding PCl₅ will increase the concentration of PCl₅ in the system. According to Le Châtelier's principle, the reaction will shift in the direction that minimizes this increase in concentration. In this case, the reaction will shift to the left (backward), consuming some of the added PCl₅ and producing more PCl₃ and Cl₂.

(d) PCl₃ is removed

Removing PCl₃ will decrease the concentration of PCl₃ in the system. According to Le Châtelier's principle, the reaction will shift in the direction that counteracts this decrease in concentration. In this case, the reaction will shift to the right (forward), consuming some of the Cl₂ and producing more PCl₅ and PCl₃ to replenish some of the removed PCl₃.

(e) H₂ gas is added

Adding H₂ gas does not directly affect the concentrations of the reactants or products in this reaction since it is non-reactive. Consequently, according to Le Châtelier's principle, there should be no shift in the equilibrium position of the reaction.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no overall change in the concentrations of reactants and products over time. However, this does not mean that the reactions have stopped; rather, they are occurring at equal rates, leading to a dynamic balance. Think of it as a tug-of-war where both teams are equally strong, keeping the rope in the same position.

For the reaction \(\mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g)\), equilibrium occurs when the conversion of reactants \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\) to product \(\mathrm{PCl}_{5}\) happens at the same rate as its decomposition back into the reactants. In most systems, this balance point does not correspond to equal concentrations; it is determined by the particular constants of the reaction at a given temperature.

Reaction Shift

A reaction shift refers to the change in the direction of a reversible reaction in response to an external stress, as predicted by Le Châtelier's principle. This principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will move to counteract the change.

In our example, when additional \(\mathrm{Cl}_{2}\) gas is added, the system responds by shifting the reaction to the right (forward) to produce more \(\mathrm{PCl}_{5}\) and reduce the extra \(\mathrm{Cl}_{2}\) concentration. Conversely, when \(\mathrm{Cl}_{2}\) is removed, the equilibrium shifts to the left (reverse) to replace the lost \(\mathrm{Cl}_{2}\). These shifts show the system's ability to adapt to maintain equilibrium in face of changes.

Equilibrium Concentration Changes

Equilibrium concentration changes occur when there are alterations in the levels of reactants or products in a reaction at equilibrium. According to Le Châtelier's principle, the system will adjust so as to minimize the effect of these changes.

For instance, the addition of a non-reactive gas like \(\mathrm{H}_{2}\) does not change the concentrations of reactants or products in our reaction, so the position of equilibrium remains unchanged. However, when the concentration of a reactive component is increased or decreased, such as the addition or removal of \(\mathrm{PCl}_{3}\) or \(\mathrm{PCl}_{5}\), the equilibrium concentrations will shift to rebalance the system. These concentration changes subsequently affect the equilibrium constant, a measure of the position of equilibrium, if the temperature remains the same.