Question

A liquid solvent for chlorine is poured into a flask in which the following reaction is at equilibrium: \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+\) heat. How is the equilibrium affected when some of the chlorine gas dissolves?

Short answer

When some of the Cl2 gas dissolves in the liquid solvent, the equilibrium of the reaction $\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+$ heat will shift towards the right, as per Le Chatelier's principle. More PCl5 will be consumed to produce more PCl3 and Cl2 gas to re-establish equilibrium.

Step-by-step solution

Write the equilibrium expression

We can start by writing the equilibrium expression for the reaction: \[K_c = \frac{[\mathrm{PCl}_{3}][\mathrm{Cl}_2]}{[\mathrm{PCl}_5]}\] Where \(K_c\) is the equilibrium constant, and the concentrations are in the square brackets.

Analyze the change (dissolving Cl2)

Since some of the Cl2 gas dissolves in the liquid solvent, its concentration in the gas phase decreases. This reduces the concentration of Cl2 in the equilibrium expression we wrote earlier.

Apply Le Chatelier's principle

When the concentration of Cl2 decreases, the reaction will shift to re-establish equilibrium. According to Le Chatelier's principle, the reaction will shift in the direction that opposes the change. In this case, the system will shift to produce more Cl2 to offset the decrease in Cl2 concentration.

Determine equilibrium shift

Since the system needs to produce more Cl2, the equilibrium will shift to the right in the reaction: \[\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+\textrm{ heat}\] This means that the reaction will use up some of the PCl5, converting it into PCl3 and Cl2 to compensate for the loss of Cl2 due to dissolution.

Summarize the effect on equilibrium

In conclusion, when some of the Cl2 gas dissolves in the liquid solvent, the equilibrium of the reaction will shift towards the right. As a result, more PCl5 will be consumed to produce more PCl3 and Cl2 gas to re-establish equilibrium.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that predicts the behavior of a system when it is subjected to changes. More simply, it states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. Imagine a seesaw that balances perfectly. If you add weight to one side, the seesaw will tilt. To restore balance, you would either need to remove the added weight or add an equal weight to the opposite side. Le Chatelier's Principle is analogous to this seesaw, where the chemical system reacts to alleviate the imposed stress and strives to achieve a new balance.

For example, introducing more reactants or removing products from a reaction mixture will generally shift the equilibrium to produce more products. Conversely, adding more product or removing reactants will usually shift it to produce more reactants. This principle is crucial in industrial processes and laboratories as it allows chemists to understand and control reaction conditions for the desired outcomes.

Equilibrium Constant

The equilibrium constant, denoted as K, Kc when expressed in terms of concentrations, or Kp in terms of partial pressures, is a number that quantifies the extent of a chemical reaction at equilibrium. It is calculated from the ratio of the concentration of the products to the reactants, each raised to the power of its coefficient in the balanced chemical equation. This ratio is constant for a reaction at a given temperature.For instance, having a large equilibrium constant (greater than 1) means that, at equilibrium, the reaction mixture contains more products than reactants. Conversely, a small equilibrium constant (less than 1) indicates that reactants are favored, and the mixture contains more reactants than products. This constant is pivotal because it tells us the point at which the forward and reverse reactions occur at the same rate, resulting in no net change in the amounts of substances in the system.

Reaction Quotient

The reaction quotient, Q, evaluates the ratio of product concentrations to reactant concentrations at any point in time during a reaction, not just at equilibrium. The formula for Q mirrors that of the equilibrium constant but does not require the system to be at equilibrium. Q is used to predict the direction a reaction will shift to reach equilibrium based on current concentrations.

If QK, it means that there are too many products, and the reaction will shift to produce more reactants. When Q equals the K value, the system is at equilibrium. By comparing Q to K, we can determine the reaction's progress and forecast subsequent changes in the system.

Shift in Equilibrium

A shift in equilibrium refers to the movement of a reaction's position of equilibrium in response to an external change. There are several factors that can cause a shift in equilibrium, such as changes in concentration, temperature, and pressure. A shift signifies that the reaction is adjusting to reestablish equilibrium between the forward and reverse reactions.For example, when the concentration of a reactant or product is changed, the equilibrium will shift in a direction that helps restore balance. In the context of our original exercise, dissolving chlorine gas from a system at equilibrium would decrease its concentration in the gas phase, causing a shift to the right as the reaction seeks to produce more chlorine gas to compensate for the reduction. This is an application of both Le Chatelier's principle and the dynamics of reaction quotients influencing the equilibrium of a chemical system.