Problem 57 - Chemistry Matter and Change

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?

Step-by-Step Solution

Answer

The equilibrium shifts to the right, producing more PCl_3(g) and Cl_2(g).

Step 1: Identify the Change

The problem states that some chlorine gas (Cl_2(g)) dissolves in the solvent, removing it from the gas phase and thus decreasing its concentration in the equilibrium mixture.

Step 2: Apply Le Chatelier's Principle

According to Le Chatelier's Principle, if a dynamic equilibrium is disturbed by changing the conditions, the equilibrium position will shift to counteract the effect of the disturbance. In this case, the removal of Cl_2(g) will cause the equilibrium to shift towards the products' side (to the right) to create more Cl_2.

Step 3: Predict the Effect on Equilibrium Position

As the equilibrium shifts to the right to re-establish the balance, more PCl_3(g) and Cl_2(g) are produced while consuming some of the PCl_5(g). This shift results in an increase in the concentrations of PCl_3 and Cl_2, and a decrease in the concentration of PCl_5.

Key Concepts

Equilibrium Shift

When dealing with chemical reactions at equilibrium, an equilibrium shift refers to the change in the concentrations of reactants and products when the system is disturbed. This shift occurs in response to an external change, such as concentration, pressure, or temperature, according to Le Chatelier's Principle. In the given exercise, dissolving some chlorine gas in a solvent reduced its concentration in the gas phase, causing the reaction to shift towards the right. This means more products are formed to make up for the loss of chlorine.

• **Disturbance**: Removing some Cl\(_2\) from the gas phase.
• **Equilibrium Shift Direction**: Towards the products.
• **Result**: Increased production of PCl\(_3\) and Cl\(_2\); decreased PCl\(_5\) concentration.

Understanding how and why equilibrium shifts occur helps in predicting the outcomes of changes in dynamic systems. Each shift aims to counteract the applied disturbance, allowing the system to establish a new state of balance.

Chemical Equilibrium

Chemical equilibrium represents a state where the concentrations of reactants and products remain unchanged over time. This happens when the forward and reverse reactions occur at equal rates. For the reaction \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+\text{heat}\), this means that the breakdown of \(\mathrm{PCl}_{5}\) into \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\) is happening at the same rate as their recombination back into \(\mathrm{PCl}_{5}\).
In practice:

• A dynamic balance exists with no net change in the concentrations.
• The equilibrium constant \(K_c\) indicates the ratio of concentrations of products to reactants at equilibrium.
• At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction.

Chemical equilibrium does not imply equal concentrations of reactants and products, but a constant ratio defined by \(K_c\). This state is sensitive to changes in conditions, as described by Le Chatelier's Principle.

Reaction Dynamics

Reaction dynamics focuses on the processes and conditions that affect the speed and outcome of chemical reactions. It explores how molecules interact, collide, and transform into products.
In the context of equilibrium reactions like the dissociation of \(\mathrm{PCl}_{5}\) into \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\), the reaction dynamics are influenced by factors such as:

• **Molecular collisions**: The frequency and energy of collisions between molecules can impact reaction rates.
• **Temperature**: Higher temperatures generally increase reaction rates by providing more energy for collisions.
• **Concentration changes**: Shifting concentrations affect the direction of the equilibrium shift and the reaction speed.

Understanding these dynamics is crucial for manipulating chemical processes in industries and research. It helps predict how fast a system can reach equilibrium and adjust conditions to favor desired outcomes. Reaction dynamics provide a deeper insight into the mechanisms behind reaching and maintaining equilibrium.