Question

Assume that the reaction $$ 2 \mathrm{HBr}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) $$ is at equilibrium and the equilibrium conditions are changed as described. Indicate whether the forward or the reverse reaction rate is faster immediately after the change and explain your choice. (a) Some \(\mathrm{HBr}(\mathrm{g})\) is added without changing the total volume. (b) Some \(\mathrm{Br}_{2}(\mathrm{~g})\) is removed without changing the total volume. (c) The total volume of the system is halved.

Short answer

(a) Forward, (b) Forward, (c) No change.

Step-by-step solution

Analyze Change in (a)

When some \( \mathrm{HBr}(\mathrm{g}) \) is added, the concentration of the reactants increases. According to Le Chatelier's Principle, the system will try to counteract this change by favoring the forward reaction, as there are more reactants available to convert into products.

Predict Reaction Rate for (a)

Immediately after adding \( \mathrm{HBr}(\mathrm{g}) \), the forward reaction rate will be faster because the system is shifting towards the products to reach a new equilibrium.

Analyze Change in (b)

When some \( \mathrm{Br}_{2}(\mathrm{~g}) \) is removed, the concentration of the products decreases. Le Chatelier's Principle states the system will shift to produce more \( \mathrm{Br}_{2} \), favoring the forward reaction to restore balance.

Predict Reaction Rate for (b)

Immediately after removing \( \mathrm{Br}_{2}(\mathrm{~g}) \), the forward reaction rate is faster, as the system needs to replace the removed \( \mathrm{Br}_{2} \) to reestablish equilibrium.

Analyze Change in (c)

Halving the total volume of the system increases the pressure, as the number of gas moles decreases. The system will favor the side with fewer moles of gas. In the given reaction, there are 2 moles of gas reactants \((2 \mathrm{HBr})\) and 2 moles of gas products \((\mathrm{H}_{2} + \mathrm{Br}_{2})\), so volume change doesn't affect the equilibrium position.

Predict Reaction Rate for (c)

As the stoichiometry of moles of gas is equal on both sides and no shift in equilibrium occurs, neither the forward nor reverse reaction will be favored by the volume change alone.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium. It predicts how a change in conditions will affect the equilibrium state of a reaction. When a system at equilibrium experiences a disturbance, such as changes in concentration, pressure, or temperature, the system shifts to counteract the imposed change and restore equilibrium.
For example, in the reaction \(2 \mathrm{HBr}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g})\), adding more \(\mathrm{HBr}(\mathrm{g})\) increases the concentration of the reactant. According to Le Chatelier's Principle, the system will shift towards the right, favoring the forward reaction to use up the excess \(\mathrm{HBr}\).

• Change in Concentration: Increasing the concentration of reactants or products alters equilibrium by shifting the reaction to consume added substances.
• Change in Pressure: If a reaction involves gases, an increase in pressure will shift equilibrium toward the side with fewer gas molecules, thus minimizing pressure change.

Understanding Le Chatelier's Principle helps in predicting how a chemical system will respond to various changes, aiding in practical applications, such as industrial synthesis and processes.

Reaction Rates

Reaction rates describe how quickly a reaction occurs, and they can be influenced by various factors such as concentration, temperature, and catalysts.
In the context of the exercise, whenever a change is applied to a system at equilibrium, an immediate change in reaction rates occurs. For instance, adding \(\mathrm{HBr}(\mathrm{g})\) increases the forward reaction rate temporarily, as the system adjusts to the new conditions.

• Concentration Influence: Higher concentrations of reactants usually lead to a higher reaction rate because more reactant particles are available to collide and react.
• Temperature Influence: Increasing temperature generally accelerates reactions by providing energy that allows more particles to exceed the activation energy.
• Catalysts: These substances increase reaction rates without being consumed, by lowering the activation energy needed.

Recognizing the factors that influence reaction rates is crucial for controlling processes in laboratories and industry, where precise reaction speeds are often required.

Gas Reactions

Gas reactions, such as the equilibrium reaction \(2 \mathrm{HBr}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g})\), involve gaseous reactants and products. The behavior of gases in a chemical reaction can be well understood using principles of gas laws and equilibrium concepts.
In the scenario where the total volume of the system is halved, pressure increases due to the ideal gas law, \(PV = nRT\). However, since the moles of gas are equal on both sides of the equilibrium, pressure changes won’t favor either the forward or reverse reaction.

• Volume and Pressure Relationship: Volume changes impact pressure in gas reactions, shifting the equilibrium towards the side with fewer moles of gas if the two sides are unequal.
• Pressure Sensitivity: Reactions involving gases are sensitive to pressure changes, which is a critical consideration in designing chemical processes.

Understanding how gas reactions respond to changes in volume and pressure is vital for fields like chemical engineering and environmental science, where control over gas-phase reactions is essential.