Question

For each of the following systems at equilibrium, predict whether the reaction will shift to the right, left, or not be affected by a decrease in the reaction container volume. (a) \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) (b) \(2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\) (c) \(2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)\)

Short answer

(a) The reaction will shift to the right. (b) The reaction will not be affected. (c) The reaction will shift to the right.

Step-by-step solution

Examine equation (a)

The equation is \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\). On the reactant side, there are 2 moles of gas (1 mole of PCl3 and 1 mole of Cl2) and there is 1 mole of gas on the product side. When the volume decreases (pressure increases), the system will want to reduce this added pressure. Therefore, the reaction will shift to the side with fewer moles of gas, which is the right (or product) side in this case.

Examine equation (b)

The equation is \(2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\). On the reactant side, there are 2 moles of NO(g) and on the product side, there are 1 mole of N2(g) and 1 mole of O2(g), adding up to 2 moles of gas. In this case, a decrease in volume (or increase in pressure) won't favour either side more than the other as there are equal moles of gas on both sides. Therefore, the system's position will remain unaffected.

Examine equation (c)

The equation is \(2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)\). On the reactant side, there are 2 moles of gas and on the product side, there is 1 mole of gas. Therefore like in case a, when the volume decreases (pressure increases), the reaction will shift to the side with fewer moles of gas to mitigate this increased pressure. The reaction will shift to the right (or towards the product).

Key concepts

Equilibrium Shift

When we talk about equilibrium shift, it's all about how a reaction at equilibrium responds to a change. Le Chatelier's Principle helps us understand and predict this behavior. It states that if you disturb a system at equilibrium, the system will adjust itself to counteract that change and re-establish equilibrium. For instance, when the volume of a reaction container decreases, pressure increases. According to Le Chatelier's Principle, the system tries to reduce this stress by shifting towards the side of the reaction with fewer gas molecules. In the example with

• Equation (a): The reaction shifts to the right because the product side has fewer moles of gas (1 mole) compared to the reactant side (2 moles).
• Equation (b): The system remains unchanged because both sides have equal moles of gas.
• Equation (c): Similarly to equation (a), the reaction shifts to the right as there are fewer moles of gas on the product side (1 mole vs. 2 moles).

This concept of equilibrium shift is essential in understanding how various conditions affect the balance of reactions.

Reaction Kinetics

Reaction kinetics involves the study of the speed or rate of chemical reactions and how different variables influence these rates. Although kinetics might not dictate the direction in which a reaction at equilibrium will shift, it does provide insight into how fast the shift happens. Factors affecting reaction kinetics include:

• Temperature: Higher temperatures increase the energy of molecules, often increasing the reaction rate.
• Concentration: A higher concentration of reactants can lead to a faster reaction rate.
• Catalysts: Speed up reactions without being consumed by lowering the activation energy.

In equilibrium shifts due to changes such as a decrease in volume, reaction kinetics can determine how quickly the system adjusts to reach a new state of balance. Understanding both equilibrium and kinetics allows us to predict not only the direction of shift but the speed at which new equilibrium is achieved.

Gas Laws

Gas laws explain how gases behave under various conditions of temperature, pressure, and volume. These fundamental principles are critical in analyzing chemical reactions involving gases. The Ideal Gas Law, \(PV = nRT\), relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). Understanding these relationships helps us predict how a system at equilibrium will respond to changes in volume or pressure. - If the volume of a container decreases, the pressure increases if temperature is held constant.- This pressure increase causes a reaction at equilibrium to shift towards the side with fewer moles of gas.For the reactions in the example,

• Equation (a) and (c) demonstrate this principle by showing a shift towards the side with fewer moles of gas.
• Equation (b) shows no shift since both sides have equal moles of gas, proving that gas laws guide but do not force a shift if balanced.

By applying gas laws, students can better understand the quantitative aspect of equilibrium shifts and the conditions that influence them.