Question

Consider the effect of a volume change on this reaction at equilibrium. $$ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) $$ Predict the effect (shift right, shift left, or no effect) of these changes. (a) increasing the reaction volume (b) decreasing the reaction volume

Short answer

Increasing the reaction volume causes the equilibrium to shift to the right, while decreasing the reaction volume causes the equilibrium to shift to the left.

Step-by-step solution

Consider Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. When the volume of the reaction container is changed for a gaseous system at equilibrium, the system will shift to alleviate the change in pressure caused by the change in volume.

Analyze the effect of increasing the volume

Increasing the volume of the reaction container will decrease the pressure. Given the reaction \(\text{I}_{2}(g) \rightleftharpoons 2 \text{I}(g)\), there are more moles of gas on the right side of the equation. According to Le Chatelier's Principle, the system will shift to the side that has more moles of gas to increase the pressure. Therefore, the system shifts to the right (toward the side with more moles of gas, which is the products side in this case).

Analyze the effect of decreasing the volume

Decreasing the volume of the reaction container will increase the pressure. According to Le Chatelier's Principle, the system will shift to the side with fewer moles of gas to decrease the pressure. In this reaction, there are fewer moles of gas on the left side of the equation (reactants side). Therefore, the system shifts to the left.

Key concepts

Chemical Equilibrium

The concept of chemical equilibrium is pivotal in understanding how reactions behave when they have reached a state where the reactants and products are formed at the same rate.

At this point, the concentrations of reactants and products remain constant over time because the forward reaction (reactants to products) and the reverse reaction (products to reactants) proceed at equal rates. It’s important to note that this does not mean the amounts of reactants and products are equal, but that their rates of formation are. This dynamic state is sometimes represented by a double-arrow in the chemical equation, indicating the reversible nature of the process.

For a balanced reaction like \(\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)\), equilibrium does not imply that the system contains equal amounts of iodine molecules (\(\mathrm{I}_{2}\)) and iodine atoms (\(\mathrm{I}\)) but rather that the conversion from molecules to atoms and vice versa occurs at an equal pace. Any change to the equilibrium conditions will invoke an automatic response by the system, aiming to restore equilibrium – a principle laid out by Henri Louis Le Chatelier, known as Le Chatelier's Principle.

Reaction Volume Change

Understanding the effects of reaction volume changes can help us understand how a system at equilibrium responds to external pressure changes.

In a closed system where gases are involved, the pressure is related to the volume and number of moles of the gas, as outlined by the ideal gas law (\(PV = nRT\)). When the volume of a gaseous system at equilibrium is increased, the pressure decreases because the moles of gas now occupy a larger space. Conversely, decreasing the volume increases the pressure, as the same number of moles are now compressed into a smaller space.

In the reaction \(\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)\), changing the volume of the system will change the pressure. According to Le Chatelier's Principle, the system will respond by shifting the equilibrium to counter this change in pressure. Therefore, an increase in volume will decrease pressure and shift the equilibrium toward the side with more moles of gas to increase the pressure back up (shift right), while a decrease in volume will increase the pressure and shift the equilibrium to the side with fewer moles to reduce pressure (shift left).

Equilibrium Shift

An equilibrium shift occurs when a system at chemical equilibrium is disturbed by changes such as pressure/volume alteration, temperature shifts, or the addition/removal of reactants or products.

Le Chatelier's Principle guides us to predict the direction of the shift. In the context of the reaction \(\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)\), when the reaction volume is increased, the pressure drops and the system shifts toward the side with more gaseous moles (shift right). Likewise, reducing the volume causes an increase in pressure, pushing the equilibrium to the side with fewer gaseous moles (shift left). This shifting is the system's way of re-establishing equilibrium under new conditions.

It is essential to recognize that while the system adjusts to moderate the effects of a disturbance, it might result in a new equilibrium position where the concentrations of reactants and products are different from the original state, hence demonstrating the dynamic nature of chemical equilibrium.