Question

For each of the following systems at equilibrium, predict whether the reaction will shift to the right, left, or not be affected by an increase in the reaction container volume. (a) \(\mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) (c) \(\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \Longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g)\)

Short answer

For reaction (a), the equilibrium will shift to the left. For reaction (b), the equilibrium will shift to the right. For reaction (c), the equilibrium will not be affected.

Step-by-step solution

Problem (a)

For the system \(\mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\), there are 5 moles of gas on the left and 3 moles of gas on the right. An increase in volume decreases the pressure and the system will shift to the direction that counteracts the decrease in pressure, i.e., the direction with more moles of gas. Hence the reaction will shift to the left.

Problem (b)

For the system \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\), there are 0 moles of gas on the left and 1 mole of gas on the right. The reaction will shift to the direction that counteracts the decrease in pressure due to increased volume, i.e., where there are more moles of gas. Hence, the reaction will shift to the right.

Problem (c)

For the system \(\mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{SO}_{3}(g)\), there are 2 moles of gas on the left and 2 moles of gas on the right. As the number of moles of gases are the same on both sides, an increase in volume (or decrease in pressure) does not favor a shift in any direction. Hence, the reaction will not be affected.

Key concepts

Le Chatelier's principle

Le Chatelier's principle is a key concept in chemistry that helps us understand how equilibrium in a chemical reaction responds to external changes. According to this principle, if a dynamic equilibrium is disturbed by an external change, such as pressure, temperature, or concentration, the system will adjust itself to minimize the impact of that change.
For example, consider a reaction at equilibrium inside a closed container. If we increase the container's volume, we effectively lower the pressure inside. Le Chatelier's principle suggests that the equilibrium will shift to counteract this pressure change. The system will shift towards the side of the reaction with more moles of gas, since increasing the number of moles can help increase the pressure and restore equilibrium.

This principle is particularly useful for predicting the direction of the shift when a reaction container undergoes changes. It allows chemists to understand how to manipulate conditions to favor the production of desired products or reactants in industrial and lab settings.

Reaction container volume

The volume of a reaction container can significantly affect the equilibrium position of a gas-phase reaction. When the volume is increased, the pressure inside the container decreases, as pressure and volume are inversely proportional (according to Boyle's Law).
This decrease in pressure will cause the equilibrium to shift towards the side of the reaction with a greater number of gas moles. Conversely, if the volume is decreased, the pressure increases, and the equilibrium will shift towards the side with fewer gas moles to compensate for the increase in pressure.
For example, in the reaction \( \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \), increasing the container volume results in a shift to the left. This happens because there are more moles of gases (5 moles) on the reactant side compared to the product side (3 moles). Such behavior aligns with Le Chatelier's principle as the reaction attempts to increase pressure by producing more gas molecules.

Gas moles in reactions

Understanding the role of gas moles in a reaction is crucial for predicting how equilibrium will shift in response to changes in volume and pressure. The number of gas moles indicates how many molecules of gas are present on each side of the chemical equation.
This becomes important when the pressure is altered, either by changing the reaction container's volume or applying external pressure. If a reaction at equilibrium experiences a decrease in pressure due to an increase in volume, it will shift towards the side with more gas moles to counteract the change. For example, if we consider the reaction system \( \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \), there are zero moles of gas on the left and one mole on the right. An increase in volume causes the equilibrium to move to the right, where the gas mole presence is greater.
By analyzing the number of moles of gases on both sides of a balanced equation, chemists can predict how a reaction will adjust under varying conditions, hence allowing control over reaction outcomes.