Question

Suppose the reaction system $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ has already reached equilibrium. Predict the effect of each of the following changes on the position of the equilibrium. Tell whether the equilibrium will shift to the right, will shift to the left, or will not be affected. a. Any liquid water present is removed from the system. b. \(\mathrm{CO}_{2}\) is added to the system by dropping a chunk of dry ice into the reaction vessel. c. The reaction is performed in a metal cylinder fitted with a piston, and the piston is compressed to decrease the total volume of the system. d. Additional \(\mathrm{O}_{2}(g)\) is added to the system from a cylinder of pure \(\mathrm{O}_{2}\).

Short answer

a. Removing liquid water will cause the equilibrium to shift to the right. b. Adding \(\mathrm{CO}_{2}\) by dropping dry ice will shift the equilibrium to the left. c. Compressing the piston to decrease the volume will shift the equilibrium to the right. d. Adding additional \(\mathrm{O}_{2}(g)\) to the system will shift the equilibrium to the right.

Step-by-step solution

a. Effect of removing liquid water

According to Le Chatelier's principle, when liquid water (a product of the reaction) is removed from the system, the equilibrium will shift to counteract the change. In this case, the equilibrium will shift to the right, producing more CO_2 and H_2O. This is to replace the removed water and re-establish the equilibrium.

b. Effect of adding \(\mathrm{CO}_{2}\) by dropping dry ice

When \(\mathrm{CO}_{2}\) is added to the system, the concentration of \(\mathrm{CO}_{2}\) (a product of the reaction) increases. According to Le Chatelier's principle, the equilibrium will shift in the direction that reduces the concentration of \(\mathrm{CO}_{2}\) to restore the original equilibrium. In this case, the equilibrium will shift to the left, consuming the additional \(\mathrm{CO}_{2}\) and producing more \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\).

c. Effect of compressing the piston to decrease the volume

When the volume of the system is reduced, the pressure increases. To minimize the increase in pressure, the equilibrium will shift in the direction that reduces the number of gas molecules. Comparing the numbers of gas molecules on both sides of the reaction, we see that there are 3 moles of gas on the left side (1 mole of \(\mathrm{CH}_{4}\) and 2 moles of \(\mathrm{O}_{2}\)) and only 1 mole of gas on the right side (\(\mathrm{CO}_{2}\)). Thus, to respond to the increase in pressure, the equilibrium will shift to the right, reducing the number of gas molecules by converting \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) into \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\).

d. Effect of adding additional \(\mathrm{O}_{2}(g)\)

When additional \(\mathrm{O}_{2}\) is added to the system, the concentration of \(\mathrm{O}_{2}\) (a reactant) increases. According to Le Chatelier's principle, the equilibrium will shift in the direction that reduces the concentration of \(\mathrm{O}_{2}\) to restore the original equilibrium. In this case, the equilibrium will shift to the right, consuming the additional \(\mathrm{O}_{2}\) and producing more \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\).

Key concepts

Chemical Equilibrium

In a chemical reaction, equilibrium is the state at which the rate of the forward reaction equals the rate of the backward reaction. This means the concentrations of reactants and products remain constant over time. The reaction \( \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \) is an example of an equilibrium reaction in a closed system.
When equilibrium is reached, the continuous change in the system no longer appears.
Le Chatelier's Principle can predict how equilibrium will adjust to initial changes in concentration, pressure, or temperature.

Reaction Shift

The term "reaction shift" refers to the movement of equilibrium in response to a change. If a change occurs, like removing a product or adding a reactant, the system shifts to counteract the change and restore equilibrium.

• If a product like water is removed, the equilibrium shifts right, producing more products to replace it.
• Adding a product like carbon dioxide shifts equilibrium left to consume the extra CO₂.

The direction of the shift depends on which side of the reaction needs to be more active to balance the modification. This aligns the equilibrium adjustments with Le Chatelier's Principle.

Pressure Effect

Pressure changes affect reactions involving gases, like our example. When a system's pressure is increased, the equilibrium tends to shift in the direction that reduces the number of gas molecules. For this reaction:

1. Left side gases: 1 mole of \( \mathrm{CH}_{4} \) and 2 moles of \( \mathrm{O}_{2} \)
2. Right side gas: 1 mole of \( \mathrm{CO}_{2} \)

Compressing the reaction volume increases pressure.
Equilibrium shifts to the right to form more \( \mathrm{CO}_{2} \), lowering the total number of gas molecules and thus pressure. This change helps to restore equilibrium consistency when pressure increases.

Concentration Change

Altering concentrations of reactants or products can make the equilibrium shift to restore balance. For example:

• Adding \( \mathrm{O}_{2} \), a reactant, increases its concentration causing a shift to the right. More \( \mathrm{CH}_{4} \) is converted to \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \).
• Removing liquid water also shifts equilibrium to the right to compensate for the loss.

Changes like these highlight the responsive nature of equilibrium to concentration variations under Le Chatelier's Principle, striving to balance the reaction system efficiently.