Question

Consider the following system at equilibrium: $$ \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g) $$ Suppose the concentration of \(\mathrm{CH}_{4}\) is decreased. (a) In which direction does the reaction shift to reestablish equilibrium? (b) What happens to the concentrations of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2}\), and \(\mathrm{H}_{2}\) as the reaction shifts to reestablish equilibrium?

Short answer

(a) The reaction shifts to the left to reestablish equilibrium. (b) The concentrations of \(\mathrm{H}_{2} \mathrm{O}\) increase, while the concentrations of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\) decrease.

Step-by-step solution

Identify the chemical equilibrium

The chemical equilibrium in question is the reaction:\[\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons\mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g)\]An equilibrium reaction reacts in both forward and backward direction.

Recognize changes to the equilibrium

The problem states that the concentration of \(\mathrm{CH}_{4}\) (methane) is decreased. This alteration is a 'stress' to the equilibrium.

Apply Le Chatelier's principle for step (a)

Le Chatelier's Principle states that if a stress is applied to a system at equilibrium, the system changes to relieve the stress. According to the principle, the system shifts in the direction that alleviates the stress. Thus, if \(\mathrm{CH}_{4}\) is decreased, the system will shift to the left to increase the concentration of \(\mathrm{CH}_{4}\) and reestablish equilibrium.

Apply Le Chatelier's principle for step (b)

If the system shifts to the left due to a decrease in \(\mathrm{CH}_{4}\) concentration, the system produces more of the reactants and consumes the products to reestablish equilibrium. Consequently, the concentrations of \(\mathrm{H}_{2} \mathrm{O}\) increase and the concentrations of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\) decrease.

Key concepts

Understanding Le Chatelier's Principle

When studying chemical reactions and how they achieve a state of balance, Le Chatelier's Principle is a cornerstone concept. Put simply, this principle offers a way to predict how a system at equilibrium will respond to changes. Imagine a crowded room where people move around to maintain personal space whenever more individuals enter or leave; similarly, chemical systems adjust to maintain equilibrium when 'stressed' by changes in conditions such as concentration, temperature, or pressure.

Under Le Chatelier's principle, if you decrease the concentration of a reactant, say methane (CH₄), the system reacts by 'trying' to produce more of that reactant. It does this by shifting the equilibrium towards the left, where methane is a product of the reverse reaction, thereby increasing its concentration until balance is reached again. This is akin to adding more chairs to a room when more guests arrive to keep everyone comfortable.

Equilibrium Shift Explained

An 'equilibrium shift' occurs when a system at balance is disturbed and it responds to restore equilibrium. This shift can be visualized as a balance scale where weights are added or removed, and the scale tips until it finds a new level.

In the context of the given chemical equation, removing CH₄ tips the balance, causing the equilibrium to shift to the left to try and replace it. We observe this shift in the reactant and product concentrations as the system seeks a new balance, which accommodates for the loss of CH₄. It’s important to note that equilibrium doesn't mean the reactants and products are equal in concentration, but rather that their ratio remains constant over time. Understanding this concept helps predict the direction of the shift and the resultant changes in reactant and product concentrations.

Reactant and Product Concentration Changes

Changing the concentration of a reactant or a product directly affects the chemical equilibrium. To visualize this, consider the concentration of substances as players in a tug-of-war: altering one concentration is like changing the strength of a participant, impacting the entire game.

When the concentration of a reactant, such as CH₄, is decreased, the reaction compensates by reducing the formation of products (CO₂ and H₂), while increasing the consumption of the remaining reactants (H₂O). This scenario results in a higher concentration of water and lower concentrations of carbon dioxide and hydrogen. Similarly, increasing a product's concentration would cause the system to shift to lower that concentration by forming more reactants. By comprehending this delicate balance, students can use Le Chatelier's principle to make accurate predictions about concentration changes in reactions under various stresses.