Question

Consider the equilibrium \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\) \(\mathrm{H}_{2}(\mathrm{~g})\). (a) If the partial pressure of \(\mathrm{CO}_{2}\) is increased, what happens to the partial pressure of \(\mathrm{H}_{2}\) ? (b) If the partial pressure of \(\mathrm{CO}\) is decreased, what happens to the partial pressure of \(\mathrm{CO}_{2}\) ? (c) If the concentration of \(\mathrm{CO}\) is increased, what happens to the concentration of \(\mathrm{H}_{2}\) ? (d) If the concentration of \(\mathrm{H}_{2} \mathrm{O}\) is decreased, what happens to the equilibrium constant for the reaction?

Short answer

Increasing the partial pressure of CO2 decreases the partial pressure of H2. Decreasing the partial pressure of CO increases the CO2 partial pressure. Increasing CO concentration increases H2 concentration. Decreasing H2O concentration does not change the equilibrium constant.

Step-by-step solution

Understand Le Chatelier's Principle

Le Chatelier's Principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to partially counteract the change imposed and a new equilibrium will be established. Examples of external changes include changing the concentration of reactants or products, pressure, volume, or temperature of the system.

Analyze the Effect of Increased CO2 Partial Pressure on H2 Partial Pressure

Applying Le Chatelier's Principle, if the partial pressure of CO2 is increased, the equilibrium will shift to the left to counteract this change by reducing the amount of CO2 and producing more CO and H2O. Consequently, the partial pressure of H2 will decrease.

Analyze the Effect of Decreased CO Partial Pressure on CO2 Partial Pressure

If the partial pressure of CO is decreased, the equilibrium will shift to the right to counteract this change by using up H2O and producing more CO2 and H2. Therefore, the partial pressure of CO2 will increase.

Analyze the Effect of Increased CO Concentration on H2 Concentration

Increasing the concentration of CO will cause the equilibrium to shift to the right, producing more CO2 and H2. As a result, the concentration of H2 will increase.

Analyze the Effect of Decreased H2O Concentration on the Equilibrium Constant

The equilibrium constant for a reaction at a given temperature is a fixed value and does not change with changes in concentration. Decreasing the concentration of H2O will cause the position of the equilibrium to shift to the right, but the equilibrium constant (K) remains the same.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, resulting in no net change in the concentration of the reactants and products. It's essential to understand that at equilibrium, the reactions are still occurring, but with no observable changes in concentration over time.

What's fascinating is this dynamic balance, where the forward and reverse reaction rates are equivalent, enabling the system to appear static, yet it's incredibly active on a molecular level. When the system is disturbed, Le Chatelier's Principle comes into play, offering insight into how the system will adjust to re-establish a new state of equilibrium.

Equilibrium Constant (K)

The equilibrium constant (K) is a value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficient in the balanced chemical equation. It is symbolized as K and is specific to a given reaction at a particular temperature.

The equation for the equilibrium constant is written as: \[ K = \frac{[\text{Products}]^{\text{coefficient}}}{[\text{Reactants}]^{\text{coefficient}}} \]
Where square brackets indicate concentration in molarity (mol/L). The value of K provides insight into the position of the equilibrium and predicts the direction of the reaction. A large K signifies a significant concentration of products at equilibrium, while a small K indicates a predominant concentration of reactants.

Reaction Quotient

The reaction quotient (Q) serves as a mathematical 'snapshot' of a reaction's position at a given point in time. It has the same form as the equilibrium constant but isn't limited to equilibrium conditions. It's calculated by substituting the actual concentrations of the reactants and products into the equilibrium expression.

When Q and K are compared, they inform whether the reaction at its current state will shift to reach equilibrium. If \( Q < K \) the reaction will proceed forward to produce more products. If \( Q > K \) the reaction will move in the reverse direction, yielding more reactants. If \( Q = K \) the system is already at equilibrium.

Partial Pressure

In reactions involving gases, the partial pressure is used as an alternative to concentration. It refers to the pressure exerted by a particular gas in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of individual gases.

Key for equilibrium involving gases, Le Chatelier's Principle, connects to changes in partial pressure similar to concentration changes. If the partial pressure of a gas is increased, the equilibrium will shift away from the gas to lower its pressure, and vice versa. It's a delicate balancing act that equilibrium plays, smartly adjusting pressure to maintain a balanced system amid changes.