Problem 65 - Chemical Principles: The Quest for Insight

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?

Step-by-Step Solution

Answer

Increasing \(CO_2\) decreases \(H_2\) pressure (a), decreasing \(CO\) increases \(CO_2\) pressure (b), increasing \(CO\) increases \(H_2\) concentration (c), and decreasing \(H_2O\) does not change the equilibrium constant (d).

Step 1: Analyze the Impact of Changing Concentrations on Equilibrium

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. This principle will be applied to predict the shifts in equilibrium when changes are made to the system.

Step 2: Part (a) – Impact of Increasing \(CO_2\) Partial Pressure

According to Le Chatelier’s principle, increasing the partial pressure of \(CO_2\) will result in the equilibrium shifting to the left to decrease the \(CO_2\) pressure. As a result, more \(CO\) and \(H_2O\) will be produced while the partial pressure of \(H_2\) decreases.

Step 3: Part (b) – Impact of Decreasing \(CO\) Partial Pressure

Decreasing the partial pressure of \(CO\) will shift the equilibrium to the right to increase the \(CO\) pressure. This shift will result in an increase in the production of \(CO_2\) and \(H_2\).

Step 4: Part (c) – Impact of Increasing \(CO\) Concentration

Increasing the concentration of \(CO\) will shift the equilibrium to the right in order to reduce the increase in \(CO\) concentration. This will cause more \(CO_2\) and \(H_2\) to form, thus increasing the concentration of \(H_2\).

Step 5: Part (d) – Impact of Decreasing \(H_2O\) Concentration

Decreasing the concentration of \(H_2O\) will shift the equilibrium to the left in an attempt to increase the \(H_2O\) concentration. The equilibrium constant \(K_c\) or \(K_p\), however, is a ratio of the concentrations or partial pressures of the products to reactants. Since this ratio is a constant at a given temperature, the equilibrium constant for the reaction remains unchanged by the concentration change.

Key Concepts

Le Chatelier's Principle

Le Chatelier's principle is a central concept in chemical equilibrium that predicts how a system at equilibrium reacts to disturbances or changes in conditions such as concentration, pressure, or temperature.

When a chemical system is at equilibrium and experiences a change in one of these conditions, the system will adjust to partially counteract the imposed change. For students to understand this concept better, imagine a balanced seesaw; if more weight is added on one side, the seesaw tilts until a new balance is achieved. Similarly, in a chemical reaction such as \( \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \), increasing the partial pressure of \( \text{CO}_2 \) (adding weight on the product side), will cause the system to shift towards the reactants side (tilts back) to reduce \( \text{CO}_2 \) pressure and restore equilibrium.

This principle helps to explain various phenomena in chemistry and is widely used in industrial processes to optimize the yield of chemical reactions.

Equilibrium Constant

The equilibrium constant, represented as \( K_c \) for molarity or \( K_p \) for partial pressures, is a value that expresses the ratio of the concentrations of products to reactants at equilibrium for a particular reaction at a constant temperature.

It's calculated using the concentrations or partial pressures of the reactants and products, raised to the power of their coefficients in the balanced chemical equation. For our reaction \( \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \), the equilibrium constant would be expressed as: \[ K_c = \frac{{[\text{CO}_2][\text{H}_2]}}{{[\text{CO}][\text{H}_2\text{O}]}}, \]
where the square brackets denote concentrations. The value of \( K_c \) or \( K_p \) does not change unless the temperature changes. If the system is at equilibrium and we alter the concentration of one or more components, the reaction will shift in a direction that brings \( K_c \) back to its original value, without the \( K_c \) itself changing.

Partial Pressure

Partial pressure is a concept that refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume on its own at the same temperature. In the context of our chemical reaction, each gas \( \text{CO}, \text{H}_2\text{O}, \text{CO}_2, \text{H}_2 \) has its own partial pressure.

When we discuss changes in the system, such as increasing or decreasing the partial pressure of a certain gas, we are dealing with how those changes affect the reaction's equilibrium. For instance, if we decrease the partial pressure of \( \text{CO} \), it's like reducing the 'presence' of \( \text{CO} \) in the gas mixture, which according to Le Chatelier's principle, will prompt the reaction to shift right, produce more \( \text{CO} \), hence increasing its partial pressure again. This adaptive behavior allows the reaction to maintain its equilibrium constant.

Reaction Quotient

The reaction quotient, \( Q \), is a measure that is similar to the equilibrium constant, but for a reaction mixture that is not at equilibrium. It's calculated in the same way as \( K_c \) or \( K_p \), using the current concentrations or partial pressures.

The reaction quotient is particularly useful for determining the direction in which a reaction will shift to reach equilibrium. If \( Q < K_c \), the reaction will proceed in the forward direction until equilibrium is reached. If \( Q > K_c \), the reaction will proceed in the reverse direction. When the system is at equilibrium, \( Q = K_c \). By understanding \( Q \), students can predict how changes like an increase in \( \text{CO} \) concentration will cause the reaction to shift right, as the system works to restore \( Q \) to the equilibrium constant, \( K_c \), and in doing so increases \( \text{H}_2 \) concentration.