Question

This reaction is endothermic. $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$$ Predict the effect (shift right, shift left, or no effect) of increasing and decreasing the reaction temperature. How does the value of the equilibrium constant depend on temperature?

Short answer

Increasing the temperature shifts the equilibrium to the right, while decreasing the temperature shifts it to the left. The value of the equilibrium constant increases with temperature for an endothermic reaction.

Step-by-step solution

Understand Endothermic Reactions

In endothermic reactions, energy is absorbed from the surroundings in the form of heat. According to Le Chatelier's principle, increasing the temperature of an endothermic reaction supplies more heat to the system, which the system will try to counteract by shifting the equilibrium position to the right to absorb the additional heat.

Predict the Effect of Increasing Temperature

For the given endothermic reaction \(\mathrm{C}(s) + \mathrm{CO}_2(g) \rightleftharpoons 2 \mathrm{CO}(g)\), increasing the temperature will cause the equilibrium to shift to the right (toward the products side), because the system will consume more heat and produce more \(\mathrm{CO}(g)\) to restore equilibrium.

Predict the Effect of Decreasing Temperature

When the temperature is decreased, the system loses heat. To counteract this, the equilibrium will shift to the left (toward the reactants side) in an attempt to produce more heat. As a result, more \(\mathrm{C}(s)\) and \(\mathrm{CO}_2(g)\) will be produced.

Determine the Effect on the Equilibrium Constant

The equilibrium constant \(K\) for a reaction is temperature-dependent. For an endothermic reaction, as the temperature increases, the equilibrium constant also increases, reflecting a greater proportion of products relative to reactants at equilibrium.

Key concepts

Le Chatelier's Principle

Le Chatelier's principle is a pivotal concept in chemical equilibrium which states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change. It's like a chemical seesaw that can tilt in response to external pressures, such as temperature changes, concentration alterations, or pressure modifications for gases.

When an endothermic reaction is subject to an increase in temperature, according to this principle, the system attempts to decrease the heat by shifting the equilibrium toward the products, which absorb the excess heat. Conversely, a decrease in temperature results in a shift toward the reactants, as the system tries to produce more heat. In essence, Le Chatelier's principle helps us predict how a reaction will respond to stress, ensuring that it finds a new balance point where the rate of the forward reaction again equals that of the reverse reaction.

Equilibrium Shift

An equilibrium shift refers to the movement of a reaction’s position of balance in response to a disturbance. This shift may occur towards the products (to the right) or reactants (to the left) and has direct implications for the concentrations of substances involved in the reaction.

In our exercise, an increase in temperature causes the equilibrium to shift to the right, favoring the formation of carbon monoxide (CO). This is observed as an increase in the concentration of CO, the product. Alternatively, a decrease in temperature would lead to a shift to the left, boosting the amounts of the original reactants, solid carbon (C) and carbon dioxide (CO2). Understanding how equilibrium shifts in response to changes enables students and chemists to manipulate and control reactions for desired outcomes.

Equilibrium Constant

The equilibrium constant, denoted as K, quantifies the relative concentrations of products and reactants at the point of chemical equilibrium for a particular reaction at a specific temperature. It is a measure of the extent of the reaction; larger values of K imply a greater concentration of products.

For the endothermic reaction in our exercise, the value of K is dependent on the temperature; specifically, K increases as the temperature increases, indicating that more products are favored at higher temperatures. Because the forward reaction (forming CO) is endothermic, increasing temperature makes the formation of CO more favorable, thus K rises. On the other hand, cooling the system down would result in a smaller K value, signifying a higher concentration of reactants. This temperature dependence of K is critical for scientists and engineers in designing processes and understanding reaction behavior under different thermal conditions.