Question

The equilibrium constant \(K_{\text {eq }}\) is \(12.5\) at \(400^{\circ} \mathrm{C}\) and \(2.4\) at \(600^{\circ} \mathrm{C}\) for the reaction $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$ Is the reaction endothermic or exothermic?

Short answer

The given reaction is Exothermic.

Step-by-step solution

Interpret the Given Equilibrium Constants

The equilibrium constant \(K_{\text{eq}}\) at \(400^{\circ} \mathrm{C}\) is \(12.5\) and at \(600^{\circ} \mathrm{C}\) it is \(2.4\). This shows that as the temperature increases, the equilibrium constant decreases.

Apply Le Chatelier's Principle

According to Le Chatelier's principle, for an exothermic reaction, an increase in temperature will shift the equilibrium to the left, favoring the reverse reaction, thereby decreasing the value of \(K_{\text{eq}}\). On the other hand, for an endothermic reaction, an increase in temperature will shift the equilibrium to the right, favoring the forward reaction and increasing the value of \(K_{\text{eq}}\).

Determine the Type of Reaction

As the temperature is increased from \(400^{\circ} \mathrm{C}\) to \(600^{\circ} \mathrm{C}\), the \(K_{\text{eq}}\) value decreases from \(12.5\) to \(2.4\). This suggests that the equilibrium shifts towards the reactants as the temperature increases, meaning that the reaction is exothermic.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle helps us understand how a system at equilibrium reacts to changes in its environment. If a system at equilibrium experiences a change in temperature, pressure, or concentration, the system will adjust to counteract that change. This principle is crucial in predicting the direction of the shift in equilibrium. For example, if you increase the temperature of a system, and the reaction is exothermic, Le Chatelier's Principle indicates the equilibrium will shift towards the reactants. This shift aims to absorb the excess heat by favoring the endothermic (reverse) reaction.

• For exothermic reactions, increased temperature favors reactants.
• For endothermic reactions, increased temperature favors products.

By understanding Le Chatelier's Principle, we can predict how changes to a reaction environment, such as temperature, affect the position of equilibrium and the composition of the reaction mixture.

Equilibrium Constant

The equilibrium constant, denoted as \(K_{\text{eq}}\), is a numerical value that describes the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their respective coefficients. The magnitude of \(K_{\text{eq}}\) gives us insight into the position of equilibrium:

• If \(K_{\text{eq}}\) is large, the equilibrium favors the products.
• If \(K_{\text{eq}}\) is small, the equilibrium favors the reactants.

Changes in temperature can alter the value of \(K_{\text{eq}}\). When the temperature increases, this change can increase or decrease \(K_{\text{eq}}\) depending on whether the reaction is endothermic or exothermic. In the problem's scenario, an increase in temperature led to a decrease in \(K_{\text{eq}}\), indicating the formation of more reactants, which implied an exothermic reaction.

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy, often in the form of heat, to its surroundings. This release of energy occurs because the products of the reaction have lower enthalpy than the reactants, resulting in a net energy release.
A key characteristic of exothermic reactions is that they are often self-sustaining once initiated. As temperature increases, the equilibrium constant for an exothermic reaction typically decreases, suggesting that the equilibrium shifts towards the reactants as observed in the original problem. This behavior aligns with Le Chatelier's Principle, predicting that added heat will drive the reaction away from producing more heat, thus favoring the reverse reaction.