Question

Examine the relationship between \(K\) eq and temperature. Use Le Châtelier's principle to deduce whether the forward reaction is exothermic or endothermic.

Short answer

To deduce whether the forward reaction is exothermic or endothermic, we need to examine the relationship between \(K_{eq}\) and temperature, and apply Le Châtelier's principle. An increase in \(K_{eq}\) with increasing temperature indicates an endothermic forward reaction, while a decrease in \(K_{eq}\) with increasing temperature indicates an exothermic forward reaction.

Step-by-step solution

Understanding Le Châtelier's Principle and Equilibrium Constants

Le Châtelier's principle states that when a system at equilibrium experiences a change, it will adjust itself to minimize the effect of the change, and eventually reach a new equilibrium. In the context of chemical reactions, this can involve shifts in the position of the equilibrium to favor either the forward or reverse reaction. The equilibrium constant, \(K_{eq}\), is the ratio of the concentrations of products and reactants at equilibrium, and is affected by changes in temperature. It can provide valuable insights into the behavior of a reaction when temperature changes occur.

Relationship between \(K_{eq}\) and Temperature for Exothermic and Endothermic Reactions

According to the Van't Hoff equation, an increase in temperature typically leads to a decrease in \(K_{eq}\) for an exothermic reaction, as heat is taken as a product. In contrast, for endothermic reactions, an increase in temperature generally causes an increase in \(K_{eq}\), as heat is considered a reactant.

Applying Le Châtelier's principle

To deduce whether the forward reaction is exothermic or endothermic, we will consider two different cases based on the behavior of \(K_{eq}\) with temperature: 1. If, upon increasing the temperature, \(K_{eq}\) increases, this indicates that the system shifts towards the products in response to the change in temperature. According to Le Châtelier's principle, this means that the forward reaction must be endothermic, as the system tries to absorb the additional heat by favoring the reaction that consumes heat. 2. Conversely, if an increase in temperature leads to a decrease in \(K_{eq}\), it means the system shifts towards reactants. In this scenario, the forward reaction must be exothermic, as the system tries to counteract the added heat by favoring the reaction that releases heat.

Conclusion

In order to deduce whether the forward reaction is exothermic or endothermic, we need to examine the relationship between \(K_{eq}\) and temperature, and apply Le Châtelier's principle. An increase in \(K_{eq}\) with increasing temperature indicates an endothermic forward reaction, while a decrease in \(K_{eq}\) with increasing temperature indicates an exothermic forward reaction.

Key concepts

Equilibrium Constant

The equilibrium constant, represented as \(K_{eq}\), is a crucial concept in chemical reactions. It is a measure of the ratio of the concentration of products to reactants when a reaction is at equilibrium. A higher \(K_{eq}\) value implies that at equilibrium, the products are favored, while a lower value suggests that the reactants are more prevalent.

Understanding \(K_{eq}\) helps us predict the direction of the reaction shift when changes occur within the system, such as temperature fluctuations. According to Le Châtelier's Principle, a system in equilibrium will adjust to counteract any changes imposed on it, thus reaching a new equilibrium state.

Exothermic Reaction

An exothermic reaction is one that releases heat as it proceeds. This is why such reactions are visually represented with heat as a product. In the context of equilibrium, if an increase in temperature results in a decrease in the equilibrium constant \(K_{eq}\), it suggests that the forward reaction is exothermic.

Upon heating, the system attempts to minimize the effect of added heat by shifting the equilibrium towards the reactants, the process that absorbs heat, in accordance with Le Châtelier’s Principle. Exothermic reactions are important in various applications, including combustion and the formation of chemical bonds.

Endothermic Reaction

Endothermic reactions, in contrast to exothermic ones, absorb heat from their surroundings. When such reactions occur, temperature plays a significant role. If increasing the temperature leads to an increase in \(K_{eq}\), the forward reaction can be deduced to be endothermic. This indicates that the system absorbs the heat by shifting the equilibrium towards the products.

This behavior is descriptive of many melting and evaporating processes where heat absorption is essential. Le Châtelier’s Principle assists in predicting how such systems will respond to temperature changes, highlighting whether heat is consumed or released.

Van't Hoff Equation

The Van't Hoff equation provides a mathematical relationship between the equilibrium constant \(K_{eq}\) and temperature. Given by the expression:\[\frac{{d \, ext{ln}(K_{eq})}}{{dT}} = \frac{{\Delta H}}{{R T^2}}\]where \( \Delta H \) is the enthalpy change and \( R \) is the universal gas constant, this equation links heat effects in reactions with changes in temperature.

By analyzing this equation, we can infer whether a reaction is exothermic or endothermic based on how \(K_{eq}\) varies with temperature. For exothermic reactions, \(K_{eq}\) decreases with an increase in temperature, as \( \Delta H \) is negative. Conversely, for endothermic reactions, \(K_{eq}\) increases with temperature, reflecting positive \( \Delta H \). The Van’t Hoff equation is a powerful tool for chemists to predict the behavior of chemical equilibria as they explore different reaction conditions.