Question

If a temperature change causes the equilibrium constant to become smaller in value, in which direction does the temperature change cause the equilibrium to shift? Explain.

Short answer

The question pertains to a decrease in the equilibrium constant due to a temperature change which indicates that the equilibrium is shifting left, favoring the reactants. This implies that the reaction must be exothermic (releasing heat), thus, temperature must be increasing.

Step-by-step solution

Understanding Le Chatelier's Principle

According to Le Chatelier's Principle, if a change is made to a system that is in equilibrium, the system will respond by shifting its equilibrium position in a way that counteracts the applied change. In the context of temperature changes, if the reaction is exothermic (releases heat), an increase in temperature will cause the system to shift to the left, favoring the reactants. If the reaction is endothermic (absorbs heat), an increase in temperature will shift the system to the right, favoring the products.

Relating Equilibrium Constant to Temperature

When the equilibrium constant (K) becomes smaller, it means that the concentration of the reactants is becoming larger compared to the concentration of the products (Since \( K = \frac{[Products]}{[Reactants]} \)). This is associated with a shift to the left in the equilibrium position.

Determining the Direction of the Shift

We know that an exothermic reaction would shift left with an increase in temperature, and we also know that a decrease in the equilibrium constant (K) corresponds to a shift to the left. Therefore, given that the equilibrium constant becomes smaller, temperature must be increasing and we can deduce that the reaction is exothermic which means that the equilibrium shifts to the left.

Key concepts

Equilibrium Constant

The equilibrium constant, often represented by the symbol \( K \), is a numerical value that describes the ratio of the concentrations of products to reactants at equilibrium. It's formulated as: \[K = \frac{[\text{Products}]}{[\text{Reactants}]}\] A high equilibrium constant means that at equilibrium, products are favored, while a low equilibrium constant indicates that reactants are favored. The value of the equilibrium constant is key in understanding the position of equilibrium in a chemical reaction.

• If \( K \) is large, products dominate at equilibrium.
• If \( K \) is small, reactants dominate at equilibrium.

The equilibrium constant is sensitive to temperature changes. When the temperature influences a reaction, \( K \) can either increase or decrease, leading to a shift in equilibrium position. Understanding this shift is integral for predicting how a reaction will respond to changes in conditions.

Temperature Change

Changes in temperature can significantly affect the equilibrium position of a reaction. According to Le Chatelier's Principle, the system will adjust to counteract the effect of the temperature change. For any reaction, the impact of a temperature change depends on whether the reaction is exothermic (releases heat) or endothermic (absorbs heat).

• Exothermic reaction: Increasing the temperature shifts the equilibrium to favor reactants, as the system tries to absorb the added heat.
• Endothermic reaction: Increasing the temperature shifts the equilibrium to favor products, helping the system utilize the extra heat.

If the equilibrium constant decreases with an increase in temperature, it suggests that the reaction is exothermic. This is important for students to understand because it demonstrates how temperature can shift equilibria in ways that might not initially seem intuitive.

Exothermic Reaction

In an exothermic reaction, heat is released into the surroundings. This occurs when the energy needed to break bonds in the reactants is less than the energy released when new bonds form in the products. Such reactions often feel hot to the touch due to this heat release. In terms of equilibrium, an increase in temperature adds extra energy into the system, which shifts the equilibrium position towards the reactants.

• This shift to the left makes reactants more prevalent, explaining the smaller value of the equilibrium constant.
• Recognizing whether a reaction is exothermic is crucial for predicting how temperature changes will affect equilibrium.

Therefore, in an exothermic reaction, when the equilibrium constant decreases with an increase in temperature, we can conclude that the equilibrium shifts to the left, favoring the formation of reactants.