Question

Is it possible for a reaction to be nonspontaneous yet exothermic? Explain.

Short answer

Yes, if entropy decreases and temperature is high enough.

Step-by-step solution

Understanding Exothermic Reactions

An exothermic reaction is one where heat is released. This implies that the enthalpy change for the reaction, denoted as \( \Delta H \), is negative. This is because the products of the reaction have lower energy than the reactants.

Spontaneity and Gibbs Free Energy

The spontaneity of a reaction at constant temperature and pressure is governed by the Gibbs free energy change, \( \Delta G \). A reaction is spontaneous if \( \Delta G < 0 \). Gibbs free energy is calculated using the formula \( \Delta G = \Delta H - T\Delta S \), where \( T \) is the temperature and \( \Delta S \) is the change in entropy.

Examining Reaction Conditions

A reaction can be nonspontaneous (\( \Delta G > 0 \)) if the term \( T\Delta S \) is significant enough and negative to outweigh a negative \( \Delta H \). This would occur if the change in entropy \( \Delta S \) is negative, indicating a decrease in disorder, and the temperature is high enough to make \( T\Delta S > \Delta H \).

Conclusion on Possibility

Given this information, it is possible for an exothermic reaction (negative \( \Delta H \)) to be nonspontaneous if it results in a decrease in entropy (negative \( \Delta S \)) and is conducted at a high temperature, making \( \Delta G \) positive.

Key concepts

Exothermic Reactions

Exothermic reactions are chemical processes that release heat energy into their surroundings. When we talk about a reaction being exothermic, we mean that the change in enthalpy, denoted as \( \Delta H \), is negative. During such reactions, the energy of the products is less than that of the reactants.

Think of a burning match. It's releasing heat, a visible sign of an exothermic process. In any exothermic reaction, like combustion, the system loses energy, making the surroundings warmer.

The negative \( \Delta H \) implies energy is released, not absorbed. This distinguishes exothermic reactions from endothermic ones, which absorb energy from their surroundings.

Reaction Spontaneity

Spontaneity in chemical reactions means whether a process can occur on its own without external influence. It is not solely reliant on heat; instead, it's governed by the Gibbs Free Energy, represented as \( \Delta G \).

For a reaction to be spontaneous at constant temperature and pressure, \( \Delta G \) must be less than zero. But keep in mind, a negative \( \Delta G \) doesn't necessarily mean fast; spontaneity relates to potential, not speed.

• Spontaneous reactions have \( \Delta G < 0 \).
• Nonspontaneous reactions have \( \Delta G > 0 \).

Gibbs Free Energy is calculated using the formula: \( \Delta G = \Delta H - T\Delta S \). Both the enthalpy change (\( \Delta H \)) and the entropy change (\( \Delta S \)) influence \( \Delta G \). By understanding these changes, we can predict spontaneity.

Entropy Change

Entropy, symbolized as \( \Delta S \), is a measure of disorder or randomness in a system. When we talk about an increase in entropy, it means that the system has become more disordered.

In a reaction, if \( \Delta S \) is positive, the disorder increases. Conversely, a negative \( \Delta S \) indicates a decrease in disorder.

• Positive \( \Delta S \): The system becomes more random.
• Negative \( \Delta S \): The system becomes more ordered.

Entropy change plays a crucial role in determining if a reaction is spontaneous. Even if a reaction is exothermic (negative \( \Delta H \)), a negative and large enough \( \Delta S \) can make it nonspontaneous at high temperatures, as the term \( T\Delta S \) becomes substantial. Understanding these dynamics helps in predicting how a reaction will proceed.