Problem 25 - Chemistry for Allied Health

Question

Under what conditions of enthalpy and entropy change is a reaction always spontaneous? Under what conditions is a reaction never spontaneous?

Step-by-Step Solution

Answer

The reaction is always spontaneous when \( \Delta H < 0 \) and \( \Delta S > 0 \); never spontaneous when \( \Delta H > 0 \) and \( \Delta S < 0 \).

Step 1: Understanding Spontaneity in Terms of Gibbs Free Energy

The spontaneity of a reaction is determined by the Gibbs Free Energy change, represented as  \( \Delta G \). A reaction is spontaneous if \( \Delta G < 0 \). The equation for Gibbs Free Energy is \( \Delta G = \Delta H - T \Delta S \), where \( \Delta H \) is the enthalpy change, \( \Delta S \) is the entropy change, and \( T \) is the temperature in Kelvin.

Step 2: Conditions for Always Spontaneous Reaction

For a reaction to always be spontaneous, \( \Delta G \) must always be less than zero (\( \Delta G < 0 \)) regardless of the temperature. This happens when \( \Delta H < 0 \) (exothermic) and \( \Delta S > 0 \) (increase in entropy), because both terms in \( \Delta G = \Delta H - T \Delta S \) will then contribute to a negative value of \( \Delta G \).

Step 3: Conditions for Never Spontaneous Reaction

For a reaction to never be spontaneous, \( \Delta G \) must always be greater than zero (\( \Delta G > 0 \)) regardless of the temperature. This occurs when \( \Delta H > 0 \) (endothermic) and \( \Delta S < 0 \) (decrease in entropy), leading to a positive value of \( \Delta G = \Delta H - T \Delta S \).

Step 4: Summary of Conditions

A reaction is always spontaneous when \( \Delta H < 0 \) and \( \Delta S > 0 \). A reaction is never spontaneous when \( \Delta H > 0 \) and \( \Delta S < 0 \).

Key Concepts

Enthalpy Change

Enthalpy change, represented by the symbol \( \Delta H \), is a measure of the total energy change in a system during a process. This energy change can be due to the absorption or release of heat. Enthalpy is an important concept in chemistry because it helps predict the energy flow in reactions.
The value of \( \Delta H \) can tell us if a reaction is:

• Exothermic—where \( \Delta H < 0 \), indicating that energy is released into the surroundings.
• Endothermic—where \( \Delta H > 0 \), indicating that energy is absorbed from the surroundings.

Knowing whether a reaction is endothermic or exothermic plays a crucial role in understanding if and when a chemical reaction can occur spontaneously.

Entropy Change

Entropy, symbolized as \( \Delta S \), is a measure of the disorder or randomness in a system. A high entropy change generally means more disorder in the system post-reaction. In thermodynamics, processes that lead to increased entropy tend to be favored energetically because they spread out energy more evenly across the system.
The nature of \( \Delta S \) can influence the spontaneity of a reaction:

• If \( \Delta S > 0 \), the process increases the system's randomness.
• If \( \Delta S < 0 \), the process decreases the system's randomness.

Increasing entropy is generally favored because it's aligned with the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time.

Reaction Spontaneity

Reaction spontaneity is whether a reaction can proceed on its own without external inputs. This is mostly discussed in terms of Gibbs Free Energy, \( \Delta G \), defined by the equation: \( \Delta G = \Delta H - T \Delta S \).
A reaction is considered spontaneous if \( \Delta G < 0 \). In other words, the process must favor conditions that naturally decrease the system's free energy:

• When \( \Delta H \) is negative (exothermic) and \( \Delta S \) is positive (entropy increases), \( \Delta G \) is always negative, favoring spontaneity.
• Conversely, if \( \Delta H \) is positive and \( \Delta S \) is negative, you have unfavorable conditions, leading \( \Delta G \) to be positive, and thus the reaction is non-spontaneous.

This understanding helps predict under what conditions reactions will occur without intervention.

Exothermic and Endothermic Reactions

Reactions can be broadly categorized into two types based on how they interact with energy from their surroundings: exothermic and endothermic reactions.

• In exothermic reactions, \( \Delta H < 0 \), meaning heat is released to the surroundings, often making reactions more favorable or spontaneous at lower temperatures.
• In endothermic reactions, \( \Delta H > 0 \), meaning heat is absorbed from the surroundings. These reactions might require continuous energy input unless other conditions, like a very high increase in entropy, drive the reaction.

Understanding whether a reaction is exothermic or endothermic helps determine the energy requirements and feasibility of chemical processes in real-world applications.