Problem 27 - Chemistry for Allied Health

Question

If the enthalpy change is favorable and the entropy change is favorable, would the reaction be spontaneous at high temperatures, low temperatures, or all temperatures?

Step-by-Step Solution

Answer

The reaction is spontaneous at all temperatures.

Step 1: Understanding Favorable Enthalpy Change

A favorable enthalpy change means that enthalpy (H) is negative, indicating that the reaction is exothermic, releasing energy.

Step 2: Understanding Favorable Entropy Change

A favorable entropy change means that entropy (S) is positive, indicating an increase in disorder as the reaction proceeds.

Step 3: Analyzing Spontaneity Condition

According to the Gibbs Free Energy equation, \[ G = H - TS \] favored enthalpy and entropy qualitatively indicate that G will be negative across all temperatures since both terms contribute to a negative G.

Step 4: Concluding Temperature Influence on Spontaneity

Given \(H\) is negative and \(S\) is positive, the reaction will have a negative \(G\) for any temperature value because the negative term, \(T\00S\), will only enhance the negativity of the entire expression. Thus, the reaction is spontaneous at all temperatures.

Key Concepts

Enthalpy Change

The concept of enthalpy change is pivotal when analyzing chemical reactions. Enthalpy change, denoted as \(\Delta H\), refers to the total heat absorbed or released during a reaction. When the enthalpy change is negative, we describe the reaction as exothermic. This means that energy is released to the surroundings, making \(\Delta H\) negative.
Exothermic reactions, being energetically favorable, often proceed spontaneously, but it's important to note that enthalpy is just part of the bigger picture governing reaction spontaneity.

Entropy Change

Entropy change, indicated by \(\Delta S\), describes the change in the disorder or randomness within a system during a reaction. A positive entropy change means that the disorder has increased.
This increase in disorder is favorable; nature tends to move towards greater randomness and dispersal of energy. Hence, when a reaction has a positive \(\Delta S\), it contributes positively to the spontaneity of the process. Understanding the concept of entropy is crucial, as it's intricately linked with both the enthalpy and the Gibbs Free Energy of a reaction.

Spontaneous Reaction

A spontaneous reaction is one that occurs naturally without needing external energy. To assess spontaneity, we utilize the Gibbs Free Energy equation: \[ \Delta G = \Delta H - T\Delta S \]This equation provides insight into whether a reaction will be spontaneous by showing the relationship between enthalpy, entropy, and temperature.
For a reaction to be spontaneous, \(\Delta G\) must be negative. When \(\Delta H\) is negative and \(\Delta S\) is positive, \(\Delta G\) will be negative for all temperatures because the term \(T\Delta S\) becomes larger, reducing \(\Delta G\) irrespective of the temperature. Thus, such a reaction is spontaneous across all temperatures.