Problem 18 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following pairs of a chemical reaction is certain to result in a spontaneous reaction? (a) exothermic and increasing disorder (b) exothermic and decreasing disorder (c) endothermic and increasing disorder (d) endothermic and decreasing disorder

Step-by-Step Solution

Answer

The pair (a) exothermic and increasing disorder is certain to result in a spontaneous reaction.

Step 1: Understand the Problem

The problem asks us to identify which pair of conditions will guarantee a spontaneous chemical reaction. A spontaneous reaction is one that occurs without external influence.

Step 2: Know the Criteria for Spontaneity

The spontaneity of a reaction depends on the Gibbs free energy change (\(\Delta G\)). The reaction is spontaneous if \(\Delta G < 0\). The Gibbs free energy is given by the equation \(\Delta G = \Delta H - T\Delta S\), where \(\Delta H\) is the enthalpy change, \(T\) is the temperature, and \(\Delta S\) is the entropy change.

Step 3: Analyze the Options

For option (a), both an exothermic reaction (\(\Delta H < 0\)) and increasing disorder (\(\Delta S > 0\)) contribute to \(\Delta G < 0\), aiding spontaneity. Option (b) has \(\Delta H < 0\) but \(\Delta S < 0\), which can be less certain for spontaneity. Option (c) has \(\Delta H > 0\) but \(\Delta S > 0\), which might not guarantee spontaneity unless \(T\Delta S\) is very high. Option (d) has \(\Delta H > 0\) and \(\Delta S < 0\), making \(\Delta G\) positive, which is never spontaneous.

Step 4: Conclusion

Based on the analysis, the pair that ensures a spontaneous reaction is (a) exothermic and increasing disorder.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy, denoted as \( \Delta G \), is a thermodynamic quantity that helps us predict whether a process is spontaneous. It combines the effects of enthalpy change (\( \Delta H \)), entropy change (\( \Delta S \)), and temperature (\( T \)). The formula for Gibbs Free Energy is:

• \( \Delta G = \Delta H - T \Delta S \)

A reaction is spontaneous when \( \Delta G \) is negative. This means the system releases free energy during the process, making it favorable to occur on its own.
When you see a negative \( \Delta G \), think of it as a green light for a chemical reaction. The reaction doesn’t need help from outside forces to happen. This is crucial because understanding \( \Delta G \) provides insight into how energy changes drive chemical processes.

Enthalpy Change

Enthalpy Change, symbolized as \( \Delta H \), is the measure of heat absorbed or released during a chemical reaction at constant pressure. It is a fundamental concept in chemistry since it helps describe the thermodynamic nature of reactions.

• If \( \Delta H \) is negative, the reaction is exothermic, meaning it releases heat to its surroundings. Exothermic reactions often lead to spontaneous reactions.
• If \( \Delta H \) is positive, the reaction is endothermic, meaning it absorbs heat from its surroundings.

In simple terms, an exothermic reaction feels warm and a spontaneous reaction is more likely. The heat change provides insight into which direction a reaction will favor. This understanding aids in predicting the reaction’s spontaneity together with entropy.

Entropy Change

Entropy Change, denoted as \( \Delta S \), revolves around the concept of disorder within a system. It's a pivotal factor in determining a reaction's spontaneity as per the Gibbs Free Energy equation.

• A positive \( \Delta S \) indicates increasing disorder, which often favors spontaneity. For example, solid to gas transformations usually have \( \Delta S > 0 \).
• A negative \( \Delta S \) suggests decreasing disorder, which might oppose spontaneity unless compensated by a significant release of heat (negative \( \Delta H \)).

Entropy can be thought of as a measure of randomness or chaos. Every system tends to favor the direction of higher disorder or randomness. The overall change in entropy, together with enthalpy change, helps forecast whether or not a reaction will occur spontaneously.