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

(a) exothermic and increasing disorder

Step 1: Understanding Spontaneity

A spontaneous reaction is one that occurs without needing to add external energy once it starts. It is determined by Gibbs Free Energy (9G), which must be negative for a reaction to be spontaneous.

Step 2: Gibbs Free Energy Equation

The equation for Gibbs Free Energy is 9G = 9H - T9S, where 9H is the change in enthalpy (heat energy), and 9S is the change in entropy (disorder). T is the temperature in Kelvin.

Step 3: Exothermic Reaction Type

An exothermic reaction has a negative 9H, meaning it releases heat. For 9G to be negative, 9H - T9S should also be negative, which is easier to achieve if 9S is positive (increasing disorder).

Step 4: Determine Which Pair Fits

We look for an exothermic reaction with increasing disorder since both conditions (negative 9H and positive 9S) contribute to a negative 9G, making the reaction spontaneous.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy is the driving force behind the spontaneity of a chemical reaction. It is represented by the symbol \( \Delta G \). For a reaction to occur on its own, \( \Delta G \) must be negative. This means the system must release free energy. The equation for Gibbs Free Energy is \( \Delta G = \Delta H - T \Delta S \), where \( \Delta H \) is the change in enthalpy and \( \Delta S \) is the change in entropy. When evaluating whether a reaction is spontaneous:

• Both enthalpy and entropy changes play a role.
• The sign of \( \Delta G \) will determine if energy is released or absorbed by the system.
• A negative \( \Delta G \) indicates a favorable and spontaneous process.

By examining \( \Delta H \) and \( \Delta S \), we can predict how temperature will affect spontaneity as well. If both \( \Delta H \) is negative and \( \Delta S \) is positive, this enhances the likelihood of a negative \( \Delta G \), promoting a spontaneous reaction.

Exothermic Reaction

An exothermic reaction releases energy in the form of heat to its surroundings. This energy release is observed as a negative change in enthalpy, \( \Delta H < 0 \). Exothermic reactions are common in everyday processes and are favorable for spontaneous reactions.Key characteristics of exothermic reactions:

• Heat is released, often noticed as temperature rise in the surroundings.
• The products of the reaction have less energy than the reactants.
• They often make \( \Delta G \) more likely to be negative, contributing to spontaneity.

The energy released can drive other processes, making these reactions integral to many chemical and biological systems. In combination with increasing disorder or entropy, an exothermic reaction becomes a very strong candidate for being spontaneous.

Entropy

Entropy, denoted by \( \Delta S \), measures the disorder or randomness in a system. The concept of entropy is crucial in determining the direction and spontaneity of processes. A positive \( \Delta S \) indicates increased disorder, which is often advantageous for spontaneous reactions.A few notes on entropy:

• Entropy tends to increase with temperature, volume, and the number of particles.
• Reactions that result in a greater number of gas molecules generally increase entropy.
• Increasing entropy contributes positively to \( \Delta G = \Delta H - T \Delta S \), especially at higher temperatures.

Most natural processes are inclined towards increasing entropy, aligning with the second law of thermodynamics. An exothermic reaction coupled with increasing entropy is particularly inclined towards spontaneity.

Enthalpy

Enthalpy, symbolized by \( \Delta H \), is the measure of total heat content in a system. It indicates how heat energy is absorbed or released in a reaction. Negative \( \Delta H \) values represent exothermic reactions, while positive values indicate endothermic reactions.Some essential points about enthalpy include:

• Enthalpy changes are influenced by the breaking and forming of chemical bonds.
• During exothermic reactions, heat is released; hence \( \Delta H \) is negative.
• For the spontaneity of a reaction, a negative \( \Delta H \), combined with a positive entropy change, favors a negative \( \Delta G \).

In summary, understanding enthalpy is vital for predicting reaction spontaneity. It provides the energy landscape over which entropy changes interact to influence \( \Delta G \). Enthalpy changes give insight into the thermal characteristics of reactions and their propensity to proceed unassisted.