Problem 124 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following conditions are favourable for the feasibility of a reaction? (a) \(\Delta \mathrm{H}=-\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}=+\mathrm{ve}\) (b) \(\Delta \mathrm{H}=-\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}=-\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}<\Delta \mathrm{H}\) (c) \(\Delta \mathrm{H}=+\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}=+\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}<\Delta \mathrm{H}\) (d) \(\Delta \mathrm{H}=+\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}=+\mathrm{ve}, \mathrm{T} \Delta \mathrm{S}>\Delta \mathrm{H}\)

Step-by-Step Solution

Answer

The reactions in conditions (a), (b), and (d) are feasible.

Step 1: Understanding Gibbs Free Energy

The feasibility of a reaction under standard conditions is determined using the Gibbs free energy equation: \[ \Delta G = \Delta H - T\Delta S \] For a reaction to be feasible, \( \Delta G \) must be negative.

Step 2: Analyzing Condition (a)

Condition (a) provides: \( \Delta H = - \text{ve} \), \( T\Delta S = + \text{ve} \). By substituting these values into the Gibbs equation, we get:\[ \Delta G = (-\text{ve}) - (+\text{ve}) = -\text{ve} - \text{ve} = -\text{ve} \]Since \( \Delta G \) is negative, the reaction is feasible.

Step 3: Analyzing Condition (b)

Condition (b) gives: \( \Delta H = - \text{ve} \), \( T\Delta S = - \text{ve} \), and \( T\Delta S < \Delta H \). Substituting these values:\[ \Delta G = (-\text{ve}) - (-\text{ve}) \] Since \( T\Delta S < \Delta H \), \( \Delta G \) remains negative, making the reaction feasible.

Step 4: Analyzing Condition (c)

Condition (c) provides: \( \Delta H = + \text{ve} \), \( T\Delta S = + \text{ve} \), and \( T\Delta S < \Delta H \). Substituting in Gibbs' equation:\[ \Delta G = (+\text{ve}) - (+\text{ve}) \] Given \( T\Delta S < \Delta H \), \( \Delta G \) is positive, meaning the reaction is not feasible.

Step 5: Analyzing Condition (d)

Condition (d) provides: \( \Delta H = + \text{ve} \), \( T\Delta S = + \text{ve} \), and \( T\Delta S > \Delta H \). Substituting yields:\[ \Delta G = (+\text{ve}) - (+\text{ve}) \] Here, since \( T\Delta S > \Delta H \), \( \Delta G \) becomes negative, making the reaction feasible.

Key Concepts

Feasibility of Reactions

The feasibility of a chemical reaction refers to whether the reaction will proceed spontaneously, producing products from reactants once it is initiated. This depends heavily on Gibbs Free Energy, denoted as \( \Delta G \).
For a reaction to be spontaneous, \( \Delta G \) should be negative.

• If \( \Delta G < 0 \): The reaction is spontaneous and feasible.
• If \( \Delta G = 0 \): The reaction is in equilibrium.
• If \( \Delta G > 0 \): The reaction is non-spontaneous and not feasible under the given conditions.

This principle guides chemists in predicting whether a reaction will occur under certain temperature and pressure conditions. Adjusting these conditions can also change the feasibility of the reaction.

Enthalpy Change

Enthalpy change, represented by \( \Delta H \), is one part of the Gibbs Free Energy equation and measures the total energy change within a reaction. It's a way to understand the heat absorbed or released during a reaction at constant pressure.

• \( \Delta H < 0 \): This indicates an exothermic reaction, which releases heat. Such reactions tend to be more feasible because energy is given off.
• \( \Delta H > 0 \): This signifies an endothermic reaction, which absorbs heat. These reactions are generally less favorable because they require energy input.

The enthalpy change gives insight into the energy profile of the reaction, helping chemists understand how energy shifts during the process and influences its spontaneity.

Entropy Change

Entropy change, denoted as \( \Delta S \), indicates the disorder or randomness within a system. Entropy is a way to understand how energy is dispersed among particles and impacts the feasibility of reactions.

• If \( T \Delta S \) is positive: The reaction generally helps in increasing disorder or randomness, which is often favorable. As temperature rises, this effect becomes more dominant in determining feasibility.
• If \( T \Delta S \) is negative: The reaction may lead to reduced disorder, which can make a reaction less spontaneous unless compensated by a significant negative \( \Delta H \).

The entropy change is crucial at higher temperatures, making it a significant factor in shifting the balance towards a feasible reaction, especially when the enthalpy change is not favorable.