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

Conditions (a), (b), and (d) are favourable for feasibility.

Step 1: Understanding Feasibility Conditions

A reaction's feasibility is determined by the sign of the Gibbs free energy change, \(9G\). A reaction is spontaneous (feasible) when \(9G < 0\). The expression for \(9G\) is given by: \(9G = 9H - T9S\), where \(9H\) is the enthalpy change and \(T9S\) is the temperature times the entropy change. The sign of \(9H\) and \(9S\) determines the reaction's spontaneity conditions.

Step 2: Analyzing each condition

Let's analyze each provided condition: (a) \(9H = -\text{ve}, T9S = +\text{ve}\). Here, both terms are favorable for spontaneity since \(9H\) is negative and \(T9S\) is positive, making \(9G\) negative, thus the reaction is feasible.(b) \(9H = -\text{ve}, T9S = -\text{ve}, T9S < 9H\). Here, \(9H\) is negative which helps decrease \(9G\), and \(T9S < 9H\), making \(9G\) negative, hence the reaction is feasible.(c) \(9H = +\text{ve}, T9S = +\text{ve}, T9S < 9H\). Here, due to \(9H\) being positive and \(T9S < 9H\), \(9G\) remains positive, so the reaction is not feasible.(d) \(9H = +\text{ve}, T9S = +\text{ve}, T9S > 9H\). \(9H\) is positive, but \(T9S\) is larger, which can make \(9G\) negative, thus feasible.

Step 3: Identify Favorable Conditions

Based on the above analysis, the conditions where \(9G < 0\) are:(a) \(9H = -\text{ve}, T9S = +\text{ve}\) and(b) \(9H = -\text{ve}, T9S = -\text{ve}, T9S < 9H\), and(d) \(9H = +\text{ve}, T9S = +\text{ve}, T9S > 9H\).These conditions allow for \(9G\) to be negative, indicating feasible reactions.

Key Concepts

Thermodynamics

Thermodynamics is a branch of physics and chemistry that deals with the study of energy and its transformations. In the context of chemical reactions, thermodynamics helps us understand whether a reaction will occur spontaneously. This is done by evaluating various energy changes that occur as the reaction proceeds. The primary focus is on how heat (enthalpy) and disorder (entropy) interplay to influence a system's energy state.

A crucial concept in thermodynamics is the Gibbs Free Energy (03G), which combines the effects of enthalpy and entropy to predict if a reaction is thermodynamically favorable. The sign and magnitude of 03G tell us whether a reaction will proceed on its own without additional energy input.

Reaction Spontaneity

Reaction spontaneity refers to the ability of a chemical reaction to occur on its own without any outside influence or energy input. The Gibbs Free Energy equation, 03G = 03H - T03S, is essential for determining spontaneity.

- 03G represents the change in Gibbs Free Energy. - 03H is the change in enthalpy, indicating the heat absorbed or released. - T is the absolute temperature in Kelvin. - 03S stands for the change in entropy, showing the system's disorder.

A negative value for 03G implies the reaction is spontaneous. This means both a drop in enthalpy (03H is negative) and an increase in entropy (03S is positive) are generally desirable. When analyzing spontaneity:

• If 03H is negative and T03S is positive, 03G is negative, favoring a spontaneous reaction.
• If both 03H and T03S are positive, 03G depends on the values of these two terms. If entropy's effect (T03S) exceeds enthalpy's effect (03H), then 03G becomes negative.
• A positive 03G indicates the reaction is non-spontaneous under the given conditions.

Enthalpy and Entropy

In thermodynamics, enthalpy (03H) and entropy (03S) are two key concepts that dictate the direction and favorability of chemical reactions.

**Enthalpy** Enthalpy is a measure of the total energy of a thermodynamic system, equivalent to the system's internal energy plus the energy required to make room for its volume by displacing its surroundings. In reactions, a negative 03H means the system releases heat to its surroundings, often favored for spontaneous reactions.

**Entropy** Entropy, symbolized as 03S, represents the degree of disorder or randomness in a system. A higher entropy value means more disorder, which is thermodynamically favored. For instance, gas molecules spreading out in a room is an increase in entropy since they move from an ordered state to a more disordered one.

When considering 03G = 03H - T03S, the balance between enthalpy and entropy influences reaction spontaneity:

• Reactions with a negative 03H (exothermic) and a positive 03S are usually spontaneous.
• Reactions with positive 03H but whose entropy term (03S) is significant enough can also be spontaneous if the temperature is high enough to make T03S greater than 03H.

Understanding these concepts leads to better predictions of reaction behavior under different conditions.