Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

For a reaction to occur spontaneously (a) \((\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S})\) must be negative (b) \((\Delta \mathrm{H}+\mathrm{T} \Delta \mathrm{S})\) must be negative (c) \(\Delta \mathrm{H}\) must be negative (d) \(\Delta \mathrm{S}\) must be negative

Step-by-Step Solution

Answer

Option (a) \((\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S})\) must be negative.

Step 1: Understanding Spontaneity in Reactions

For a reaction to occur spontaneously, the Gibbs free energy change, \( \Delta G \), must be negative. The equation for Gibbs free energy is \( \Delta G = \Delta H - T \Delta S \) , where \( \Delta H \) is the enthalpy change, \( T \) is temperature, and \( \Delta S \) is the entropy change.

Step 2: Identifying the Correct Condition

A spontaneous reaction requires \( \Delta G < 0 \). Solving for \( \Delta G = \Delta H - T \Delta S \), the term \( \Delta H - T \Delta S \) must be less than zero. Therefore, the correct condition that ensures the negativity of \( \Delta G \) is \( \Delta H - T \Delta S < 0 \).

Step 3: Matching with Options

Among the given options, option (a) \( (\Delta H- T \Delta S) \) must be negative corresponds directly to the requirement that \( \Delta G < 0 \). Thus, option (a) is the correct choice.

Key Concepts

Spontaneity of reactions

Understanding the spontaneity of reactions is crucial in thermodynamics. A spontaneous reaction is one that occurs naturally without any external intervention. Consider something as simple as iron rusting over time, or ice melting at room temperature. These processes occur spontaneously. The key to determining spontaneity lies in understanding the concept of Gibbs free energy.

• Spontaneous reactions decrease the system's Gibbs free energy.
• This phenomenon is driven by natural tendencies towards equilibrium.

In essence, for a reaction to be spontaneous, it must lead to a decrease in the free energy of the system, making it more stable.

Enthalpy change

The enthalpy change, denoted as \( \Delta H \), is a measure of the total heat content in a thermodynamic system. It reflects the energy absorbed or released during chemical reactions.

• A negative \( \Delta H \) indicates an exothermic reaction, where heat is released to the surroundings.
• A positive \( \Delta H \) signifies an endothermic reaction, where heat is absorbed from the surroundings.

Enthalpy change plays a key role in determining reaction spontaneity. Even though it is an essential factor, it is not solely responsible for predicting spontaneity without considering entropy and temperature.

Entropy change

Entropy, represented as \( \Delta S \), measures the disorder or randomness in a system. In simple terms, it evaluates how energy is dispersed or spread out within a system. For example:

• An increase in entropy (positive \( \Delta S \)) implies that the system becomes more disordered.
• A decrease in entropy (negative \( \Delta S \)) indicates a system moving towards more orderly states.

When evaluating spontaneity, both entropy and temperature influence the outcome. A process that increases the entropy of a system often has a favorable condition for spontaneity, much like how a deck of cards naturally scatters rather than being neatly ordered by itself.

Negative Gibbs free energy

Negative Gibbs free energy is the hallmark of a spontaneous process. Gibbs free energy change, \( \Delta G \), is determined by the relationship \( \Delta G = \Delta H - T \Delta S \). When \( \Delta G \) is negative, it indicates that a reaction can occur spontaneously:\[ \Delta G < 0 \text{ indicates spontaneity} \]

• This requires the effect of \( \Delta S \) and temperature \( T \) to be significant enough to overcome a positive \( \Delta H \) if present.
• When \( \Delta H \) is negative and \( \Delta S \) is positive, you almost always have spontaneity.

Thus, the interplay between enthalpy, entropy, and temperature is crucial for predicting the nature of reactions.

Thermodynamic equations

Thermodynamic equations link various properties of a system in order to understand and predict the behavior of chemical reactions. The Gibbs free energy equation is one of the most significant:- \( \Delta G = \Delta H - T \Delta S \)
This equation serves as a tool to assess the conditions under which reactions are favorable. - Enthalpy, entropy, and temperature are interlinked concepts that must be evaluated together.Through these equations:

• One can decide whether alterations in temperature would shift a reaction towards spontaneity or not.
• They act as a guide for understanding energy transformations within chemical reactions.

In summary, knowing how to apply thermodynamic equations enables predictions about the practical feasibility of chemical processes.