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

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

Step 1: Understand Gibbs Free Energy

A reaction is spontaneous when the change in Gibbs free energy (\( \Delta G \)) is negative. The equation relating Gibbs free energy, enthalpy (\( \Delta H \)), and entropy (\( \Delta S \)) is \( \Delta G = \Delta H - T \Delta S \), where \( T \) is the temperature in Kelvin.

Step 2: Analyze Option (a)

For (a), if \( (\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}) \) is negative, it directly implies that \( \Delta G \) is negative because \( \Delta G = \Delta \mathrm{H} - \mathrm{T} \Delta \mathrm{S} \). This means the process is spontaneous.

Step 3: Analyze Option (b)

For (b), \( (\Delta \mathrm{H}+\mathrm{T} \Delta \mathrm{S}) \) would mean redefining Gibbs free energy. However, the concept doesn't align with the known condition for spontaneity (negative \( \Delta G \)), so this condition can't be correct.

Step 4: Analyze Option (c)

For (c), having \( \Delta H \) negative characterizes an exothermic reaction, which may not be sufficient on its own for spontaneity without considering entropy \( \Delta S \).

Step 5: Analyze Option (d)

For (d), if \( \Delta S \) is negative, this implies a decrease in entropy. A negative entropy alone, especially when combining it with enthalpy, doesn't necessarily guarantee \( \Delta G \) will be negative.

Step 6: Identify the Correct Condition

The only option directly describing a necessary condition for spontaneity is (a), because \( (\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}) \) is equivalent to \( \Delta G \), and for a reaction to be spontaneous, \( \Delta G \) must be negative.

Key Concepts

Gibbs Free Energy

Gibbs free energy, often denoted as \( \Delta G \), is a crucial concept in predicting whether a chemical reaction will occur spontaneously. It's a thermodynamic potential that balances the energies in play during a reaction. The equation \( \Delta G = \Delta H - T \Delta S \) connects Gibbs free energy with enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)), where \( T \) represents the temperature in Kelvin. A reaction is considered spontaneous when \( \Delta G \) is negative, implying that the free energy of the system decreases.
Here’s how it works:

• \( \Delta G < 0 \): The process is spontaneous.
• \( \Delta G = 0 \): The system is in equilibrium.
• \( \Delta G > 0 \): The process is non-spontaneous.

A negative \( \Delta G \) suggests that the energy released by forming products is greater than the energy required to break the reactants, leading to a favorable reaction. Temperature and the nature of the substances involved can influence this outcome. Understanding how \( \Delta G \) changes gives valuable insights into reaction feasibility and conditions required for spontaneity.

Enthalpy

Enthalpy, symbolized by \( \Delta H \), refers to the total heat content of a system. It's a measure often used to understand energy changes during a chemical reaction. When we say \( \Delta H \) is negative, we imply that the reaction releases heat, making it exothermic. In the context of Gibbs free energy, the enthalpy component plays a substantial role:

• Negative \( \Delta H \): Typically indicates that energy is released, favoring spontaneity.


• Positive \( \Delta H \): Indicates that energy is absorbed, which might hinder spontaneity unless compensated by favorable entropy (\( \Delta S \)).

While negative enthalpy suggests a potential for a spontaneous reaction, it's not the full story. It must be combined with other factors, such as entropy, to determine the complete spontaneity of a reaction. This comprehensive view ensures that both energetic and disorder aspects are considered, leading to a more complete understanding of chemical processes.

Entropy

Entropy, denoted as \( \Delta S \), is a measure of disorder or randomness in a system. A higher entropy implies greater disorder. For spontaneity in chemical reactions, entropy is an equally important factor as enthalpy. Here's what you need to know about entropy:

• Magnitude of \( \Delta S \): A positive \( \Delta S \) suggests increased disorder, favoring spontaneity.


• Negative \( \Delta S \): Indicates decreased disorder, which might oppose spontaneity unless the enthalpy change is largely favorable.

Entropy's role in Gibbs free energy is particularly important when combined with temperature. At higher temperatures, the \( -T \Delta S \) term becomes more significant, potentially driving the spontaneity of reactions even when \( \Delta H \) might not be very negative or is slightly positive. Thus, entropy changes, alongside enthalpy, provide a deeper insight into the natural progression of chemical reactions and their spontaneity.