Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following conditions may lead to a nonspontaneous change? (a) \(\Delta \mathrm{H}=-\mathrm{ve} ; \Delta \mathrm{S}=+\mathrm{ve}\) (b) \(\Delta \mathrm{H}=-\mathrm{ve} ; \Delta \mathrm{S}=-\mathrm{ve}\) (c) \(\Delta \mathrm{H}\) and \(\Delta \mathrm{S}\) are both \(+\mathrm{ve}\) (d) \(\Delta \mathrm{H}=+\mathrm{ve} ; \Delta \mathrm{S}=-\mathrm{ve}\)

Step-by-Step Solution

Answer

Condition (d) leads to a nonspontaneous change.

Step 1: Understand the Parameters

First, to determine the spontaneity of a reaction, we need to see how the Gibbs free energy change (G) is affected by the enthalpy change (H) and the entropy change (S). The formula is given by: \[\Delta G = \Delta H - T \Delta S\]where \(T\) is the temperature in Kelvin.

Step 2: Analyzing Condition (a)

For condition (a):- \(\Delta H = -\text{ve}\) and \(\Delta S = +\text{ve}\) - Substituting these into the formula results in a negative \(\Delta G\), which typically means the process is spontaneous at all temperatures.

Step 3: Analyzing Condition (b)

For condition (b):- \(\Delta H = -\text{ve}\) and \(\Delta S = -\text{ve}\) - Here, \(\Delta G = \Delta H - T \Delta S\) can be negative or positive depending on the size of \(T) \Delta S\) versus \(\Delta H\). It may be nonspontaneous at higher temperatures when \(T \Delta S\) is larger than \(\Delta H\).

Step 4: Analyzing Condition (c)

For condition (c):- \(\Delta H = +\text{ve}\) and \(\Delta S = +\text{ve}\)- \(\Delta G\) can be negative when \(T \Delta S\) exceeds \(\Delta H\), typically spontaneous at high temperatures, but nonspontaneous at low temperatures.

Step 5: Analyzing Condition (d)

For condition (d):- \(\Delta H = +\text{ve}\) and \(\Delta S = -\text{ve}\)- In this case, \(\Delta G\) will be positive as both terms contribute to a positive value, making it nonspontaneous at all temperatures.

Step 6: Conclusion

The conditions in (d) inherently lead to a nonspontaneous change since both \(\Delta H\) is positive and \(\Delta S\) is negative, ensuring a positive \(\Delta G\) under all temperature conditions.

Key Concepts

Enthalpy Change

What is enthalpy change, and why is it important? Enthalpy change, symbolized as \( \Delta H \), refers to the heat absorbed or released during a chemical reaction at constant pressure. It's crucial for understanding how energy moves in and out of a system.

Key points to consider:

• A negative \( \Delta H \) (exothermic) indicates heat is released, which can favor spontaneity.
• A positive \( \Delta H \) (endothermic) means heat is absorbed, often opposing spontaneity.

Enthalpy change helps predict whether a reaction might proceed on its own or needs external energy. Think of it as understanding the energy exchange within your cooking pot. When you heat water, you supply energy (positive \( \Delta H \)), and when it cools, the energy goes out (negative \( \Delta H \)).

Understanding how \( \Delta H \) plays a role in Gibbs Free Energy equations helps determine the favorability of reactions. It works alongside entropy in the formula \( \Delta G = \Delta H - T \Delta S \).

Entropy Change

Entropy, symbolized as \( \Delta S \), measures the disorder or randomness in a system. Imagine your room. A messy room with clothes everywhere has high entropy, while a tidy room has low entropy.

Here's why it matters:

• If \( \Delta S \) is positive, the system becomes more disordered, often favoring spontaneity.
• If \( \Delta S \) is negative, the system becomes more ordered, which may not favor spontaneity.

In chemical reactions, entropy change tells us about molecular freedom during the process. More disorder (positive \( \Delta S \)) usually means more possible microstates and higher probability of spontaneous reactions.

Entropy interacts with enthalpy in the Gibbs Free Energy equation to identify whether a reaction will happen by itself or not. It shows how changes in system organization affect the reaction's favorability.

Spontaneity of Reactions

Spontaneity of reactions refers to a reaction's ability to occur without external intervention. The Gibbs Free Energy equation \( \Delta G = \Delta H - T \Delta S \) helps determine this.

Consider these:

• A negative \( \Delta G \) means the reaction is spontaneous, proceeding on its own.
• A positive \( \Delta G \) indicates nonspontaneous reactions, needing energy input.

Example: Melting ice is spontaneous at room temperature because the system gains disorder (positive \( \Delta S \)) and the surroundings provide necessary heat despite the enthalpy change. Considerations like temperature can sway the direction of \( \Delta G \), emphasizing the critical role both \( \Delta H \) and \( \Delta S \) play.

It's a balancing act: enthalpy and entropy fight for favorability. This dynamic relationship elucidates why certain reactions spontaneously occur while others don't under specific conditions.