Problem 134 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following Column-I (a) \(\Delta \mathrm{G}<0\) (b) \(\Delta \mathrm{S}_{\text {Total }}<0\) (c) \(\Delta \mathrm{S}_{\text {total }}=0\) (d) \(\Delta \mathrm{G}=0\) Column-II (p) spontaneous (q) equili brium (r) \(\Delta \mathrm{H}>\mathrm{T} \Delta \mathrm{S}\) (s) \(\Delta \mathrm{H}<\mathrm{T} \Delta \mathrm{S}\) (t) \(\Delta \mathrm{H}=\Delta \mathrm{E}\)

Step-by-Step Solution

Answer

(a) matches (p), (b) matches (r), (c) matches (q), (d) matches (q).

Step 1: Understanding Column-I

Column-I lists various conditions related to thermodynamics. The conditions are (a) \( \Delta G < 0 \), which indicates a spontaneous process, (b) \( \Delta S_{\text{Total}} < 0 \), signifying a non-spontaneous process, or more energy is needed than is available, (c) \( \Delta S_{\text{total}} = 0 \), representing a system in equilibrium or no net change in entropy, and (d) \( \Delta G = 0 \), indicating an equilibrium condition.

Step 2: Understanding Column-II

Column-II lists the consequences or states corresponding to the scenarios in Column-I. They are: (p) spontaneous, (q) equilibrium, (r) \( \Delta H > T \Delta S \) which indicates a condition where enthalpy change is greater than thermal energy contribution to entropy, (s) \( \Delta H < T \Delta S \) which signifies a condition where the entropy term dominates, and (t) \( \Delta H = \Delta E \), indicating that the change in enthalpy equals the change in energy.

Step 3: Match Condition (a)

For \( (a) \ \Delta G < 0 \), a negative Gibbs Free Energy implies the reaction is spontaneous. So, (a) matches with (p) - spontaneous.

Step 4: Match Condition (b)

For \( (b) \ \Delta S_{\text{Total}} < 0 \), this signifies a non-spontaneous process or that the system requires energy input. This matches with \( (r) \ \Delta H > T \Delta S \), where the enthalpy term is greater than what entropy contributes to the system, resulting in a non-spontaneous reaction.

Step 5: Match Condition (c)

For \( (c) \ \Delta S_{\text{Total}} = 0 \), the system is in equilibrium with no net entropy change. This matches with \((q)\) - equilibrium.

Step 6: Match Condition (d)

For \( (d) \ \Delta G = 0 \), Gibbs Free Energy at zero indicates an equilibrium state. So, (d) matches with (q) - equilibrium.

Step 7: Compile Matches

Using the above matches, we finalize the answers: (a) matches (p), (b) matches (r), (c) matches (q), and (d) matches (q).

Key Concepts

Gibbs Free Energy

Gibbs Free Energy, denoted as \( \Delta G \), is a cornerstone concept in thermodynamics that helps predict the direction of chemical reactions. In a chemical process, if \( \Delta G < 0 \), the reaction is spontaneous, meaning it can occur without any additional energy input from the surroundings.

This is because the system releases free energy, making the reaction energetically favorable. For instance, when paper burns, it turns into ashes and releases energy, a process marked by a negative \( \Delta G \).

• **Spontaneous Process (\( \Delta G < 0 \)):** Energy is released, and the process occurs naturally.
• **Equilibrium State (\( \Delta G = 0 \)):** The system is in balance; no net change occurs.

Understanding Gibbs Free Energy can help us determine whether a given reaction can happen under specific conditions, which is invaluable in various scientific and industrial applications.

Entropy Changes

Entropy is a measure of disorder or randomness in a system. When we talk about entropy changes, \( \Delta S \), we focus on how the disorder in a system increases or decreases over time. In many thermodynamic processes, such as chemical reactions, energy spreads out as the system evolves.

• If \( \Delta S_{\text{Total}} > 0 \), it means the disorder is increasing, which typically corresponds to a spontaneous process.
• If \( \Delta S_{\text{Total}} = 0 \), the system is at equilibrium, showcasing no overall change in disorder.
• If \( \Delta S_{\text{Total}} < 0 \), the system requires external energy input to proceed. This is non-spontaneous and often seen when a more ordered state is formed.

Entropy changes are essential for understanding the balance between energy provided by a reaction and the resulting degree of chaos or order it brings. In the real world, cleaning your messy room requires effort, akin to decreasing entropy, which is a non-spontaneous activity.

Chemical Equilibrium

Chemical equilibrium occurs when the forward and reverse reactions in a chemical process occur at the same rate. At this point, the concentrations of products and reactants remain constant over time. Equilibrium doesn't mean that all reactions cease; rather, for every molecule reacting to form products, a molecule of product is converted back into reactant.

• **Achieving Equilibrium:** It's the state where \( \Delta G = 0 \), and the reaction has no net tendency to shift either forwards or backwards.
• At equilibrium, \( \Delta S_{\text{Total}} = 0 \) implies no net entropy change in the system, indicating stability.

Understanding chemical equilibrium helps chemists control reaction conditions to favor either product formation or reactant preservation by adjusting factors like temperature, pressure, and concentration. Think of it as a busy city intersection where cars keep moving without any buildup; the flow remains steady but continues in all directions.