Problem 189 - A Complete Resource Book in Chemistry for JEE Main

Question

For a spontaneous reaction the \(\Delta \mathrm{G}\), equilibrium constant \((\mathrm{K})\) and \(E_{\mathrm{ccll}}^{\circ}\) will be respectively (a) \(-\mathrm{ve},>1,+\mathrm{ve}\) (b) \(+\mathrm{ve},>1,-\mathrm{ve}\) (c) \(-\mathrm{ve},<1,-\mathrm{ve}\) (d) \(-v \mathrm{e},>1,-v e\)

Step-by-Step Solution

Answer

The correct option is (a): \(-\Delta G, K > 1, E_{\circ} > 0\).

Step 1: Understand the Concepts Involved

In a spontaneous reaction, the Gibbs free energy change \( \Delta G \) is negative, indicating that the reaction releases free energy. The equilibrium constant \( K \) for the reaction is greater than 1 for spontaneous reactions because the products are favored. The standard cell potential \( E_{\circ} \) is positive, indicating a favorable reaction direction.

Step 2: Analyze the Options

We analyze each of the provided options:- Option (a): \( \Delta G = -ve \), \( K > 1 \), \( E_{\circ} = +ve \)- Option (b): \( \Delta G = +ve \), \( K > 1 \), \( E_{\circ} = -ve \)- Option (c): \( \Delta G = -ve \), \( K < 1 \), \( E_{\circ} = -ve \)- Option (d): \( \Delta G = -ve \), \( K > 1 \), \( E_{\circ} = -ve \)

Step 3: Match with Right Conceptual Understanding

For a reaction to be spontaneous, it should have a negative Gibbs free energy \( \Delta G < 0 \), an equilibrium constant \( K > 1 \), and a positive cell potential \( E_{\circ} > 0 \). Among the provided options, (a) has all these features correctly represented.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy, represented as \( \Delta G \), is a crucial concept in thermodynamics that helps predict whether a chemical process will occur spontaneously. A spontaneous reaction is one that proceeds without needing any additional energy input. For any chemical process, the sign of \( \Delta G \) informs us about its spontaneity.

• A negative \( \Delta G \) (pronounced as "delta G") indicates that the reaction releases energy and is, therefore, spontaneous under constant temperature and pressure conditions.
• In contrast, if \( \Delta G \) is positive, the reaction is not spontaneous, meaning it needs energy to proceed.

Understanding the Gibbs Free Energy change is crucial for predicting how different conditions affect the progress and direction of chemical reactions. This concept is vital when examining reactions in various fields such as chemistry, biology, and environmental science.

Equilibrium Constant

The Equilibrium Constant, denoted as \( K \), provides insight into the balance between reactants and products in a chemical reaction at equilibrium. When a reaction reaches equilibrium, the concentrations of the reactants and products remain constant over time.

• If \( K > 1 \), it suggests that at equilibrium, the concentration of products is greater than that of the reactants, indicating a product-favored reaction and often spontaneous under standard conditions.
• If \( K < 1 \), the reaction favors the reactants, meaning the process is less likely to reach completion.

The value of \( K \) doesn't change with concentration changes or pressure but varies with temperature. Through \( K \), one can deduce the position of the equilibrium and estimate how much product or reactant will remain at equilibrium.

Standard Cell Potential

Standard Cell Potential, symbolized as \( E_{\circ} \), is a measure of the electromotive force (emf) of a galvanic cell under standard conditions (1 M concentration, 1 atm pressure, and a specific temperature, usually 25 °C).

• When \( E_{\circ} \) is positive, it indicates that the reaction is spontaneous and the electrochemical cell can do work, making the process favorable.
• If \( E_{\circ} \) is negative, the cell requires an external voltage to drive the reaction, hence non-spontaneous.

The standard cell potential is determined using the difference in potential between the two half-cells. This concept is particularly essential in electrochemistry, helping predict the voltage of cells and the direction of electron flow. Understanding \( E_{\circ} \) is key in designing batteries, calculating cell efficiencies, and understanding energy conversion processes.