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 \(E_{\text {eell }}^{\circ}\) will be respectively \(\mid 2005]\) (a) \(-\mathrm{ve},>1,+\mathrm{ve}\) (b) \(+\mathrm{ve},>1,-\mathrm{ve}\) (c) \(-\mathrm{ve},<1,-\mathrm{ve}\) (d) \(-\mathrm{ve},>1,-\mathrm{ve}\)

Step-by-Step Solution

Answer

The correct answer is (a) \(-\text{ve}, >1, +\text{ve}\).

Step 1: Calculate the Sign of ΔG

A spontaneous reaction has a negative Gibbs free energy change. Therefore, \( \Delta G \) should be negative.

Step 2: Understand the Equilibrium Constant K

For a spontaneous reaction, the equilibrium constant \( K \) is greater than one. This indicates that the reaction favors the formation of products at equilibrium.

Step 3: Determine the Sign of Standard Cell Potential

In electrochemistry, a spontaneous reaction implies a positive standard cell potential \( E_{cell}^{\circ} \). A positive \( E_{cell}^{\circ} \) means the reaction can proceed on its own without additional energy.

Step 4: Match with Given Options

By knowing the signs and properties: \( \Delta G < 0 \), \( K > 1 \), and \( E_{cell}^{\circ} > 0 \), the correct match is option (a): \(-\text{ve}, >1, +\text{ve}\).

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a key concept when discussing spontaneous reactions in chemistry. This thermodynamic property helps determine whether a reaction will proceed on its own without any external input of energy. The criterion for spontaneity hinges largely on the sign of G.

A negative G indicates that a reaction releases energy, allowing it to proceed spontaneously under constant temperature and pressure. Conversely, a positive G would mean the reaction requires energy, implying it is non-spontaneous. This is reflected as follows:

• If G < 0, the reaction is spontaneous.
• If G > 0, the reaction is non-spontaneous.
• If G = 0, the system is at equilibrium.

Understanding this key concept is crucial, as it sets the groundwork for analyzing the other aspects of a reaction, like the Equilibrium Constant and Standard Cell Potential.

Equilibrium Constant

The Equilibrium Constant (K) offers insight into the position of equilibrium in a chemical reaction. It is directly tied to the concentrations of the reactants and products at equilibrium. Importantly, the Equilibrium Constant can tell us whether products or reactants are favored.

In a spontaneous reaction, K plays a substantial role and generally is greater than 1.

• A K value greater than 1 implies the equilibrium lies to the right, favoring the formation of products.
• A K value less than 1 suggests the equilibrium favors the reactants.

This relationship can be visualized mathematically through the equation G = -RT ln(K), where a negative G correlates with a K greater than 1, reinforcing the idea of a product-favored reaction. As such, knowing K helps in predicting the direction the reaction will favor and its overall spontaneity.

Standard Cell Potential

Standard Cell Potential (E_{cell}^{\circ}) is another important aspect of understanding spontaneous reactions, especially within the realm of electrochemistry. This measurement tells us the voltage difference between two half-cells in a galvanic (or voltaic) cell under standard conditions.

For a reaction to be spontaneous in an electrochemical cell, the Standard Cell Potential must be positive.

• A positive E_{cell}^{\circ} means the reaction can occur spontaneously, generating electrical energy.
• A negative E_{cell}^{\circ} suggests the reaction is not spontaneous.

The relationship between the Standard Cell Potential and Gibbs Free Energy is given by the equation: \[ G = -nFE_{cell}^{\circ} \]where n is the number of moles of electrons transferred, and F is Faraday's constant. This equation highlights how a positive E_{cell}^{\circ} results in a negative G, confirming the reaction's spontaneity. Understanding this relationship is vital for predicting and explaining reactions involving electricity generation and consumption.