Problem 55 - A Complete Resource Book in Chemistry for JEE Main

Question

The enthalpy and entropy change for a chemical reaction are \(-2.5 \times 10^{3} \mathrm{~J} \mathrm{~mol}^{-1}\) and \(7.4 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) respec- tively. The reaction at \(298 \mathrm{~K}\). is (a) non-spontaneous (b) spontaneous (c) reversible (d) irreversible

Step-by-Step Solution

Answer

The reaction is spontaneous (b) because \( \Delta G < 0 \).

Step 1: Understand the Gibbs Free Energy Equation

The spontaneity of a reaction is determined by its Gibbs free energy change (\( \Delta G \)). The equation to calculate Gibbs free energy is:\[ \Delta G = \Delta H - T \Delta S \]where \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.

Step 2: Substitute Given Values Into the Equation

We know \( \Delta H = -2.5 \times 10^3 \text{ J mol}^{-1} \), \( \Delta S = 7.4 \text{ JK}^{-1} \text{ mol}^{-1} \), and \( T = 298 \text{ K} \). Substitute these values into the Gibbs free energy equation:\[ \Delta G = (-2500) - (298)(7.4) \]

Step 3: Calculate the Temperature Term

First, calculate the product of temperature and entropy change:\[ 298 \times 7.4 = 2205.2 \text{ J mol}^{-1} \]

Step 4: Solve for Gibbs Free Energy

Subtract the temperature-entropy product from the enthalpy change:\[ \Delta G = -2500 - 2205.2 \]\[ \Delta G = -4705.2 \text{ J mol}^{-1} \]

Step 5: Analyze Gibbs Free Energy Result

A reaction is spontaneous when \( \Delta G < 0 \). Here, \( \Delta G = -4705.2 \text{ J mol}^{-1} \), which means the reaction is spontaneous since the value is negative.

Key Concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), represents the heat absorbed or released in a reaction under constant pressure conditions. It indicates whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat). In our example, \( \Delta H = -2.5 \times 10^3 \text{ J mol}^{-1} \), which means the reaction releases heat, making it exothermic.

• Positive \( \Delta H\) implies absorbing heat (endothermic).
• Negative \( \Delta H\) implies releasing heat (exothermic).

Enthalpy changes are crucial in understanding how energy is transferred during a reaction and provides insight into the thermic nature of a chemical process.

Entropy Change

Entropy change, represented as \( \Delta S \), describes the degree of disorder or randomness in a system. A higher value of \( \Delta S \) indicates more disorder. In chemical reactions, entropy changes help to determine the spontaneity along with temperature effects.The given problem has \( \Delta S = 7.4 \text{ JK}^{-1} \text{ mol}^{-1} \), suggesting a slight increase in disorder within the system during the reaction.

• Positive \( \Delta S \) suggests increasing disorder.
• Negative \( \Delta S \) implies a decrease in disorder.

Entropy is a pivotal factor when combined with enthalpy to gauge the spontaneity of reactions using the Gibbs free energy equation.

Spontaneous Reaction

A reaction is termed spontaneous if it proceeds on its own without external energy input. It’s driven by favorable conditions of enthalpy and entropy at a given temperature.To determine spontaneity, the Gibbs free energy change \( \Delta G \) is used. The criteria are:

• If \( \Delta G < 0 \), the reaction is spontaneous.
• If \( \Delta G > 0 \), the reaction is non-spontaneous.
• If \( \Delta G = 0 \), the reaction is at equilibrium (neither spontaneous nor non-spontaneous).

In the given case, a significant negative \( \Delta G = -4705.2 \text{ J mol}^{-1} \) confirms that the reaction is spontaneous, proceeding without continuous input of energy.

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that studies the energy changes, particularly in the form of heat, during chemical reactions. It provides the tools to evaluate if a process is feasible and predict the direction of chemical reactions.Key aspects in chemical thermodynamics include:

• Enthalpy (\( \Delta H \)) - reflects heat exchange.
• Entropy (\( \Delta S\)) - reflects disorder or randomness.
• Gibbs Free Energy (\( \Delta G\)) - determines spontaneity.

The Gibbs free energy equation \( \Delta G = \Delta H - T \Delta S \) combines these concepts to assess whether a reaction will occur under set conditions, thus highlighting the interconnected nature of thermal energy changes and disorder within systems.