Problem 60 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard entropies of \(\mathrm{CO}_{2}(\mathrm{~g}), \mathrm{C}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{~g})\) are \(213.5,5.74\) and \(205 \mathrm{~J} \mathrm{~K}^{-1}\) respectively. The standard entropy of the formation of \(\mathrm{CO}_{2}(\mathrm{~g})\) is (a) \(1.16 \mathrm{JK}^{-1}\) (b) \(2.76 \mathrm{JK}^{-1}\) (c) \(1.86 \mathrm{JK}^{-1}\) (d) \(2.12 \mathrm{JK}^{-1}\)

Step-by-Step Solution

Answer

The standard entropy change for the formation of \( \text{CO}_2(g) \) is option (b) - 2.76 J/K.

Step 1: Write the Reaction

The formation reaction for \( \text{CO}_2(g) \) from its elements in their standard states is: \[ \text{C(s)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

Step 2: Calculate Entropy Change

The standard entropy change of the reaction (\( \Delta S^\circ \)) is calculated using the formula: \[ \Delta S^\circ = S^\circ(\text{products}) - S^\circ(\text{reactants}) \] where \( S^\circ(\text{products}) = S^\circ(\text{CO}_2(g)) = 213.5 \) J/K, \( S^\circ(\text{reactants}) = S^\circ(\text{C(s)}) + S^\circ(\text{O}_2(g)) = 5.74 + 205 \) J/K.

Step 3: Calculate Product and Reactants Total Entropy

For the reactants, sum up their standard entropies: \( S^\circ(\text{C(s)}) + S^\circ(\text{O}_2(g)) = 5.74 + 205 = 210.74 \) J/K.

Step 4: Compute Standard Entropy of Reaction

Substitute the values into the equation for \( \Delta S^\circ \): \[ \Delta S^\circ = 213.5 - 210.74 = 2.76 \text{ J/K} \]

Step 5: Select the Correct Option

The calculated standard entropy change is \( 2.76 \text{ J/K} \), which corresponds to option (b).

Key Concepts

Standard Entropy

Standard entropy, often symbolized as \( S^\circ \), is a quantifiable measure of the amount of energy in a system that is unavailable to do work due to the degree of randomness or disorder. Every substance has its own standard entropy value, typically expressed in units of \( ext{J K}^{-1} \).

These values are determined at a standard pressure of 1 bar and a common reference temperature, generally 298 K. When learning about standard entropy, it's useful to compare different substances. For example, a gaseous substance like \( \text{CO}_2(\text{g}) \) has a relatively high standard entropy compared to a solid substance like \( \text{C(s)} \), reflecting the greater disorder among gas particles. Understanding these differences can help in evaluating and predicting reaction outcomes.

• Gases typically have higher standard entropy than liquids and solids.
• Pure elements have different entropy values due to their structural differences.

Entropy Change

Entropy change, denoted as \( \Delta S^\circ \), describes how the disorder in a system changes as a reaction proceeds. It can help us understand the degree of randomness before and after a chemical reaction.

To calculate the standard entropy change for a reaction, we use the formula: \[ \Delta S^\circ = S^\circ(\text{products}) - S^\circ(\text{reactants}) \] This allows us to determine whether a reaction results in an increase or decrease in disorder.

In our exercise, the entropy change for the formation of \( \text{CO}_2(\text{g}) \) was found by subtracting the combined standard entropies of the reactants \( \text{C(s)} \) and \( \text{O}_2(\text{g}) \) from the standard entropy of the product \( \text{CO}_2(\text{g}) \). Understanding this change is important for predicting the spontaneity of reactions.

• An increase in entropy (positive \( \Delta S^\circ \)) suggests products are more disordered.
• A decrease in entropy (negative \( \Delta S^\circ \)) suggests the system becomes more ordered.

Thermodynamics

Thermodynamics is the study of energy and the transformations between different states of matter. It helps us comprehend how energy moves and changes forms in various processes.

One of the cornerstones of thermodynamics is the second law, which states that the total entropy of an isolated system will always tend to increase over time, moving towards disorder or equilibrium. This concept is foundational for predicting whether a chemical reaction will occur spontaneously. Spontaneity is not just about energy release, but also about whether a reaction increases the overall entropy.

By engaging with thermodynamics, we learn to apply principles like conservation of energy and to evaluate system changes through parameters such as entropy, temperature, and enthalpy.

• Energy conservation is central, but the direction of processes is governed by entropy.
• Understanding enthalpy and entropy helps predict reaction feasibility.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. This transformation involves reordering of atoms and changes in energy levels.

In any reaction, understanding the role of entropy is crucial. It tells us about changes in the disorder of the system, and along with enthalpy, it helps to determine if a reaction can occur spontaneously. In the formation of \( \text{CO}_2(\text{g}) \), we see how entropy changes as carbon and oxygen combine to form a more disordered gaseous product.

The calculation of entropy change in reactions offers deep insights into the energy dynamics taking place, aiding us in predicting and controlling chemical processes.

• Reactions can be endothermic or exothermic based on how energy is absorbed or released.
• Combining entropy and enthalpy changes gives the Gibbs free energy, crucial for assessing spontaneity.