Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

The entropy values in \(\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\) of \(\mathrm{H}_{2}(\mathrm{~g})=130.6\), \(\mathrm{Cl}_{2}(\mathrm{~g})=223\) and \(\mathrm{HC} 1(\mathrm{~g})=186.7\) at \(298 \mathrm{~K}\) and 1 atm pressure. Then entropy change for the reaction \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HC} 1(\mathrm{~g})\) is (a) \(+540.3\) (b) \(+727.3\) (c) \(-166.9\) (d) \(+19.8\)

Step-by-Step Solution

Answer

The entropy change is \( +19.8 \text{ J K}^{-1} \text{ mol}^{-1} \).

Step 1: Understand the Reaction

The reaction given is \( \mathrm{H}_{2}(\mathrm{~g}) + \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \ \mathrm{HC}1(\mathrm{~g}) \). We need to calculate the change in entropy for this reaction using the provided standard molar entropy values for each compound.

Step 2: Write the Entropy Change Formula

The formula to find the entropy change \( \Delta S \) for a reaction is: \[ \Delta S = \sum ( S_{\text{products}}) - \sum ( S_{\text{reactants}}) \]Where \( S \) represents the standard molar entropy of the components. For this reaction, we calculate using the given molar entropy values.

Step 3: Calculate the Entropy of Products

The product is \( 2 \mathrm{HC}l(\mathrm{~g}) \), and its entropy is given as 186.7 J K⁻¹ mol⁻¹. So, the total entropy for \( 2 \mathrm{HC}l \) is: \( 2 \times 186.7 = 373.4 \) J K⁻¹ mol⁻¹.

Step 4: Calculate the Entropy of Reactants

For the reactants, we have \( \mathrm{H}_{2}(\mathrm{~g}) \) and \( \mathrm{Cl}_{2}(\mathrm{~g}) \) with entropies of 130.6 and 223 J K⁻¹ mol⁻¹, respectively. The total entropy for the reactants is: \( 130.6 + 223 = 353.6 \) J K⁻¹ mol⁻¹.

Step 5: Find the Entropy Change

Now, substitute the values into the entropy change formula: \[ \Delta S = 373.4 - 353.6 = 19.8 \text{ J K}^{-1} \text{ mol}^{-1} \]. This result matches one of the options provided.

Key Concepts

Standard Molar Entropy

Standard molar entropy is a critical concept in understanding how heat and energy are distributed in a chemical system. It's defined as the entropy content of one mole of substance under standard conditions, typically at 298 K and 1 atm pressure. This standardization allows chemists to compare entropy values across different substances and reactions.

In essence, standard molar entropy provides insight into the spontaneity of reactions and the disorder within a system. A higher value indicates more disorder or randomness, which is common in gases due to their free-moving particles. Calculating the standard molar entropy for substances involved in a reaction helps predict the energetic favorability of the reaction and its potential direction.

• Helps in calculating the total entropy change.
• Important for understanding temperature and pressure conditions.
• Aids in determining the spontaneity of reactions.

Understanding standard molar entropy involves grasping that it's not just a mathematical figure but a descriptor of system behaviors when energy is involved.

Thermodynamics

Thermodynamics is the study of the changes in energy and matter within chemical processes. It provides the framework for understanding how entropy, enthalpy, and free energy connect and influence chemical reactions.

A core principle in thermodynamics is the Second Law, which states that the entropy of an isolated system will increase over time, ultimately reaching maximum disorder. This concept is critical for calculating the entropy change in reactions. When a reaction occurs, the entropy change can hint at the system's tendency to become more disordered.

• Examines energy exchanges in reactions.
• Uses the Second Law to understand entropy increase.
• Links to predicting reaction spontaneity and equilibrium.

Thermodynamics provides the tools to understand how and why reactions proceed as they do, essential for studying chemical processes and predicting their outcomes.

Chemical Reactions

Chemical reactions involve the conversion of reactants into products, often accompanied by changes in energy and matter configuration. Calculating the entropy change gives valuable insight into these transformations.

In the reaction given in the exercise, the reactants, hydrogen gas and chlorine gas, combine to form hydrogen chloride gas. By understanding standard molar entropy and thermodynamics, you can determine the entropy change of this specific reaction. If the products' entropy is greater, it suggests an increase in disorder, typical in energy-favorable reactions.

• Requires knowledge of reactants and products' entropies.
• Depends on the changes in the molecular arrangement and energy release or absorption.
• Lends insight into reaction kinetics and equilibrium.

Comprehending the effect of a chemical reaction on entropy helps predict the conditions under which a reaction will occur and its possible extent.

Molar Entropy Values

Molar entropy values are essential for quantitative assessments in reaction calculations. Each substance in a chemical reaction has a particular molar entropy, measurable in J K⁻¹ mol⁻¹ (joules per kelvin per mole).

In a balanced chemical equation, these values allow you to compute the total entropy change of the reaction. For instance, in the exercise, the molar entropy for each component – hydrogen gas, chlorine gas, and hydrogen chloride – must be known to find the final entropy change. By summing the standard molar entropies of the products and subtracting those of the reactants, you achieve the reaction's net entropy change, which tells you whether the process is energetically favorable.

• Used for calculating reaction entropy change.
• Assists in understanding reaction spontaneity.
• Important for analyzing energy transformations.

Molar entropy values and their computations are indispensable tools for chemists to examine and unravel the complexities of a reaction's energy dynamics.