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 \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(\mathrm{g})\) is (a) \(+540.3\) (b) \(+727.3\) (c) \(-166.9\) (d) \(+19.8\)

Step-by-Step Solution

Answer

The entropy change for the reaction is +19.8 J/K.

Step 1: Write the Reaction Equation

The given reaction is: \[ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(\mathrm{g}) \] This equation shows that one mole of hydrogen gas reacts with one mole of chlorine gas to produce two moles of hydrogen chloride gas.

Step 2: Use the Standard Entropy Formula

Entropy change \( \Delta S \) for a reaction is given by the formula: \[ \Delta S = \sum S_{\text{products}} - \sum S_{\text{reactants}} \] where \( \sum S_{\text{products}} \) is the sum of the entropies of the products and \( \sum S_{\text{reactants}} \) is the sum of the entropies of the reactants.

Step 3: Calculate Total Entropy of Products

The products are 2 moles of \( \mathrm{HCl}(\mathrm{g}) \), with an entropy of 186.7 J/K mol. Thus, \( \sum S_{\text{products}} = 2 \times 186.7 = 373.4 \text{ J/K} \).

Step 4: Calculate Total Entropy of Reactants

The reactants are 1 mole of \( \mathrm{H}_{2}(\mathrm{~g}) \) and 1 mole of \( \mathrm{Cl}_{2}(\mathrm{~g}) \), with entropies of 130.6 J/K mol and 223 J/K mol, respectively. Thus, \( \sum S_{\text{reactants}} = 130.6 + 223 = 353.6 \text{ J/K} \).

Step 5: Calculate Entropy Change

Substitute the values into the entropy change formula: \[ \Delta S = 373.4 - 353.6 = 19.8 \text{ J/K} \].

Step 6: Choose the Correct Option

The calculated entropy change \( \Delta S \) is 19.8 J/K, which corresponds to option (d).

Key Concepts

Standard Entropy Formula

Entropy is often a difficult concept for students to grasp initially, but it becomes easier when we can focus on formulas. The Standard Entropy Formula allows chemists to predict the change in entropy during a chemical reaction.
It is expressed as:

• \( \Delta S = \sum S_{\text{products}} - \sum S_{\text{reactants}} \)

In this formula, \( \Delta S \) represents the change in entropy. It calculates the difference between the sum of the entropies of the products and the sum of the entropies of the reactants.
This is crucial for understanding how entropy evolves, indicating whether a reaction results in increased or decreased disorder. By substituting known entropy values into this formula, you can deduce the overall entropy change (\( \Delta S \)) in a straightforward manner.

Reaction Equation

The heart of understanding any chemical process lies in the reaction equation. It symbolically represents the transformation of reactants into products. For this exercise, the given reaction is:

• \( \mathrm{H}_{2} (\mathrm{g}) + \mathrm{Cl}_{2} (\mathrm{g}) \rightarrow 2 \mathrm{HCl} (\mathrm{g}) \)

This equation provides critical information:

• One mole of hydrogen gas (\(\mathrm{H}_{2}\)) reacts with one mole of chlorine gas (\(\mathrm{Cl}_{2}\)).
• The products are two moles of hydrogen chloride gas (\(\mathrm{HCl}\)).

Understanding the reaction equation is essential as it indicates the stoichiometry: the ratio of reactants to products. Moreover, it shows us which molecules' entropy values we need to consider in calculations. This equation guides the calculations of entropy change using the provided standard entropy values of reactants and products.

Entropy of Products and Reactants

To calculate the change in entropy, you begin by considering the entropy values of both products and reactants. Each molecule involved in the reaction has a specific entropy, denoted in \( \mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1} \), a measure of disorder at a molecular level.

• Reactants in our equation are \(\mathrm{H}_{2}(\mathrm{~g}) = 130.6\) and \(\mathrm{Cl}_{2}(\mathrm{~g}) = 223\).
• Products are 2 moles of \(\mathrm{HCl}(\mathrm{~g}) = 2 \times 186.7\).

For calculations:

• Sum the entropy values of the reactants: \(130.6 + 223 = 353.6\).
• Calculate the total entropy of the products: \(373.4\) (from \(2 \times 186.7\)).
• Apply these sums to the formula \( \Delta S = \sum S_{\text{products}} - \sum S_{\text{reactants}} \).
• This results in \(\Delta S = 373.4 - 353.6 = 19.8 \) \( \mathrm{J} \mathrm{K}^{-1} \).

This calculation shows the net entropy change during the reaction, illustrating the increase or decrease in molecular disorder, which is a key aspect in determining the spontaneity of reactions.