Problem 145 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements are true? (a) \(392 \mathrm{~g}\) of ferrous ammonium sulphate is required to reduce \(31.6 \mathrm{~g} \mathrm{KMnO}_{4}\) in aqueous acidic medium. (b) Molality of a solution does not vary with temperature. (c) \(\mathrm{KBrO}_{3}\) can quantitatively convert \(\mathrm{Br}^{-}\)to \(\mathrm{Br}_{2}\). (d) The oxidation state of \(\mathrm{S}\) in \(\mathrm{CNS}\) - is zero.

Step-by-Step Solution

Answer

Statements (a), (b), and (c) are true; statement (d) is false.

Step 1: Identify the Statements to Analyze

Review the provided statements, summarizing each one to determine what needs to be assessed for truthfulness.

Step 2: Analyze Statement (a)

Statement (a): Calculate if 392 g of ferrous ammonium sulfate is required to reduce 31.6 g KMnO4. The balanced reaction is \[ 10 ext{FeSO}_4 + 2 ext{KMnO}_4 + 8 ext{H}_2 ext{SO}_4 \rightarrow 5 ext{Fe}_2( ext{SO}_4)_3 + 2 ext{MnSO}_4 + ext{K}_2 ext{SO}_4 + 8 ext{H}_2 ext{O} \] Calculate moles of each to find out if this stoichiometry matches the statement.

Step 3: Calculate for Statement (a)

Calculate the molar mass of KMnO4: \( ext{K} = 39, ext{Mn} = 55, ext{O} = 16 \) Thus, \( ext{K} = 39 + 55 + 64 = 158 ext{ g/mol} \).\( ext{Moles of KMnO}_4 = \frac{31.6}{158} \approx 0.2 ext{ mol} \).Using stoichiometry, 5 moles of FeSO4 are needed for 1 mole KMnO4, 0.2 moles KMnO4 require 1 mole FeSO4.Molar mass of ferrous ammonium sulphate = 392 g/mol, thus 392 g is required.

Step 4: Validate Conclusion for Statement (a)

Our calculations confirm that 392 g of ferrous ammonium sulfate is required for 31.6 g of KMnO4, thus statement (a) is true.

Step 5: Analyze Statement (b)

Statement (b): Molality is defined as moles of solute per kilogram of solvent. It does not rely on volume, thus it remains unaffected by temperature change. Therefore, this statement is true.

Step 6: Analyze Statement (c)

Statement (c): In the reaction \[ ext{KBrO}_3 + 6 ext{Br}^- + 6 ext{H}^+ \rightarrow 3 ext{Br}_2 + ext{K}^+ + 3 ext{H}_2 ext{O} \], eact \( ext{Br}^- \) can be converted to \( ext{Br}_2 \). Therefore, statement (c) is true.

Step 7: Analyze Statement (d)

Statement (d): Determine the oxidation state of sulfur in \( ext{CNS}^- \). The sum of oxidation states in ions equals charge:\[ ext{C} = +4, ext{N} = -3, ext{S} = x \]. Set up equation\( +4 + (-3) + x = -1 \), solving gives: \( x = -2 \). Therefore, statement (d) is false.

Key Concepts

Stoichiometry

Stoichiometry is a core concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. To use stoichiometry effectively, it is important to understand a balanced chemical equation, which shows the proportions of reactants and products.

For example, consider the reaction from the exercise involving ferrous ammonium sulfate and potassium permanganate. The balanced equation is:

• \[ 10 \text{FeSO}_4 + 2 \text{KMnO}_4 + 8 \text{H}_2\text{SO}_4 \rightarrow 5 \text{Fe}_2(\text{SO}_4)_3 + 2 \text{MnSO}_4 + \text{K}_2\text{SO}_4 + 8 \text{H}_2\text{O} \]

This equation tells us the molar ratio of reactants to products. By calculating the moles of each substance, we can determine if the quantities used in a reaction are in the correct proportions.

For instance, if you have 0.2 moles of KMnO4, stoichiometry tells us that you'll need 1 mole of FeSO4 to react completely because the ratio is 5:1 as per the balanced equation.

Oxidation State

Oxidation state, also known as oxidation number, is a concept used in chemistry to describe the level of oxidation of an atom within a compound. It indicates the number of electrons that an atom uses to bond with atoms of another element. In essence, the oxidation state is a bookkeeping system to keep track of electron movements.

For example, in the ion \( \text{CNS}^- \), we need to find the oxidation state of sulfur (S). Let's break it down:

• Carbon (C) is generally assigned an oxidation state of +4.
• Nitrogen (N) typically has an oxidation state of -3.
• The sum of the oxidation states of all atoms in the ion must equal the charge of the ion, which is -1.

This leads to the equation:\[ +4 + (-3) + x = -1 \] where \( x \) is the unknown oxidation state of sulfur.

Solving this equation, we find \( x = -2 \). Thus, the oxidation state of sulfur in \( \text{CNS}^- \) is -2, not zero as originally thought.

Acidic Medium Reactions

Acidic medium reactions are reactions that occur in the presence of an acid, usually indicated by the presence of \( \text{H}^+ \) ions in the reaction environment. These conditions are necessary for certain redox reactions to proceed.

In the context of the exercise, the reaction of potassium bromate (\( \text{KBrO}_3 \)) with bromide ions (\( \text{Br}^- \)) is an example of a redox reaction occurring in an acidic medium. The simplified reaction is:

• \[ \text{KBrO}_3 + 6 \text{Br}^- + 6 \text{H}^+ \rightarrow 3 \text{Br}_2 + \text{K}^+ + 3 \text{H}_2\text{O} \]

In this reaction, \( \text{Br}^- \) ions are oxidized to \( \text{Br}_2 \) molecules, and \( \text{KBrO}_3 \) acts as the oxidizing agent. The presence of \( \text{H}^+ \) ions facilitates this redox process, allowing the transfer of electrons to be balanced.

Understanding the role of the acidic medium is essential for predicting the behavior and outcome of similar chemical reactions.