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: Analyze Statement (a)

First, calculate the moles of potassium permanganate (KMnO4). Given mass is 31.6 g. Its molar mass is 158 g/mol.\[\text{Moles of } \mathrm{KMnO}_4 = \frac{31.6}{158} \approx 0.2 \text{ moles}\]In an acidic medium, the reaction between KMnO4 and ferrous ammonium sulphate can be represented as:\[ \mathrm{5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O} \]1 mole of KMnO4 reacts with 5 moles of FeSO4. The molar mass of ferrous ammonium sulphate is 392 g/mol. Hence, moles of FeSO4 needed: \(5 \times 0.2 = 1 \text{ mole}\).\[\text{Mass needed} = 1 \times 392 = 392 \text{ g}\]Statement (a) is true.

Step 2: Analyze Statement (b)

Molality is defined as the number of moles of solute per kilogram of solvent. Since both moles and mass of the solvent are independent of temperature, molality remains constant with temperature changes. Statement (b) is true.

Step 3: Analyze Statement (c)

KBrO3 is a strong oxidizing agent and it can oxidize bromide ions (Br\(^-\)) to bromine (Br\(_2\)). The balanced reaction is:\[\mathrm{6Br^- + BrO_3^- + 6H^+ \rightarrow 3Br_2 + 3H_2O} \]KBrO3 can quantitatively convert Br\(^-\) to Br\(_2\), making statement (c) true.

Step 4: Analyze Statement (d)

In the thiocyanate ion (CNS\(^-\)), the oxidation state of S must be determined. Let \(x\) be the oxidation state of S in CNS\(^-\):The oxidation state equation is:\[\text{C: } +4,\; \text{S: } x,\; \text{N: } -3,\; \text{ion charge: } -1\]\[+4 + x - 3 = -1\]Solving for \(x\) gives:\[ x = -2\]Therefore, the oxidation state of S is -2, not zero. Statement (d) is false.

Key Concepts

Oxidation States

Oxidation states, also known as oxidation numbers, are essential in determining how electrons are distributed in a compound. This concept helps us understand the transfer of electrons in a chemical reaction.
The oxidation state of an element in a molecule or ion represents the effective charge on that atom. This is a hypothetical charge given to the atom assuming that the electrons in all chemical bonds are assigned to the more electronegative atom. For example: - In water (H₂O), oxygen has an oxidation state of -2 because it "gains" electrons from the hydrogen atoms. - Hydrogen, being less electronegative, is assigned a +1 oxidation state.
These values allow us to determine whether a reaction is a redox reaction, where oxidation and reduction occur. The oxidation state changes as electrons are gained or lost. In the exercise, identifying the oxidation states was crucial in verifying whether statement (d) regarding the thiocyanate ion (CNS⁻) was true. According to standard rules, sulfur had an oxidation state of -2, not zero as some might guess by counting only the atoms. Understanding and calculating these states are significant especially when balancing reactions like in the cases of KMnO₄ or KBrO₃.

Stoichiometry in Chemical Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is the part of chemistry that studies the amounts, or ratios, of reactants and products in a collective chemical reaction. By understanding these relationships, we can predict the outcomes of reactions precisely.
For any chemical reaction, it is vital to start with a balanced equation, which follows the conservation of mass.
In the original exercise, when determining if 392 g of ferrous ammonium sulfate suffices to react with 31.6 g of KMnO₄, stoichiometry was the backbone of the analysis. We used the balanced chemical equation:

• 5Fe²⁺ + MnO₄⁻ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O

From this equation, the molar relationship of 5 moles of Fe²⁺ (from ferrous ammonium sulfate) to 1 mole of MnO₄⁻ was evident, allowing precise calculations to be performed.
Stoichiometry ensures the reactants are converted in exact proportions, which allows chemists to optimize the efficiency of reactions and confirmations of analysis results.

Solution Concentration Terms

Concentration terms are vital when studying solutions in chemistry, as they describe the amount of solute in a given amount of solvent or solution. One common term used is molality.
Molality (\[ ext{mol/kg}\]) is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, which can change with temperature due to volume expansion or contraction, molality remains constant because it is based on mass, not volume.

• Molality: Number of moles of solute / Kilogram of solvent

In the exercise, statement (b) regarding molality staying constant with temperature aligns with this property. Consequently, molality is particularly useful in scenarios where temperature varies significantly.
Alongside molality, other terms include molarity and percent concentration, each having unique uses based on the conditions of the reaction being observed. Molality's consistency with temperature makes it a reliable term for studies involving energy changes or thermodynamics.