Problem 74 - A Complete Resource Book in Chemistry for JEE Main

Question

The equivalent weight of \(\mathrm{MnSO}_{4}\) is half its molecular weight when it is converted to (a) \(\mathrm{MnO}\) (b) \(\mathrm{MnO}_{4}^{2-}\) (c) \(\mathrm{MnO}_{2}\) (d) \(\mathrm{MnO}_{4}^{-}\)

Step-by-Step Solution

Answer

The equivalent weight is half its molecular weight when converted to (c) \( \mathrm{MnO}_{2} \).

Step 1: Understanding the Concept of Equivalent Weight

The equivalent weight of a compound is calculated by dividing its molecular weight by the number of electrons lost or gained by one molecule of the substance during a chemical reaction. Here, it is stated that the equivalent weight is half the molecular weight.

Step 2: Calculating Molecular Weight of MnSO4

The molecular weight of MnSO4 is calculated by adding the atomic weights of Mn, S, and O4. Using approximate atomic weights: - Mn: 55 - S: 32 - O: 16 The molecular weight of MnSO4 is:\[ 55 + 32 + (16 \times 4) = 151 \]

Step 3: Determining Electron Transfer for Each Conversion

For each conversion, determine how many electrons are involved in the redox reaction. - (a) MnSO4 to MnO: Mn changes from +2 in MnSO4 to +2 in MnO, no electron transfer. - (b) MnSO4 to MnO4^2-: Mn changes from +2 to +6, losing 4 electrons. - (c) MnSO4 to MnO2: Mn changes from +2 to +4, losing 2 electrons. - (d) MnSO4 to MnO4^-: Mn changes from +2 to +7, losing 5 electrons.

Step 4: Calculating the Equivalent Weight for Each Option

The equivalent weight is the molecular weight divided by the number of electrons lost. We are looking for half the molecular weight.- (a) No electron transfer, not applicable.- (b) \( \text{Equivalent weight} = \frac{151}{4} \)- (c) \( \text{Equivalent weight} = \frac{151}{2} = 75.5 \) which is half the molecular weight.- (d) \( \text{Equivalent weight} = \frac{151}{5} \)

Step 5: Identifying the Correct Answer

From the calculations, only option (c) \( \mathrm{MnSO}_{4} \to \mathrm{MnO}_{2} \) involves losing 2 electrons, making the equivalent weight exactly half of the molecular weight.

Key Concepts

Redox Reaction

Redox reactions are a special type of chemical processes where electrons are transferred between atoms or molecules. The name "redox" is derived from two related phenomena: "reduction," where a substance gains electrons, and "oxidation," which involves the loss of electrons. Usually, both occur simultaneously; when one species is oxidized, another is reduced.

• **Oxidation**: Loss of electrons.
• **Reduction**: Gain of electrons.
• **Oxidizing Agent**: The species that gets reduced and causes oxidation.
• **Reducing Agent**: The species that gets oxidized and facilitates reduction.

In the context of chemistry exercises, understanding redox reactions helps in determining equivalent weights. The process of determining how many electrons are exchanged helps calculate these weights accurately.
Whenever you face a redox reaction problem, identify what gets oxidized and what gets reduced, and pay special attention to the electron transfer between them.

Molecular Weight

Molecular weight, sometimes called molar mass, is the sum of the atomic weights of all atoms in a molecule. It reflects the mass of a given molecule and is crucial for stoichiometric calculations in chemistry.

• **Atomic Weight**: The weight of a single atom, measured in atomic mass units (amu).
• **Molecular Formula**: Indication of the type and number of atoms in a molecule, e.g., MnSO₄.

To find molecular weight, you simply sum up the atomic weights of each constituent element, taking into account the number of atoms present in each element, as shown in the step-by-step solution provided for MnSO₄. This understanding ensures calculations of other properties, like equivalent weights, are accurate.
For instance, MnSO₄'s weight is calculated as 151 amu, which directly influences determining its equivalent weight when it undergoes electron transfer during chemical conversions.

Electron Transfer

Electron transfer is central to many chemical reactions, especially those involving redox processes. During these reactions, electrons are shuffled between substances, leading to changes in oxidation states.

• **Oxidation State**: Indicates the degree of oxidation of an atom in a compound.
• **Electron Loss**: Signifies oxidation, with potential increase in oxidation state.
• **Electron Gain**: Marks reduction, with a possible decrease in oxidation state.

When calculating equivalent weights, it is essential to determine how many electrons the molecule loses or gains. For example, when MnSO₄ is converted into MnO₂, manganese loses 2 electrons, helping in equating the molecular weight to the number of electrons involved, giving half the molecular weight as the equivalent weight.
Understanding these principles aids in grasping complex reactions and identifying correct stoichiometric calculations.

Chemistry Olympiad

Chemistry Olympiads are competitive examinations that test a student’s knowledge and understanding of chemistry concepts. They often feature advanced problems that stimulate analytical thinking and problem-solving.

• **Challenging Problems**: Include various aspects of chemistry from atomic theory to thermodynamics.
• **Practical Importance**: Fosters deeper understanding of chemical processes.
• **Advanced Concepts**: Expands learning beyond basic high school curriculum.

Participating in a Chemistry Olympiad requires understanding topics like redox reactions, molecular weight, and electron transfer. These events are designed not just to assess theoretical knowledge, but also to apply it practically in complex scenarios.
Mastering these topics prepares students for advanced levels and is often seen as a stepping stone towards an academic or professional career in chemistry.