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) \(\mathrm{MnO}_{4}^{-}\)

Short answer

The equivalent weight is half the molecular weight when \( \text{MnSO}_4 \) converts to \( \text{MnO}_2 \).

Step-by-step solution

Understand Equivalent Weight

The equivalent weight of a substance in redox reactions is calculated by dividing its molar mass by the number of electrons transferred in the half-reaction. In this problem, we need to find the scenario where the equivalent weight is half the molecular weight of \( \text{MnSO}_4 \). This implies that the number of electrons transferred \( n \) is 2 (as equivalent weight = \( \frac{{\text{molecular weight}}}{n} \)).

Determine the Change in Oxidation State

Identify the oxidation states of manganese in \( \text{MnSO}_4 \) and each of the products: \( \text{MnO} \), \( \text{MnO}_{4}^{2-} \), \( \text{MnO}_{2} \), and \( \text{MnO}_{4}^{-} \). In \( \text{MnSO}_4 \), manganese has an oxidation state of +2.

Calculate Oxidation State for Option (a) MnO

In \( \text{MnO} \), the oxidation state of manganese is +2, the same as in \( \text{MnSO}_4 \), so no electrons are transferred. Thus, it does not satisfy the condition.

Calculate Oxidation State for Option (b) MnO4^{2-}

In \( \text{MnO}_{4}^{2-} \), the oxidation state of manganese is +6. Therefore, the change in oxidation state is 4 (from +2 to +6), transferring 4 electrons. This does not satisfy the condition.

Calculate Oxidation State for Option (c) MnO2

In \( \text{MnO}_{2} \), the oxidation state of manganese is +4. Thus, the change is +2 to +4, resulting in a transfer of 2 electrons. This scenario gives an equivalent weight that is half the molecular weight.

Calculate Oxidation State for Option (d) MnO4^{-}

In \( \text{MnO}_{4}^{-} \), the oxidation state of manganese is +7. The change is +2 to +7, transferring 5 electrons. This does not match the condition needed.

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes where electrons are transferred between two substances. This electron transfer results in a change in the oxidation states of the reactants. In a redox reaction, one element undergoes oxidation, meaning it loses electrons, while another undergoes reduction, gaining those electrons. These reactions are crucial in various fields, from biological processes like cellular respiration to industrial applications like the production of metal compounds. Key Characteristics of Redox Reactions:

• Oxidation: Increase in oxidation state due to electron loss.
• Reduction: Decrease in oxidation state due to electron gain.
• Redox Pair: Always involves a pair, one undergoing oxidation and the other undergoing reduction.

Understanding redox reactions is essential when analyzing chemical changes, as they reflect how elements and compounds interact and transform.

Oxidation State

The oxidation state, also known as the oxidation number, of an element in a compound is a number that represents its degree of oxidation. It indicates the total number of electrons that an atom gains or loses to form a stable compound. These values are crucial for balancing chemical equations, especially in the case of redox reactions, as they help in identifying which atoms are oxidized and which are reduced. In manganese compounds, for instance, the oxidation state can vary significantly, which drastically affects their chemical properties and reaction pathways. How to Determine Oxidation States:

• Elemental State: The oxidation state is zero.
• Simple Ions: The oxidation state is equal to the ion charge.
• Complex Ions and Compounds: Use known oxidation states (like oxygen usually at -2) to deduce the unknown states.

In our exercise, determining the change in oxidation state allowed us to find reactions where the equivalent weight of a compound was half its molecular weight.

Manganese Compounds

Manganese is a versatile element, forming a variety of compounds with different oxidation states, typically ranging from +2 to +7. These compounds are used extensively in industrial catalysis, batteries, and even biological systems. The distinctive oxidation states of manganese compounds make them interesting for studying redox reactions, as each state plays a unique role in electron transfer processes. Consider some common manganese compounds:

• Manganese(II) sulfate (\(\mathrm{MnSO}_4\)): A +2 oxidation state, commonly used in supplements and industrial applications.
• Permanganate ion (\(\mathrm{MnO}_{4}^{-}\)): Exhibits a +7 oxidation state, highly oxidizing, often used in analysis and oxidation processes.
• Manganese dioxide (\(\mathrm{MnO}_2\)): A +4 oxidation state, used in batteries and as a catalyst.

The study of these compounds reveals how manganese's oxidation state changes impact its chemical behavior and utility in various reactions.