If \(\mathrm{Mn}^{3+}\) ions are unstable in solution and undergo disproportionation to give \(\mathrm{Mn}^{2+}, \mathrm{MnO}_{2}\) and \(\mathrm{H}^{+}\) ions. What will be the balanced equation for the reaction? (a) \(3 \mathrm{Mn}^{3+}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{MnO}_{2}+\mathrm{Mn}^{2+}+8 \mathrm{H}^{+}\) (b) \(\mathrm{Mn}^{3+}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{MnO}_{2}+4 \mathrm{H}^{+}\) (c) \(\mathrm{Mn}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{MnO}_{2}+4 \mathrm{H}^{+}\) (d) \(2 \mathrm{Mn}^{3+}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{MnO}_{2}+\mathrm{Mn}^{2+}+4 \mathrm{H}^{+}\)

Redox reactions, short for reduction-oxidation reactions, are processes where electrons are transferred between substances. These reactions are fundamental in chemistry, as they are involved in a variety of biological systems and industrial applications.

In a redox reaction, one substance gets oxidized (loses electrons) and another gets reduced (gains electrons). It's essential to identify the species being oxidized and reduced to understand the reaction fully. In the exercise example, a single element, manganese (Mn), is present in different oxidation states and undergoes both oxidation and reduction, which is a special type of redox reaction known as disproportionation.

To improve comprehension, consider this analogy: A redox reaction is like a dance between two partners - oxidation and reduction - where electrons are the handshakes transferred between them. In disproportionation, one dancer (the element) cleverly splits into two, and exchanges handshakes with themselves in a different guise.

Balancing chemical equations is a critical skill in chemistry that involves equating the number of atoms of each element on both sides of the equation. It ensures the law of conservation of mass is upheld in a chemical reaction. The balancing task can be tackled by approaching the equation systematically, as illustrated by the exercise.

Steps to balance chemical equations involve:

• Writing the unbalanced equation.
• Counting and listing the number of atoms of each element in both reactants and products.
• Using coefficients to balance elements one at a time (except for H and O, which are usually balanced last).
• Balancing oxygen atoms with water and hydrogen atoms with hydrogen ions (H+).
• Balancing the charges with electrons.
• Ensuring that the total number of atoms and the charge are equal on both sides.

Remember, balancing equations is like solving a puzzle. Each piece, or atom, must fit perfectly to complete the picture - the correct balanced chemical equation.

Understanding oxidation states (or oxidation numbers) is key to working with redox reactions and balancing equations. Oxidation states indicate the degree of oxidation of an atom in a compound. They are essential for identifying how electrons are distributed in chemical bonds and for determining which atoms are oxidized or reduced in a reaction.

Here's a simplified guide:

• The oxidation state of an uncombined element is zero.
• For monoatomic ions, the oxidation state equals the charge of the ion.
• Oxygen usually has an oxidation state of -2, and hydrogen is usually +1 when bonded to non-metals.
• The sum of oxidation states in a neutral compound must be zero, while in an ion, it must equal the charge of the ion.

In the exercise, Mn undergoes a change in oxidation states from +3 to +2 (reduction) and from +3 to +4 (oxidation). Tracking these changes is crucial for correctly balancing the overall redox reaction. As you dive into redox chemistry, imagine oxidation states as tags that keep track of each atom's 'electron wallet' - it helps you predict who gains or loses electrons during the dance of a chemical reaction.