Problem 38 - A Complete Resource Book in Chemistry for JEE Main

Question

For decolourization of one mole of \(\mathrm{KMnO}_{4}\) the number of moles of \(\mathrm{H}_{2} \mathrm{O}_{2}\) required are (a) \(1 / 2\) (b) \(3 / 2\) (c) \(5 / 2\) (d) \(7 / 2\)

Step-by-Step Solution

Answer

The correct answer is (c) \(5/2\) moles of \(\mathrm{H}_2\mathrm{O}_2\) are required.

Step 1: Identify the Reaction

The decolourization of potassium permanganate (KMnO_4) occurs in acidic medium and involves the conversion of MnO_4^- ions to Mn^{2+} ions by hydrogen peroxide (H_2O_2), a reducing agent.

Step 2: Write the Balanced Equation

The balanced chemical equation for the reaction in acidic medium is: \[ 2 \mathrm{KMnO}_{4} + 5 \mathrm{H}_{2} \mathrm{O}_{2} + 6\mathrm{H}^+ \rightarrow 2 \mathrm{Mn}^{2+} + 5\mathrm{O}_{2} + 8\mathrm{H}_{2}\mathrm{O} \] This shows that 5 moles of H_2O_2 reduce 2 moles of \mathrm{KMnO}_{4}.

Step 3: Calculate the Moles Required

According to the balanced equation, to decolourize 1 mole of \mathrm{KMnO}_4, half of the amount of H_2O_2 is needed compared to when 2 moles of \mathrm{KMnO}_{4} are involved. Therefore, \[ \text{For 1 mole of } \mathrm{KMnO}_{4}: \quad \frac{5}{2} \text{ moles of } \mathrm{H}_{2} \mathrm{O}_{2} \text{ are required.} \]

Key Concepts

Redox reactions

Redox reactions are a type of chemical process where oxidation and reduction occur simultaneously. In a redox reaction, one substance loses electrons (oxidation) while another gains electrons (reduction). This type of reaction is essential in many biochemical and industrial processes.

• **Oxidation:** A substance loses electrons, increasing its oxidation state.
• **Reduction:** A substance gains electrons, decreasing its oxidation state.

In the decolourization of potassium permanganate ( KMnO₄) by hydrogen peroxide (H₂O₂), the permanganate ions ( MnO₄⁻) act as the oxidizing agent and are reduced to manganese ions ( Mn²⁺). Meanwhile, hydrogen peroxide serves as the reducing agent and, in the process, loses electrons.

Balanced chemical equation

A balanced chemical equation is crucial for accurately representing a chemical reaction. It ensures that the number of atoms for each element is the same on both sides of the equation. This is a fundamental principle based on the law of conservation of mass.
By balancing chemical equations, we can understand the stoichiometry of the reaction, which shows the exact proportions of reactants and products.
When examining the reaction between potassium permanganate and hydrogen peroxide, the balanced equation is: \[ 2 \mathrm{KMnO}_{4} + 5 \mathrm{H}_{2} \mathrm{O}_{2} + 6\mathrm{H}^{+} \rightarrow 2 \mathrm{Mn}^{2+} + 5\mathrm{O}_{2} + 8\mathrm{H}_{2}\mathrm{O} \]
This equation indicates that 5 moles of H₂O₂ are necessary to fully react with 2 moles of KMnO₄ under acidic conditions.

Chemical reaction stoichiometry

Stoichiometry involves using relationships derived from balanced chemical equations to calculate the quantities of reactants and products in a chemical reaction. It helps in predicting how much of each component is needed or produced.
To solve stoichiometric problems, you can follow these steps:

• Write a balanced chemical equation for the reaction.
• Convert known quantities of substances to moles.
• Use the balanced equation to set up mole ratios.
• Use mole ratios to calculate the desired quantities.

In the exercise example, the stoichiometry of the reaction reveals that to decolourize 1 mole of KMnO₄, you need \( \frac{5}{2} \) moles of H₂O₂. This calculation is pivotal for understanding how different quantities of reactants interact in the reaction.