Question

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

Short answer

Option (b) \(\frac{3}{2}\) moles of \(\mathrm{H}_2\mathrm{O}_2\) are required.

Step-by-step solution

Write the Redox Reaction

First, consider the balanced reaction between potassium permanganate (\(\mathrm{KMnO}_4\)) and hydrogen peroxide (\(\mathrm{H}_2\mathrm{O}_2\)) in acidic medium. The reaction is characterized by the change in oxidation states where \(\mathrm{Mn}^{7+}\) goes to \(\mathrm{Mn}^{2+}\) and \(\mathrm{H}_2\mathrm{O}_2\) is oxidized to \(\mathrm{O}_2\). The reaction is:\[\mathrm{2 KMnO}_4 + 3 \mathrm{H}_2\mathrm{O}_2 + 3 \mathrm{H}_2\mathrm{SO}_4 \rightarrow \mathrm{2 MnSO}_4 + 3 \mathrm{O}_2 + 4 \mathrm{H}_2\mathrm{O} + \mathrm{K}_2\mathrm{SO}_4\]

Determine Moles of Reactants

In the balanced reaction provided, you see that 2 moles of \(\mathrm{KMnO}_4\) require 3 moles of \(\mathrm{H}_2\mathrm{O}_2\) for complete reaction.

Calculate Moles Ratio

Since the reaction needs 2 moles of \(\mathrm{KMnO}_4\) to be decolorized by 3 moles of \(\mathrm{H}_2\mathrm{O}_2\), the ratio of moles required is:\[\frac{3}{2} \text{ moles of } \mathrm{H}_2\mathrm{O}_2 \text{ for 1 mole of } \mathrm{KMnO}_4\]

Conclusion

Therefore, for the decolorization of 1 mole of \\(\mathrm{KMnO}_4\), you require \(\frac{3}{2}\) moles of \(\mathrm{H}_2\mathrm{O}_2\).

Key concepts

Potassium Permanganate

Potassium Permanganate (\(\mathrm{KMnO}_4\)) is a common compound used in redox reactions. It appears as a solid with a deep purple color and is well known for its oxidizing properties. When dissolved in water, it can affect the color of other substances through oxidation.
In acidic solutions, Potassium Permanganate acts as a powerful oxidizing agent due to the high oxidation state of manganese, which is +7 in \(\mathrm{KMnO}_4\). This oxidation state changes to a lower state, specifically +2, as manganese transitions from \(\mathrm{KMnO}_4\) to manganese sulfate \(\mathrm{(MnSO}_4\)). This process typically results in the decolorization of the permanganate solution.
Some key points about Potassium Permanganate include:

• Its ability to react with a variety of reducing agents.
• The noticeable color change from purple to colorless or light pink as it is reduced.
• It is used extensively in both qualitative and quantitative analysis in the laboratory.

Hydrogen Peroxide

Hydrogen Peroxide (\(\mathrm{H}_2\mathrm{O}_2\)) is a versatile chemical compound often used as a disinfectant and bleaching agent. In chemical reactions, it serves as a two-way agent: it can either act as an oxidizer or as a reducer, depending on the substances it reacts with.
In the context of redox reactions involving \(\mathrm{KMnO}_4\) in an acidic medium, it functions as a reducing agent. By donating electrons, it causes the reduction of manganese in \(\mathrm{KMnO}_4\) while itself being oxidized to oxygen gas \(\mathrm{O}_2\).
Here are a few things to note about \(\mathrm{H}_2\mathrm{O}_2\):

• It decomposes into water and oxygen, which is a self-sustaining exothermic reaction.
• Its dual nature allows it to participate in various chemical processes, including cleaning and antiseptic purposes.
• Attention is required when handling \(\mathrm{H}_2\mathrm{O}_2\), as it can be reactive and may cause irritation or burns.

Acidic Medium Reactions

Reactions occurring in an acidic medium are distinguished by the presence of more \(\mathrm{H}^+\) ions, usually supplied by acids such as \(\mathrm{H}_2\mathrm{SO}_4\). These \(\mathrm{H}^+\) ions can greatly influence the behavior of redox reactions.
For example, in the reaction between \(\mathrm{KMnO}_4\) and \(\mathrm{H}_2\mathrm{O}_2\), the acidic medium plays a crucial role in facilitating the reduction of \(\mathrm{Mn}^{7+}\) in \(\mathrm{KMnO}_4\) to \(\mathrm{Mn}^{2+}\). The acidic conditions promote the formation of manganese sulfate and, simultaneously, the oxidation of \(\mathrm{H}_2\mathrm{O}_2\) to \(\mathrm{O}_2\).
Some important characteristics of reactions in an acidic medium include:

• Increased oxidation or reduction potential of substances present.
• Frequently involves the release or consumption of hydrogen ions.
• Acidic solutions are often used to facilitate certain redox processes that would otherwise not proceed as efficiently in a neutral or basic medium.