Problem 38 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Hydroxylamine reduces iron (III) according to the equation: \(2 \mathrm{NH}_{2} \mathrm{OH}+4 \mathrm{Fe}^{3+} \rightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g}) \uparrow+\mathrm{H}_{2} \mathrm{O}+4 \mathrm{Fe}^{2+}+4 \mathrm{H}^{+}\) Iron (II) thus produced is estimated by titration with a standard permanganate solution. The reaction is : $$ \mathrm{MnO}_{4}^{-}+5 \mathrm{Fe}^{2+}+8 \mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+}+5 \mathrm{Fe}^{3+}+4 \mathrm{H}_{2} \mathrm{O} $$ A \(10 \mathrm{~mL}\). sample of hydroxylamine solution was diluted to 1 litre. \(50 \mathrm{~mL}\). of this diluted solution was boiled with an excess of iron (III) solution. The resulting solution required \(12 \mathrm{~mL}\). of \(0.02 \mathrm{M} \mathrm{KMnO}_{4}\) solution for complete oxidation of iron (II). Calculate the weight of hydroxylamine in one litre of the original solution. \((\mathrm{H}=1, \mathrm{~N}=14, \mathrm{O}\) \(=16, \mathrm{~K}=39, \mathrm{Mn}=55, \mathrm{Fe}=56)\) [1982 - 4 Marks]

Step-by-Step Solution

Answer

The weight of hydroxylamine in one liter of the original solution is 0.0396 grams.

Step 1: Determine Moles of KMnO4 Used

The molarity of the KMnO4 solution is given as 0.02 M, and the volume used is 12 mL or 0.012 L. To find the moles of KMnO4 used, multiply molarity by volume:\[moles\,of\,KMnO_4 = 0.02 \times 0.012 = 2.4 \times 10^{-4}\,\text{moles}\]

Step 2: Relate KMnO4 to Fe^{2+} Moles

According to the balanced equation, 1 mole of KMnO4 reacts with 5 moles of Fe^{2+}. Therefore, calculate the moles of Fe^{2+}:\[moles\,of\,Fe^{2+} = 5 \times 2.4 \times 10^{-4} = 1.2 \times 10^{-3} \] moles.

Step 3: Calculate Moles of Fe^{3+} Reduced by NH2OH

Since 4 moles of Fe^{3+} are reduced to Fe^{2+} per 2 moles of NH2OH, the moles of Fe^{3+} reduced is equal to the moles of Fe^{2+} formed. Therefore:\[moles\,of\,Fe^{3+} = 1.2 \times 10^{-3}\]

Step 4: Relate Fe^{3+} Reduced Back to NH2OH

Recall the balanced reaction: 4 moles of Fe^{3+} are reduced by 2 moles of NH2OH. So, the moles of NH2OH used is:\[moles\,of\,NH_2OH = \frac{1.2 \times 10^{-3}}{2} = 6.0 \times 10^{-4}\,\text{moles}\]

Step 5: Calculate Moles of NH2OH in 1 L of Diluted Solution

The calculation in step 4 corresponds to 50 mL of the diluted solution. Scale up to find the moles in 1 L:\[\text{Moles in 1 L} = \frac{6.0 \times 10^{-4}\,\text{moles}}{50 \times 10^{-3}\,\text{L}} \times 1\,\text{L}= 1.2 \times 10^{-2}\,\text{moles}\]

Step 6: Determine Moles of NH2OH in Original Solution

Since the sample was diluted from 10 mL to 1 L (1000 mL):\[\text{Moles in original solution} = \frac{1.2 \times 10^{-2}\,\text{moles}}{100} = 1.2 \times 10^{-4} \times \frac{1000}{10} = 1.2 \times 10^{-3}\,\text{moles}\]

Step 7: Calculate Weight of NH2OH in Original Solution

The molar mass of NH2OH is \(2(1) + 14 + 16 = 33\,\text{g/mol}\). Multiply moles by molar mass to find the mass:\[mass = 1.2 \times 10^{-3} \times 33 = 0.0396\,\text{g}\]

Key Concepts

Chemical Equations

Chemical equations are a way to represent chemical reactions using symbols and formulas to convey what happens during the reaction. They illustrate how reactants are transformed into products. A balanced chemical equation ensures that the number of atoms for each element is equal on both sides of the equation, obeying the Law of Conservation of Mass.

For example, consider the equation given in the problem where hydroxylamine (\(\text{NH}_2\text{OH}\)) reduces iron(III) ions (\(\text{Fe}^{3+}\)):

• Left side (reactants): \(2 \text{NH}_2\text{OH} + 4 \text{Fe}^{3+}\)
• Right side (products): \(\text{N}_2\text{O} + \text{H}_2\text{O} + 4 \text{Fe}^{2+} + 4 \text{H}^+\)

This specific equation shows that two molecules of hydroxylamine reduce four ferric ions into ferrous ions, while releasing nitrogen monoxide gas, water, and hydrogen ions.

Balancing chemical equations is crucial in stoichiometry, which helps us determine the correct proportions of reactants needed to form desired amounts of products. Without balancing, it would be impossible to predict the outcomes accurately, including mole relationships like those used extensively in the step-by-step solution provided.

Mole Concept

The mole concept is fundamental to understanding chemical quantities and calculations. It allows chemists to count atoms, molecules, or ions through weighing them instead of counting individually. A mole is defined as \(6.022 \times 10^{23}\) entities (Avogadro's number), simplifying calculations in chemistry by converting mass to accessible terms.
For example, using the mole concept in this exercise helps calculate the amount of hydroxylamine.

Here’s how it works:

• Moles of \(\text{KMnO}_4\): Calculated using its molarity (0.02 M) and volume (0.012 L) resulted in \(2.4 \times 10^{-4}\) moles.
• The reaction between \(\text{MnO}_4^-\) and \(\text{Fe}^{2+}\) indicates the mole ratio of 1:5, allowing calculation of \(\text{Fe}^{2+}\) moles.
• Further calculations connected these conversions back to \(\text{NH}_2\text{OH}\) moles, revealing \(1.2 \times 10^{-2}\) moles of \(\text{NH}_2\text{OH}\) in a liter of diluted solution, crucial for computing the weight of hydroxylamine.

Understanding these mole relationships allows translating chemical reactions effectively from theoretical equations to practical chemical measurement and use.

Oxidation-Reduction

Oxidation-reduction, or redox reactions, involve the transfer of electrons between two substances. One substance gets oxidized (loses electrons), and another gets reduced (gains electrons).

In this exercise, hydroxylamine reduces \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) while being oxidized itself, evident by the change in oxidation states. This is where hydroxylamine's electrons transfer to iron, allowing the redox process to take place and forming new products.

• Reduction: \(\text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}\)
• Oxidation: \(\text{NH}_2\text{OH} \rightarrow \text{N}_2\text{O}\)

Understanding redox principles is pivotal in such titrations as permanganate serves as a titrant in the second equation, oxidizing \(\text{Fe}^{2+}\) back to \(\text{Fe}^{3+}\) while reducing itself.
These redox reactions help determine concentrations of unknown solutions and are vital across fields like biochemistry, industrial applications, and environmental science, establishing their central role in chemistry.