Question

A volume of $20{\text{ ml}}$ of $1{\text{M}}$ ${\text{KMn}}{{\text{O}}_{\text{4}}}$ solution is diluted to ${\text{150ml}}$ . In this solution, 50 ml of $10{\text{M}}$ ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ is added. 25 ml of this mixture is titrated with 20 ml of ${\text{Fe}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}$ solution. The molarity of ${\text{Fe}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}$ solution is:
(A) $0.0416$
(B) $0.208$
(C) $0.625$
(D) $0.125$

Answer 1

To answer this question, you must recall the concept of gram equivalents of a substance. We know that, n- factor of a substance can be defined as the combining capacity or valency of the substance. For instance, if we consider an acid, so the n- factor of the acid is its basicity. Similarly in case of a redox reaction, the n- factor represents the number of electrons transferred per molecule of the substance.

Formula used: $N = M \times n$
Where, $N$ denotes the normality of the reacting solution
$M$ denotes the molarity of the reacting solution
And $n$ represents the n- factor of the substance reacting.

Complete step by step solution
$20{\text{ ml}}$ of $1{\text{M}}$ ${\text{KMn}}{{\text{O}}_{\text{4}}}$ contains ${\text{20 meq}}$ . 50 ml of $10{\text{M}}$ ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ will contain $500{\text{ meq}}$ of the acid and is mixed in the above potassium permanganate solution.
So the mixture contains ${\text{20 meq}}$ ${\text{KMn}}{{\text{O}}_{\text{4}}}$ and $500{\text{ meq}}$ ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ in 200 mL of the solution.
So, 25 mL of the solution will contain $2.5{\text{ meq}}$ of ${\text{KMn}}{{\text{O}}_{\text{4}}}$ and $62.5{\text{ meq}}$ of ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ .
When titrated with ferrous oxalate, the reaction occurring between potassium permanganate and ferrous oxalate in presence of sulphuric acid is a redox reaction, i.e. both reduction and oxidation reactions take place. Both the ferrous ions as well as oxalate ions are oxidized by potassium permanganate in acidic medium.
One mole of permanganate ion accepts 5 electrons while one mole of ferrous oxalate loses 3 electrons per mole. So we can say that the n- factor of potassium permanganate is 5 while that of ferrous oxalate is 3. So we can write,
${N_1}{V_1} = {N_2}{V_2}$
$\Rightarrow 2.5 \times 5 = 20 \times M \times 3$
$\therefore M = 0.208{\text{ M}}$
The correct answer is B.

Note
When a given solution is diluted, only the volume and concentration of the solution changes. The amount of the solute remains constant, and thus the initial number of moles in the substance can be used to calculate the concentration of the diluted solution.