Question

The strength of a mixture of $ {\text{HCl}} $ and $ {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} $ is $ {\text{0}}{\text{.1N}} $ . On treatment with an excess of $ {\text{AgN}}{{\text{O}}_{\text{3}}} $ solution. $ 20{\text{ ml}} $ of this acid mixture gives $ 0.1435{\text{ g}} $ of $ {\text{AgCl}} $ . The strength of the $ {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} $ is:
(A) $ 24.5{\text{ g}}{{\text{L}}^{ - 1}} $
(B) $ 2.45{\text{ g}}{{\text{L}}^{ - 1}} $
(C) $ 49{\text{ g}}{{\text{L}}^{ - 1}} $
(D) $ 4.9{\text{ g}}{{\text{L}}^{ - 1}} $

Answer 1

Hint: Strength of a solution gives us the mass of the solute present per liter of the solution. To answer this question, you must recall the reaction occurring when $ {\text{AgN}}{{\text{O}}_{\text{3}}} $ is added to the given mixture of acids and solve is using the laws of stoichiometry. We shall find the moles of HCl produced and calculate its normality and thus, the normality and strength of sulfuric acid.

Formula used: $ {\text{Strength}} = \dfrac{{\text{w}}}{{\text{V}}} $ or $ {\text{strength}} = {\text{M}} \times {{\text{M}}_{\text{o}}} $
Where, $ {\text{M}} $ represents the molarity of the given solution
 $ {\text{V}} $ represents the volume of the given solution
 $ w $ represents the given mass of the substance
And, $ {{\text{M}}_{\text{o}}} $ represents the molar mass of the given substance.

Complete step by step solution:
When silver nitrate is added to the mixture of acids, it reacts with hydrochloric acid to form a precipitate of silver chloride. From the amount of silver chloride produced, we can find the amount of hydrochloric acid in the solution and thus the amount of sulphuric acid.
The reaction occurring is given as: $ {\text{HCl}} + {\text{AgN}}{{\text{O}}_{\text{3}}} \to {\text{AgCl}} + {\text{HN}}{{\text{O}}_3} $
From the reaction, we can see that one mole of hydrochloric acid produces one mole of silver chloride. In the question, it is given that $ 0.1435{\text{ g}} $ of silver chloride is formed. So, the number of moles produced are $ = \dfrac{{0.1435}}{{143.5}} = {10^{ - 3}}{\text{ moles}} $ .
So the number of moles of hydrochloric acid in $ 20{\text{ ml}} $ of the acid $ = {10^{ - 3}} $
The normality of $ {\text{HCl}} $ can be calculated as $ = \dfrac{{{{10}^{ - 3}}}}{{\left( {\dfrac{{20}}{{1000}}} \right)}} = 0.05{\text{M}} = 0.05{\text{N}} $
So, let the molarity of $ {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} $ be x.
So we can write:
 $ 0.05 + 2x = 0.1{\text{N}} $
 $ \Rightarrow x = 0.025{\text{N}} $
So the strength of $ {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}} $ in the solution is $ = 0.025 \times 98 $
 $ \therefore {\text{strength}} = 2.4{\text{ g/L}} $
The correct answer is B.

Note:
The law of multiple proportions proposes that two elements can combine in more than one proportion to give a variety of products. The law of definite proportions proposes that two elements for forming a certain compound must always react in a definite whole number ratio. The law of conservation of mass proposes that mass is neither created nor destroyed, or in other words, the mass of a system is always conserved.