Question

The density (in ${\text{g m}}{{\text{L}}^{{\text{ - 1}}}}$) of a \[{\text{3}}{\text{.6 M}}\] sulphuric acid solution having \[29\% \]$ {{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ ​ [molar mass =\[{\text{98 gmo}}{{\text{l}}^{{\text{ - 1}}}}\]] by mass, will be:
1. \[{\text{1}}{\text{.45}}\]
2. \[{\text{1}}{\text{.65}}\]
3. \[{\text{1}}{\text{.88}}\]
4. \[{\text{1}}{\text{.22}}\]

Answer 1

Hint:Density is the ratio of mass of the solution and volume of solution. By introducing this ratio into the molarity of solution formula then we can find the density of the solution by using the given mass percent and molarity values of the solution.

Complete step by step answer:
From the given,
Molarity of solution = \[{\text{3}}{\text{.6 M}}\]
Means one litre of solution contains \[{\text{3}}{\text{.6 }}\] moles of sulfuric acid.
Molar mass of sulfuric acid = \[{\text{98 g/mol}}\]
One litre of solution contains \[{\text{3}}{\text{.6 X 98 gms of }}{{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}\].
Mass percent of solution = \[{\text{29% }}\]
Means 100 grams of solution contains \[{\text{29}}\] grams of sulfuric acid.
Let’s calculate the density of solution;

\[{\text{Molarity of the solution = }}\dfrac{{{\text{Moles of solute}}}}{{{\text{Volume of solution in Litres}}}}\]……………………..(1)
\[{\text{Volume of solution = }}\dfrac{{{\text{Mass}}}}{{{\text{Density}}}}\]……………………………….(2)
From equation (1) and (2)
\[{\text{Molarity of the solution = }}\dfrac{{{\text{Moles of solute}}}}{{\dfrac{{{\text{Mass}}}}{{{\text{Density}}}} X 1000}}\]
\[{\text{Molarity of the solution = }}\dfrac{{{\text{Moles of solute X Density}}}}{{{\text{Mass}}}} X 1000\]………………………………(3)
Substitute the all given values in equation (3)
\[{\text{3}}{\text{.6 X 98 = }}\dfrac{{{\text{29 X Density}}}}{{{\text{100}}}}{\text{ X 1000}}\]
\[{\text{Density = }}\dfrac{{{\text{352}}{\text{.8}}}}{{{\text{290}}}}{\text{ = 1}}{\text{.22g/ml}}\]
Hence, the answer is \[{\text{d = 1}}{\text{.22 g/ml}}\].
Therefore, the correct option is (4).

Additional information:
Molarity and molality are the ways to measure the concentration of a chemical solution. The main difference between the two comes down to mass versus quantity.
Molality describes the moles of a solvent with respect to the mass of a solvent, whereas molarity describes the moles of a solvent in relation with the volume of a solution.

Note:
The mass percent describes the component of elements in a particular mixture. During a given mass of solution, it shows the mass of solute present.