Question

Concentrated aqueous solution of sulphuric acid is \[98\% \] by mass and has density of\[1.80g/ml\]. What is the volume of acid required to make one liter \[0.1M\]\[{H_2}S{O_4}\] solution?
1. \[16.65mL\]
2. \[22.20mL\]
3. \[5.55mL\]
4. \[11.10mL\]

Answer 1

Hint: We have to know that the sulphuric acid is the chemical element having the molecular formula \[{H_2}S{O_4}\]. The number of moles of solute present in one liter of the solution is known as molarity. The molarity is also known as molar concentration of a solution. It can be find out by dividing the number of moles of solute by the mass of the solvent. Here we need to find the molarity of the sulphuric acid.

Complete answer:
The required volume of acid is not equal to \[16.65mL\]. Hence, option (1) is incorrect.
The volume of acid required to make one liter is not equal to \[22.20mL\]. Hence, the option (2) is incorrect.
According to the question, the concentration of sulphuric acid is given in terms of percentage which is equal to \[98\% \] and the density is equal to \[1.80g/ml\].
Here, first we need to find out the normality of sulphuric acid by using the formula,
$Normality = \dfrac{{\text{Weight Percentage} \times \text{Density} \times 10}}{{\text{Equivalent Weight}}}$
Substitute the given values in the above equation. The equivalent weight of sulphuric acid is equal to $49g$.
$Normality = \dfrac{{98 \times 1.8 \times 10}}{{49}} = 36N$
Let, ${N_1}{V_1} = {N_2}{V_2}$, Where ${N_1}$ is equal to $36N$.
Hence, $36 \times {V_1} = 0.2 \times 1000$
Therefore,
${V_1} = \dfrac{{0.2 \times 1000}}{{36}} = 5.55mL$
Thus, the volume of acid required to make one liter \[0.1M\]\[{H_2}S{O_4}\] solution is equal to $5.55mL$. Hence, option (3) is correct.
The volume of acid needed to make one liter is not equal to \[11.10mL\]. Hence, the option (4) is incorrect.
So, the correct answer is “Option 3”.

Note:
We have to know that the normality of a compound can be found by dividing the number of gram equivalents solute by the volume of solvent present in a liter. The concentration of an acid will measure the acid ions which are available to dissolve in a solvent. The volume of acid required to make a particular concentration can be found by using their normality. The normality is always greater than or equal to the molar concentration of the solution.