Question

The ${{pH}}$ of the aqueous solution containing $0.49{{ g}}$of ${{{H}}_2}{{S}}{{{O}}_4}$ in one litre is:
A.$2$
B.$1$
C.$1.7$
D.$0.3$

Answer 1

${{pH}}$ of a solution is the measure of amount of or concentration of hydrogen ions in a given solution. In this question, we are given that there is an aqueous solution of sulphuric acid, which is a strong acid as such. So we can calculate the ${{pH}}$ of the solution from the given data.

Complete answer:
We can calculate the molar concentration of sulphuric acid. It can be calculated by adding the atomic masses of all the elements contained in the formula of sulphuric acid, ${{{H}}_2}{{S}}{{{O}}_4}$ .
Molecular weight or molecular mass of sulphuric acid $=$ $\left( {2 \times 1} \right){{ }} + {{ 32 + }}\left( {4 \times 16} \right)$ ${{g mo}}{{{l}}^{ - 1}}$
$=$ $98$ ${{g mo}}{{{l}}^{ - 1}}$ .
We know that,
The mass of sulphuric acid, ${{{H}}_2}{{S}}{{{O}}_4}$ in grams $=$ $0.49{{ g}}$.
The molecular weight of sulphuric acid, ${{{H}}_2}{{S}}{{{O}}_4}$ $=$ $98$ ${{g mo}}{{{l}}^{ - 1}}$ .
We also know the formula to calculate molar concentration of a substance,
${{C = }}\dfrac{{{n}}}{{{V}}}$ ,
Where, ${{C}}$ is the molar concentration of the substance,
${{n}}$ is the number of moles of the substance,
${{V}}$ is the volume of solution in litres.
We also know that, number of moles of a substance can be calculated using the formula,
${{n = }}\dfrac{{{m}}}{{{M}}}$ ,
Where, ${{n}}$ is the number of moles of the substance,
${{m}}$ is the mass of the substance in grams,
${{M}}$ is the molar mass of the substance.
$\therefore$ Molar concentration, ${{C}}$ $=$ $\dfrac{{0.49{{ g}}}}{{98{{ g mo}}{{{l}}^{ - 1}}}}$ $\because$ Volume $=$ $1{{ L}}$
${{C}}$ $=$ $0.005$ moles
Therefore, the concentration of acid (hydrogen ions) $=$ $0.005$ moles
Sulphuric acid, ${{{H}}_2}{{S}}{{{O}}_4}$ is a dibasic acid, meaning that it produces two acidic hydrogen ions on dissociation of the acid. Basicity of an acid can also be described as the number of ionisable ions in that acid. ${{{H}}_2}{{S}}{{{O}}_4}$ is a dibasic acid, meaning that it can produce two ionisable hydrogen ions.
$\left[ {{{{H}}^ + }} \right]$ $=$ $2{{ }} \times {{ }}0.005$ $=$ $0.01{{ M}}$
${{pH}}$ is calculated as the negative logarithm of the concentration of hydrogen ions.
${{pH}}$ $=$ $- \log \left[ {{{{H}}^ + }} \right]$
${{pH}}$ $=$ $- \log \left[ {0.01} \right]$ $=$ $2$
Therefore the ${{pH}}$ of the solution is $2$ , indicating that it is still a concentrated acidic solution. Acids have a ${{pH}}$ of less than $7$ while bases have a ${{pH}}$ of more than $7$ .

Hence, option (A) is the correct answer.

Note:
Here, we calculated the ${{pH}}$ of the sulphuric acid solution by first calculating the molar concentration of the solution by using the values of mass and molar mass. Once, the value of concentration of hydrogen ions is known, we can calculate the value of ${{pH}}$ .