Question

A solution of $2.5{\text{ molar}}$ sulphuric acid contains the following:
A) $29.5{\text{ g}}$ of sulphuric acid per litre of solution.
B) $245.0{\text{ g}}$ of sulphuric acid per $1000{\text{ ml}}$ of solution.
C) $24.5{\text{ g}}$ of sulphuric acid per $100{\text{ ml}}$ of solution.
D) $59.0{\text{ g}}$ of sulphuric acid per litre of solution.

Answer 1

To solve this we must know that the molarity of a solution is the number of moles of solute per litre of solution. We are given $2.5{\text{ molar}}$ sulphuric acid. Calculate the mass of sulphuric acid in $2.5{\text{ molar}}$ sulphuric acid to find the correct answer.

Complete solution:
We know that the molarity of a solution is the number of moles of solute per litre of solution. Thus,
${\text{Molarity}}\left( {\text{M}} \right) = \dfrac{{{\text{Number of moles}}\left( {{\text{mol}}} \right)}}{{{\text{Volume of solution}}\left( {{\text{litre}}} \right)}}$
We are given $2.5{\text{ molar}}$ sulphuric acid. The $2.5{\text{ molar}}$ sulphuric acid indicates that there are $2.5{\text{ moles}}$ of sulphuric acid per litre or per $1000{\text{ ml}}$ of solution.
We know that the number of moles of any substance is the ratio of its mass to molar mass. Thus,
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$
Rearrange the equation for the mass as follows:
${\text{Mass}}\left( {\text{g}} \right) = {\text{Number of moles}}\left( {{\text{mol}}} \right) \times {\text{Molar mass}}\left( {{\text{g/mol}}} \right)$
We know that the molar mass of sulphuric acid i.e. ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ is $98.079{\text{ g/mol}}$. Now, calculate the mass of sulphuric acid in $2.5{\text{ moles}}$ of sulphuric acid using the equation as follows:
${\text{Mass of }}{{\text{H}}_2}{\text{S}}{{\text{O}}_4} = {\text{2}}{\text{.5 mol}} \times 98.079{\text{ g/mol}}$
${\text{Mass of }}{{\text{H}}_2}{\text{S}}{{\text{O}}_4} = {\text{2}}45.0{\text{ g}}$
Thus, $2.5{\text{ molar}}$ sulphuric acid contains ${\text{2}}45.0{\text{ g}}$ of sulphuric acid per $1000{\text{ ml}}$ of solution.
Now, if $2.5{\text{ molar}}$ sulphuric acid contains ${\text{2}}45.0{\text{ g}}$ of sulphuric acid per $1000{\text{ ml}}$ of solution then $100{\text{ ml}}$ solution contains $24.5{\text{ g}}$ of sulphuric acid.
Thus, $2.5{\text{ molar}}$ sulphuric acid contains $24.5{\text{ g}}$ of sulphuric acid per $100{\text{ ml}}$ of solution.
Thus, $2.5{\text{ molar}}$ sulphuric acid contains ${\text{2}}45.0{\text{ g}}$ of sulphuric acid per $1000{\text{ ml}}$ of solution and $24.5{\text{ g}}$ of sulphuric acid per $100{\text{ ml}}$ of solution.

Thus, the correct options are (B) and (C).

Note: Remember that the molarity of a solution is the number of moles of solute per litre of solution. Molarity is a common term used to express concentration of the solution. The units of molarity are ${\text{mol/L}}$ or ${\text{M}}$.