Question

Concentrated aqueous sulphuric acid is 98% $H_2SO_4$ by mass and has a density of \[1.80mg{L^{ - 1}}\]. Find the volume of acid required to make one liter of 0.1M $H_2SO_4$ solution.

Answer 1

Hint: Molarity is the number of moles of solute per liter of solution. In the question we find $H_2SO_4$ is 98% by weight which means 98 gram of $H_2SO_4$ is dissolved in 100 g of solution.

Complete step by step solution:
First we have to calculate the number of moles in the solution. We can use the following equation to find it.
\[No.\,of\,moles = \dfrac{{given\,mass}}{{mass\,of\,solute}} = \dfrac{{98g}}{{98g}} = 1\,mole\]
Given,
Density of solution = \[1.80mg{L^{ - 1}}\]
Now, we can calculate the volume of solution.
We know,
\[Density = \dfrac{{mass}}{{volume}}\]
Therefore on substituting the values in this equation we get,
\[Volume = \dfrac{{mass}}{{density}} = \dfrac{{100g}}{{1.80mg{L^{ - 1}}}} = 55.5mL\]
Now to calculate the molarity we use the formula:
\[Molarity = \dfrac{{mole\,of\,solute \times 1000}}{{Volume\,of\,solution\,in\,m{L_{}}}}\]
Therefore on substituting the values in this equation we get,
\[Molarity = \dfrac{{1 \times 1000}}{{55.5\,mL}} = 18M\]
According to law of neutralization,
We know,
\[{M_1}{V_1} = {M_2}{V_2}\]
Substituting the values in this equation we get,
\[18 \times {V_2} = 0.1 \times 1000mL\]
Or, \[{V_2} = 5.5mL\]
Hence, the volume of acid required is 5.5mL.

Additional Information:
Molarity, molality, and normality are all units of concentration. Molarity is defined as the number of moles of solute per liter of solution. Molality is defined as the number of moles of solute per kilogram of solvent and Normality is defined as the number of equivalents per liter of solution. We should use Molality instead of Molarity in experiments involving significant temperature changes. This is because as the volume of a solution increases with temperature, heating causes molarity to decrease; however, since molality is based on mass rather than volume, molality remains unchanged.

Note: Molar concentration can be used to convert between the mass or moles of solute and the volume of the solution. Molarity is a measurement of the moles in the total volume of the solution, whereas Molality is a measurement of the moles in relationship to the mass of the solvent. Hence, the two should never be confused.