Question

Concentrated aqueous solution of ${{H}_{2}}S{{O}_{4}}$ is 98% by mass and has a density of $1.80g/mL$. What is the volume of acid required to make one litre of 0.1M ${{H}_{2}}S{{O}_{4}}$ solution?

Answer 1

Hint:. With the above given data, it is better to take out the normality of the acid. Now, using the relation between normality and volume, volume can be calculated, by substituting the normality in the equation.

Complete step by step answer:
In order to answer the given question, let us learn about the unit of concentration, that is normality. Before that, it is important to know about the gram equivalent of a substance. Gram equivalent is the measurement of the relative capacity a molecule possesses. So, a solute is the important thing when normality is considered. Normality can be also said as the equivalent concentration that a solution holds, solute is responsible for that.
Now as normality is a measure of equivalent concentration, it is mathematically represented as:
$Normality=\dfrac{wt%\times density\times 10}{eq.wt}$
Now, let us find the value of normality for the acid by substituting the values in the above equation, which are given in the question:
$Normality=\dfrac{98\times 1.8\times 10}{49}=36N$
Also, there is an equation that relates normality to the volume of a solution. The equation is represented by: ${{N}_{1}}{{V}_{1}}={{N}_{2}}{{V}_{2}}$…….( i )
hence it means that the product of normality and volume is constant for every solution. Now, let us find out the volume required to make 0.1M of the acid. So, we have
$36\times V=0.2\times 1000$, from equation (i)
So, $V=\dfrac{0.2\times 1000}{36}=5.55mL$
So, we require a volume of 5.55mL to make 0.1 M of the acid, which is our final answer.

Note: It is to be noted that the product of normality and volume is constant for every solution. That means normality is inversely proportional to the volume. On increasing the volume, normality reduces, and vice versa.