Question

How Many Litres Of A $90\%$ Solution Of Concentrated Acid Needs To Be Mixed With A $75\%$ Solution Of Concentrated Acid To Get A $30\mathrm{L}$ Solution Of $78\%$ Concentrated Acid?

• A. $24\mathrm{L}$
• B. $22.5\mathrm{L}$
• C. $6\mathrm{L}$
• D. $17.5\mathrm{L}$

Answer 1

The correct option is C

$6\mathrm{L}$

The explanation for the correct option:

Option (C):$6\mathrm{L}$

Step 1: Given data:

The initial percentage of the concentrated acid solution is given by:
$N_1$= $90\mathrm{\%}$

The final percentage of the concentrated acid solution is given by:
$N_2$ = $75\mathrm{\%}$

The volume of solution that has to be prepared is given as :
$V$ = $30\mathrm{L}$
$N$ is given as the final per cent obtained solution.

The volume of a final solution that was mixed from two different percentages can be determined by considering the total per cent as $100\mathrm{\%}$ .

Step 2: Formula applied for calculation of the final volume :

As the number of moles in both the solutions before and after the mixing of solutions is the same.

hence, by the definition of normality, the number of moles is equal to the product of normality and volume, which can be given as:
${\mathrm{N}}_1\mathrm{V}+{\mathrm{N}}_2\left(30-\mathrm{V}\right)=\mathrm{N}\times 30$

Step 2: Calculating the final volume of the solution:

By putting the given value, we can calculate the final volume of the solution as:
$90\times \mathrm{V}+75\left(30-\mathrm{V}\right)=78\times 30$

$\Rightarrow \mathrm{V}=6\mathrm{litres}$

Thus, option (C) $6\mathrm{L}$ of a$90\mathrm{\%}$ solution of concentrated acid needs to be mixed with a $75\mathrm{\%}$ solution of concentrated acid to get a solution of $30\mathrm{L}$concentrated acid.