Question

How to prepare 0.4% of NaOH (36%) in a water tank to get a final volume of 4000 litre?

Answer 1

Hint: Approach this question with the help of the dilution concept because we have to prepare a dilute solution as per requirement. As we know that dilution is the process of adding solvent to a solution in order to decrease its concentration. In this process, usually the amount of solute remains constant and the amount of the whole solution increases due to which the concentration of solution decreases.
Formula used:
We will require the following formula:-
${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$

Complete answer:
Let us first discuss about dilution as follows:-
-Dilution: It can be described as the process of adding additional solvent to a solution in order to decrease the overall concentration of the solution. During dilution, the amount of solute remains constant but we increase the total amount of solution by adding solvent to it, thereby decreasing its final concentration.

-To prepare a solution of 0.4% of NaOH:-
${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}$
where,
${{M}_{1}}$= concentration of original solution
${{V}_{1}}$= volume of original solution
${{M}_{2}}$ = concentration of diluted solution
${{V}_{2}}$ = volume of diluted (final) solution
-Values are given as follows:-
${{M}_{1}}$= concentration of original solution = 36% = 0.36 M
${{V}_{1}}$= volume of original solution =?
${{M}_{2}}$ = concentration of diluted solution = 0.4% = 0.004 M
${{V}_{2}}$ = volume of diluted (final) solution = 4000L
On substituting these values in the above formula, we get:-
$\begin{align}
  & \Rightarrow {{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}} \\
 & \Rightarrow 0.36M\times {{V}_{1}}=0.004M\times 4000L \\
 & \Rightarrow {{V}_{1}}=\frac{16}{0.36}L \\
 & \Rightarrow {{V}_{1}}=44.44L \\
\end{align}$

Hence we will require 44.44L of 36% NaOH to prepare a 0.4% concentrated NaOH in a 4000L tank.

Note:
-Remember that dilution can also be obtained through mixing a solution of higher concentration with a less concentrated identical solution.
-Also while calculating dilution factors make sure that units of volume and concentration are the same for both sides of the equation to avoid any errors.