Question

What volumes of 12N HCl and 3N HCl must be mixed to form one litre 6N HCl?

Answer 1

To solve this question we have to use the formula of mixing that is given as ${{N}_{1}}{{V}_{1}}+{{N}_{2}}{{V}_{2}}={{N}_{3}}{{V}_{3}}$. In the question the values of normality for all the solutions are given but the volume is only given for the third one that is 1 litre (1000 ml). So, you have to find the volume of two other solutions by using the formula.

Complete answer:
From your chemistry lessons you have learnt about the normality and the equation of normality for a mixture of solutions.
In the question we have to find the volume of a solution in a mixture. Therefore here we are going to deal with the equation of normality for a mixture. It is the equation that helps us to find the volume of the solution which is required for the preparation of a solution of different normality. The equation of normality is given as:
$Initial\,normality({{N}_{1}})\times Initial\,Volume({{V}_{1}})=Final\,normality\,of\,solution({{N}_{2}})\times Final\,Volume\,of\,solution({{V}_{2}})$
Now, in the question three different solutions with the same solute of volume and normality are mixed. Hence the equation of normality will be given as:
${{N}_{1}}{{V}_{1}}+{{N}_{2}}{{V}_{2}}={{N}_{3}}{{V}_{3}}$…………… (1)
Where,${{N}_{1}}{{N}_{2}}$ = normality of Solute (HCl)
${{V}_{1}}{{V}_{2}}$ = volume of solute (HCl)
${{N}_{3}}{{V}_{3}}$= Normality and volume of the solution (HCl)
So, the value of normality for solute is given as 12N, 2N and the value of normality and volume of the solution is given as 6N and one lire (1000 ml). Here we have to find the volumes of the solute.
Let us take xml as the volume of 12N HCl and y ml as the volume 3 N HCl and they are mixed to form 1000 ml of 6N HCl. Therefore the sum of the volume will be:
$x+y=1000$…… (2)
Now, put all the values given in the equation (1)we will get:
$12x+3y=6\times 1000$……. (3)
Now, put the value of y = (1000-x) from the equation (2)in equation (3), we will get:
$12x+3(1000-x)=6000$
12x+3000-3x=6000$$$$$$ 9x=3000$$\therefore x=\dfrac{3000}{9}=333.3ml$Therefore the value of y will be :$y=(1000-x)=(1000-333.3)=666.7,ml$$
Thus 333.3 ml of 12N HCl and 666.7 ml of 3N HCl are mixed to form 1000 ml of 6N solution.

Note:
Normality is defined as the mole equivalents of solute or number of gram present in one litre of a solution. It is used to measure the concentration of the solution. Normality is denoted by 'N'. The formula to calculate the normality is given as:
$Normality=\dfrac{no.\,of\,gram\,equivalent}{Volume\,of\,solution\,in\,litre}$