Question

The volume of \[10N\] and $4HCl$ required to make $1L$ of $7N$ $HCl$ are:
A. $0.5L$ of $10N$ $HCl$ and $0.50L$ of $4N$ $HCl$
B. $0.6L$ of $10N$ $HCl$ and $0.40L$ of $4N$ $HCl$
C. $0.8L$ of $10N$ $HCl$ and $0.20L$ of $4N$ $HCl$
D. $0.75L$ of $10N$ $HCl$ and $0.25L$ of $4N$ $HCl$

Answer 1

Hint: According to the law of equivalence, the sum of the equivalents of the same acid divided by the total volume of the mixture is equal to the equivalent of the resulting mixture of the two solutions. The resultant mixture will have a different normality as compared to the two individual components of the mixture.

Complete answer:
As we know from the mathematical equation of law of equivalence,
${N_1}{V_1} + {N_2}{V_2} = N{V_{mix}}$
Here, ${N_1} = 10N$
$N = 7N$
Let the volume of $10N$ $HCl$ mixed in the solution be $'V'L$ .
Let the volume of $4N$$HCl$ mixed in the solution be $'1 - V'L$ .
Thus, from the mathematical equation, we can deduce that the sum of the products of the normality and volume of the individual acids is equal to the product of the normality and total volume of the resulting mixture.
Thus, the normality of the resulting mixture is equal to:
$\dfrac{{{N_1}{V_1} + {N_2}{V_2}}}{{{V_{mix}}}} = N$ ….(i)
In the above equation, ${V_{mix}} = {V_1} + {V_2}$
Substituting the values in the equation (i), we have:
$\dfrac{{10 \times V + 4(1 - V)}}{{V + 1 - V}} = 7$
Thus, on solving, we have the value of the volume of $10N$ $HCl$ equal to:
$V = \dfrac{3}{6} = 0.5L$
Thus, the volume of $10N$ $HCl$ mixed in the solution = $V = 0.5L$
The volume of $4N$$HCl$mixed in the solution is = $1 - V = 1 - 0.5 = 0.5L$

Thus, the correct option is A. $0.5L$ of $10N$ $HCl$ and $0.50L$ of $4N$ $HCl$ .

Note:
To prepare a solution of a desired concentration, two things are important:
(i) Volume of the individual reactants which together form a solution of combined volume of the two components.
(ii) Normality of the individual solutions.