Question

$2N$ $HCl$ solution is isomolar with:
(A) $0.5N$ ${H_2}S{O_4}$
(B) $4N$ ${H_2}S{O_4}$
(C) $2N$ ${H_2}S{O_4}$
(D) $0.4N$ ${H_2}S{O_4}$

Answer 1

Here, it has been asked in the question to find $2N$ $HCl$ solution has to be isomolar with. Now, we have to understand the meaning of $2N$ $HCl$ that there is $2$ moles of $HCl$ in solution to release $2$ moles of ${H^ + }$ ions. So, here we have to check the molarity of the $HCl$ and then check all the options if any matches the molarity of it.
Useful formula is: ${\text{molarity = }}\dfrac{{{\text{normality}}}}{{{\text{acidic hydrogen}}}}$

Complete answer:
Let us first understand the meaning of molarity of any solution: the moles of a solute per liter of a solution. Molarity is also known as the molar concentration of a solution. Normality is defined as a measure of concentration equal to the gram equivalent weight per liter of solution. And isomolar means that the molarity of two or more solutions should be the same.
Now, we have to use the formula for calculating the molarity of $2N$ $HCl$ solution as:
${\text{molarity = }}\dfrac{{{\text{normality}}}}{{{\text{acidic hydrogen}}}}$ …. $(1)$
Here, for normality of $HCl$ solution it is important to understand that one normal of the solution is equal to one mole of the solution that means $1N = 1M$
Therefore, here the normality of $HCl$ solution is $2$ since, here two moles of $HCl$ solution are used to obtain an isomolar solution from the options given.
In equation $(1)$
${\text{molarity = }}\dfrac{2}{1} = 2M$ …. $(2)$ (only one ${H^ + }$ in $HCl$ )
Thus, the molarity of the $2N$ $HCl$ solution is $2M$
Now to match this molarity we have to check all the given options to obtain the correct answer.
$0.5N$ ${H_2}S{O_4}$
${\text{molarity = }}\dfrac{{0.5}}{2} = 0.25M$
$4N$ ${H_2}S{O_4}$
${\text{molarity = }}\dfrac{4}{2} = 2M$
$2N$ ${H_2}S{O_4}$
${\text{molarity = }}\dfrac{2}{2} = 1M$
$0.4N$ ${H_2}S{O_4}$
${\text{molarity = }}\dfrac{{0.4}}{2} = 0.2M$
Here, only option B is matching the molarity of $HCl$ solution.

Note:
Here, it has been asked to find the isomolar solution of $2N$ $HCl$ solution and we used the molarity formula for this, we have to understand the concept of normality and acidic ion in the solution that the acidic hydrogen is the acidic one in the solution and it is only one for one $HCl$ and common for both moles.