Question

Hydrochloric acid solution A and B have a concentration of 0.5N and 0.1N respectively. The volume of solutions A and B required to make 2 litres of 0.2N \[HCl\] are:
A. 0.5L of A + 1.5L of B
B. 1.5L of A + 0.5L of B
C. 1.0L of A + 1.0L of B
D. 0.75L of A + 1.25L of B

Answer 1

Hint: In this question we have to prepare a 2 litre solution of \[HCl\] having 0.2 normality or N. Thus, the combined volume of solution A and B will be 2 litres. The formula of normality will be helpful to solve this question, which is normality into volume of one solution plus normality into volume of second solution equals to the normality into volume of the final solution.

Complete answer:
The correct answer to this question is option A, to make a 2 litre solution of hydrochloric acid (\[HCl\]) having a normality of 0.2, we have to mix 0.5L of solution A and 1.5L of solution B. Let us see how.
Let us first list all the things given in the question. Let the normality of solution A be \[{{N}_{1}}\], thus
\[{{N}_{1}}=0.5N\]
And let the normality of solution B be \[{{N}_{2}}\], thus
\[{{N}_{2}}=0.1N\]
Also, let the volume of solution A be \[{{V}_{1}}\] and that of solution B be \[{{V}_{2}}\]. Let the normality of the final solution be \[N\] and the volume of the final solution be \[V\].
Thus we can get our answer by applying just a simple formula with the given values. We know that adding the product of normality and volume of two solutions will give us the product of normality and volume of the final solution.
Thus, \[{{N}_{1}}{{V}_{1}}+{{N}_{2}}{{V}_{2}}=NV\]
Putting the given value in to the above equation, we get
\[0.5\times {{V}_{1}}+0.1\times {{V}_{2}}=0.2\times 2\]
Now, we know that the volume of the final solution will be 2 litres, thus
\[{{V}_{1}}+{{V}_{2}}=2\],
\[{{V}_{2}}=2-{{V}_{1}}\]
Now, putting the above obtained equation into the original equation.
Thus, \[0.5\times {{V}_{1}}+0.1\times (2-{{V}_{1}})=0.2\times 2\]
Therefore, after solving the above equation, we get the value of \[{{V}_{1}}\] as 0.5, thus\[{{V}_{1}}=0.5\].
Now, putting the value of \[{{V}_{1}}\] in\[{{V}_{1}}+{{V}_{2}}=2\].
Therefore, the value of \[{{V}_{2}}\] becomes 1.5. Thus \[{{V}_{2}}=1.5\].
Now, the volume \[{{V}_{1}}\] represents the volume of solution A, therefore we will need 0.5 litres of solution A, and the volume \[{{V}_{2}}\] represents the volume of solution B, therefore we will need 1.5 litres of solution B.
Therefore the correct answer is option A.

Note:
Hydrochloric acid is used industrially to process steel, the material of choice for suspension bridges and cars and trucks. Hydrochloric acid is also used in the production of batteries, photoflash bulbs and fireworks. It's even used to process sugar and make gelatin.