Question

$1$ L of $0.15M$ $HCl$ and $1$ L of $0.3M$ $HCl$ is given. What is the maximum volume of $0.2M$ $HCl$ which one can make from these two solutions? No water is added.

• A. $1.2L$
• B. $1.5L$
• C. $1.3L$
• D. $1.4L$

Answer 1

The correct option is B $1.5L$

Since, no water has been added, the volume of solution cannot exceed $2$ L. So, less concentrated solution should be taken in its total volume.
Only the small portion of more concentrated solution is to be mixed so that the total concentrated is less than $0.3M$ $HCl$.
Let $x$ L of $0.3M$ solution is mixed.
Total volume $=(x+1)$ litres
$M_1{V}_1+M_2{V}_2=M_3{V}_3[V_3=(1+x\left)L\right]$
$⟹0.3\times x+0.15\times 1=M_3(1+x)$ litres
Final molarity $=0.2M$
$0.3x+0.15=0.2(1+x)$
$⟹x=0.5L$
Maximum volume $=1+0.5=1.5$ litres