Question

$20ml$ of $0.5{\text{M HCl}}$ is mixed with $30ml$ of $0.3{\text{M HCl}}$, the molarity of the resulting solution is:
A.${\text{0}}{\text{.8M}}$
B.${\text{0}}{\text{.53M}}$
C.${\text{0}}{\text{.38M}}$
$D.{\text{0}}{\text{.83M}}$

Answer 1

Hint: When two acids are mixed with each other, they generally do not react but if one acid is stronger and the other one is weak acid then they both will react similar to the acid base reaction, the weak acid will act as a base against the stronger acid.

Complete step by step answer:
When two acids are mixed with different \[{\text{pH}}\] values than the resulting acid will have the \[{\text{pH}}\] value in between the strong and weak acid.
The \[{\text{pH}}\] value of the resulting acid will also depend upon the volumes of both the acids. If the volume of stronger acid is minute and the volume of weak acid is more, then the resulting acid will have \[{\text{pH}}\] value nearer to the \[{\text{pH}}\] value of weak acid.
So we can say that the resulting \[{\text{pH}}\] value will depend upon the concentration and volume of both the acids.
Formula to calculate the resulting \[{\text{pH}}\] value is:
${\text{M(}}{{\text{V}}_1}{\text{ + }}{{\text{V}}_2}{\text{)}} = {{\text{M}}_1}{{\text{V}}_1}{\text{ + }}{{\text{M}}_2}{{\text{V}}_2}$ --------------(1)
Where,
${\text{M}}$ is the concentration of resulting acid in terms of molarity.
${{\text{M}}_1}{\text{,}}{{\text{M}}_2}$ are the concentration of the acids before mixing.
${{\text{V}}_1}{\text{ and }}{{\text{V}}_2}$ are the volumes of both the acids before mixing.
The volumes and the concentrations of the acids before mixing are provided to us,
${{\text{M}}_1} = 0.5$, ${{\text{M}}_2} = 0.3$ and ${{\text{V}}_1} = 20ml$, ${{\text{V}}_2} = 30ml$
  Hence by putting the values in eq.(1)
${\text{M(20 + 30)}} = 0.5 \times 20 + 0.3 \times 30$
${\text{M}} = \dfrac{{19}}{{50}} = 0.38$
Hence the concentration (molarity) of the resulting solution is ${\text{0}}{\text{.38M}}$.
So, option (C) is correct.

Note:
The volumes which we are putting in the eq(1) must have same units, if one of them is in ${\text{ml}}$ then other must have the same unit ${\text{ml}}$ and the concentration used should be in terms of molarity or mole per liter.