Question

$10ml$ of a strong acid solution of $pH=2.00$ is mixed with $990ml$ of another strong acid solution of $pH=4.00$. The $pH$ of the resulting solution will be

• A. $4.002$
• B. $4.000$
• C. $4.200$
• D. $3.72$

Answer 1

The correct option is D $3.72$

As we know that,
$pH=-\log \left[H^{+}\right]$
$\Rightarrow \left[H^{+}\right]={10}^{-pH}$
Therefore,
$\left[H^{+}\right]$ in solution of $pH1$ is ${10}^{-2}M$.
$\left[H^{+}\right]$ in solution of $pH4$ is ${10}^{-4}M$.
As we know that,
$Molarity=\frac{\text{No. of moles of solute}}{{\text{Volume of solution}}_{\left(inL\right)}}$
Therefore,
No. of moles of solute in solution of $pH2={10}^{-2}times\frac{10}{1000}={10}^{-4}$
No. of moles of solute in solution of $pH4={10}^{-4}+(9.9\times {10}^{-5})=1.99\times {10}^{-4}$
Therefore,
Molarity of solution $=\frac{1.99\times {10}^{-4}}{1}=1.99\times {10}^{-4}M$
Therefore,
$pH=-\log (1.99\times {10}^{-4})$
$\Rightarrow pH=4-\log \left(1.99\right)=3.7$
Hence the $pH$ of the resulting solution is $3.7$.