Question

Given, pH of a solution A is $3$ and is mixed with another solution B having pH $2$. If both are mixed, then the resultant pH of the solution will be:

• A. $3.2$
• B. $1.9$
• C. $3.4$
• D. $3.5$

Answer 1

The correct option is B $1.9$

Let the volume of the each solution be V.

Let number of $H^{+}$ ions be $n_1$ and $n_2$ respectively.

For the first solution,

$P^H=-log\left[H^{+}\right]$

$3=-log\left[\frac{n_1}{V}\right]$

$n_1={10}^{-3}V$

For the second solution,

$P^H=-log\left[H^{+}\right]$

$2=-log\left[\frac{n_2}{V}\right]$

$n_2={10}^{-2}V$

Resultant solution;

Total volume=$1V$

Total number of $H^{+}$ ions=$n_1+n_2$

$\left[H^{+}\right]=\frac{n_1+n_2}{2V}$

$\left[H^{+}\right]=\frac{{10}^{-3}+{10}^{-2}}{1}$

$P^H=-log\left[H^{+}\right]$

$P^H=-log\left[\frac{{10}^{-3}+{10}^{-2}}{1}\right]$

$1.958$