Question

$pH$ of a solution at ${25}^0$C is $2.5$. On dilution, pH increased to 3.0. The number of times of dilution is:

• A. $10$
• B. $\sqrt{10}$
• C. $50$
• D. $\sqrt{50}$

Answer 1

The correct option is B $\sqrt{10}$

$pH=2.5$ then $\left[H^{+}\right]={10}^{-3+0.5}=M_1$
$pH=3$ then $\left[H^{+}\right]={10}^{-3+}=M_2$
Let $V_1=$x and the solution is dilute by $n$ times then $V_2=$ $nx$
$M_1{V}_1=M_2{V}_2$
${10}^{-3+0.5}\times x={10}^{-3}\times nx$
$n=\frac{{10}^{-3+0.5}}{{10}^{-3}}={10}^{0.5}\left(or\right)\sqrt{10}$