Question

The $pH$ of ${10^{ - 6}}M{\text{ }}HCl,{\text{ }}{10^{ - 7}}M{\text{ }}HCl\,{\text{and }}{10^{ - 8}}M{\text{ }}HCl$ respectively is:
(A) $6,7,8$
(B) $6,6.79,6.98$
(C) $6,6.79,7.02$
(D) $6,6.98,8$

Answer 1

Hint:$pH$ is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions are measured to have lower $pH$ values than basic or alkaline solutions. The $pH$ scale is logarithmic and inversely indicates the concentration of hydrogen ions in solution.

Complete step by step answer:We know that, $pH = - \log \left[ {{H^ + }} \right]$
So, when $\left[ {{H^ + }} \right] = {10^{ - 6}}$ (as $HCl$ has ${10^{ - 6}}M$)
We can neglect the concentration of water.
$pH = - \log \left[ {{H^ + }} \right] = - \log \left( {{{10}^{ - 6}}} \right) = 6$
Now for, \[M = {10^{ - 7}}M{\text{ }}HCl\]
We can say that $\left[ {{H^ + }} \right] = {10^{ - 7}}$
Here, we have to consider concentration of water which is ${10^{ - 7}}M$
So, total concentration of ${H^ + } = 2 \times {10^{ - 7}}M$
Hence, $pH = - \log \left[ {{H^ + }} \right] = - \log \left( {2 \times {{10}^{ - 7}}} \right)$
$ = - \log 2 + 7 = 6.79$
For, ${10^{ - 8}}M{\text{ }}HCl$
$\left[ {{H^ + }} \right] = {10^{ - 8}}$
Here, we have to consider the concentration of water i.e. ${10^{ - 7}}M$
So, the total concentration of ${H^ + } = {10^{ - 8}} + {10^{ - 7}}$
$ = 1.1 \times {10^{ - 7}}$
Hence, $pH = - \log \left[ {{H^ + }} \right] = - \log \left( {1.1 \times {{10}^{ - 7}}} \right)$
$ = 6.98$
We have taken the water’s ${H^ + }$ concentration, as you know, pure water undergoes self-ionization to form hydronium ions, ${H_3}{O^ + }$, and hydroxide ions, $O{H^ - }$
$2{H_2}O\left[ l \right] \rightleftharpoons {H_3}{O^ + }\left( {aq.} \right) + O{H^ - }\left( {aq.} \right)$
Here, the value of $\left[ {{H_3}{O^ + }} \right] = {10^{ - 7}}$
Moreover, we remember that $HCl$ is a strong acid and $pH$ of an acidic solution can never, ever be higher than $7$.
So, the answer to the question is (B) $6,6.79,6.78$.


Note:The $pH$ of $7$ is considered neutral. A $pH$ less than $7$ is acidic, whereas, $pH$ greater than $7$ is basic. The $pH$ scale is logarithmic. It plays a very crucial role in daily life like, if soil will have lesser $pH$ than usual range, plants will not be able to grow and produce products. $pH$ controls many vital processes in the human body from drinking to digestion of food in the stomach.