Question

An aqueous solution of $HCl$ has a $pH$ of 2.0 When water is added to increase the $pH$ to 5.0, the hydrogen ion concentration
A.Remains the same
B.Decreases three-fold
C.Increases three- folds
D.Decreases thousand folds

Answer 1

As we know,$pH$ is a scale used to specify the acidity or basicity of an aqueous solution. $pH$ can also be defined as the negative logarithm (to base 10) of the hydrogen ion concentration in $mol$ ${L^ - }^1$.
$pH = - {\log _{10}}[{H^ + }]$
Where, $[{H^ + }]$ is the concentration of hydrogen ions in $mol$ ${L^ - }^1$.

Formula used: $[{H^ + }] = {10^{ - pH}}$

Complete step by step answer:
As mentioned in the hint already $pH$ is a measure of the amount of hydrogen ions $[{H^ + }]$or protons present in an aqueous solution. We all know acid is a substance that can donate hydrogen ions or protons (${H^ + }$). Water has $pH$ of 7 and is neutral that is neither acidic nor basic, solutions with $pH$ less than 7 are considered acidic and solutions with $pH$ more than 7 are considered basic. That means with increasing value of $pH$ the hydrogen ion concentration decreases.
To calculate the concentration of hydrogen of a given solution from its $pH$ value we use the formula
$[{H^ + }] = {10^{ - pH}}$
Where $[{H^ + }]$ is the concentration of hydrogen ions or protons present in the solution.
As mentioned in the question the aqueous solution of $HCl$ has a $pH$ of 2.0. So, using the above formula we can calculate the hydrogen ion concentration of it
For $pH = 2$; $[{H^ + }] = {10^{ - 2}}$
Now, after we added water the $pH$ increases to 5.0, using the same formula we used above we can calculate the hydrogen ion concentration for this solution as well
For $pH = 5$;$[{H^ + }] = {10^{ - 5}}$
To calculate the difference in hydrogen ion concentration of both the solutions of $pH = 2$ and $pH = 5$, Simply divide the hydrogen ion concentration $[{H^ + }]$ of both.
$\dfrac{{HCl(pH = 5)}}{{HCl(pH = 2)}} = \dfrac{{[{H^ + }] = {{10}^{ - 5}}}}{{[{H^ + }] = {{10}^{ - 2}}}}$=${10^{ - 3}}$

Therefore, the correct option is the option D, which decreases thousand folds.

Note:
Always remember $pH$ is negative logarithm of hydrogen ions concentration $[{H^ + }]$ which means increase in hydrogens ion concentration of a solution will decrease the the $pH$ value of that solution, $pH$ can be measured by both $pH$ paper and $pH$ meter.