Question

For $0.1{\text{ }}mol\;HCl$ is dissolved in distilled water of volume $V$ then $\mathop {\lim }\limits_{V \to \infty } {(pH)_{solution}}$ is equal to
A.Zero
B.$1$
C.$7$
D.$14$

Answer 1

$pH$, denoting 'potential of hydrogen' or 'power of hydrogen' is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions (solutions with higher concentrations of ${H^ + }$ ions) are measured to have lower $pH$ values than basic or alkaline solutions. $pH$ is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, ${a_{{H^ + }}}$, in a solution.

Complete answer:
In the above question, it is given that $0.1{\text{ }}mol\;HCl$ is dissolved in distilled water. Hence, ${K_W} = [{H^ + }][O{H^ - }]$. Here, ${K_W}$ is the self-ionization constant of water. It is also given that $0.1{\text{ }}mol\;HCl$ is being dissolved in an infinite volume of distilled water. After a certain stage of dissolving, $[{H^ + }] < {10^{ - 7}}M$.
On taking the logarithm of the above equation, we will get $pOH = p{K_W} - pH$. For $[{H^ + }]$, the equation is modified to $pH = p{K_W} + pOH$. Here, $p{K_W} = {10^{ - 7}}$ and $pOH = {10^{ - x}}$ where $x > 7$
Hence, $[{H^ + }] = {10^{ - 7}}M + {10^{ - x}}M$
This makes the whole solution neutral and we know that the $pH$ of a neutral solution is $7$.
Hence, the correct option is C.

Additional information:
At $25^\circ C$, solutions with a pH less than $7$ are acidic, and solutions with a $pH$ greater than $7$ are basic. Solutions with a $pH$ of $7$ at this temperature are neutral (example: pure water). The neutral value of the $pH$ depends on the temperature – being lower than $7$ if the temperature increases. The $pH$ value can be less than $0$ for very strong acids, or greater than $14$ for very strong bases.

Note:
The $pH$ scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution. This is because the formula used to calculate $pH$ approximates the negative of the base $10$ logarithm of the molar concentration of hydrogen ions in the solution as we saw above. More precisely, $pH$ is the negative of the base 10 logarithm of the activity of the ${H^ + }$ ion.