Question

When a drop of concentrated ${\text{HCl}}$ solution is added to one liter of pure water at ${\text{2}}{{\text{5}}^{\text{o}}}{\text{C}}$ , the pH drops from about 7 to 4. When second drop of same ${\text{HCl}}$ solution is added, the pH further drops to
(A) $3.7$
(B) 1
(C) 2
(D) $3.4$

Answer 1

To answer this question, you need to recall the formula for the pH of a solution. From the given pH, we can determine the amount of hydrogen ions being added and then calculate the change in pH further.

Formula used: ${\text{pH}} = - \log \left[ {{{\text{H}}^ + }} \right]$
Where, $\left[ {{{\text{H}}^ + }} \right]$ denotes the concentration of hydrogen ions in the given solution.

Complete step by step solution:
We are given the initial pH of pure water as 7. We know that concentrated ${\text{HCl}}$ solution is an acid. When we add a strong acid to a neutral solution, the pH of the solution will decrease.
Initially the pH of water is 7 so the hydrogen ion concentration is ${10^{ - 7}}{\text{ M}}$ . After the addition of one drop of ${\text{HCl}}$ , the pH drops to 4, so the hydrogen ion concentration thus becomes ${10^{ - 4}}{\text{ M}}$ .
The change in the hydrogen ion concentration on addition of one drop of acid $= {10^{ - 4}} - {10^{ - 7}} \approx {10^{ - 4}}$
So the hydrogen ion concentration on addition of second drop of acid $= 2 \times {10^{ - 4}}{\text{ M}}$
So the pH of the solution is $= - {\text{log}}\left[ {{{\text{H}}^{\text{ + }}}} \right] = - \log \left( {2 \times {{10}^{ - 4}}} \right)$
$\therefore {\text{pH}} = 3.7$
The correct answer is A.

Note:
The pH of a solution is known as the power of Hydrogen and it tells the nature of a solution, whether acidic or basic, on the basis of the concentration of hydrogen ions in the solution. If the pH of a solution is less than 7, the solution is said to be acidic in nature. If the pH of a solution is greater than 7, the solution is said to be basic in nature. A neutral solution has a pH value of 7.