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

Hint: 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.