Question

The label of a bottle containing a dilute aqueous solution of acid becomes damaged, only its concentration is readable. A pH meter was nearby, and a quick measurement showed that the hydrogen ion concentration is equal to the value on the label. Which of the following four acids that could have been the solution if the pH changed one unit after a tenfold dilution?
This question has multiple correct options.
A.\[{\text{HCl}}{{\text{O}}_{\text{4}}}\]
B.${{\text{H}}_{\text{3}}}{\text{B}}{{\text{O}}_3}$
C.${\text{C}}{{\text{H}}_3}{\text{COOH}}$
D.${\text{HN}}{{\text{O}}_3}$

Answer 1

Hint: The pH is a measure of the concentration of hydrogen ion. When tenfold dilution of the acid is made, the pH of an only strong acid is changed because strong acid completely dissociates in water, and the concentration of hydrogen ion reduces. Weak acids do not dissociate completely so its pH remains the same as the concentration of hydrogen ion remains the same.

Complete Step-by-Step Solution:
Given,
After the damage on the label of a bottle containing a dilute aqueous solution of an acid, only concentration is readable. The concentration of hydrogen ion is equal to the value on the label.We have to find the acid whose pH changed one unit after a tenfold dilution.
Tenfold dilution is made by adding $1{\text{ ml}}$extract to $9{\text{ ml}}$. This means that the concentration of the acid reduces. So if the acid is strong and dissociates completely in the water then only the pH will change one unit. As weak acid cannot dissociate completely in water then its concentration in the water will be the same so its pH will not change after tenfold dilution.
Here among the given acid, \[{\text{HCl}}{{\text{O}}_{\text{4}}}\] and ${\text{HN}}{{\text{O}}_3}$ are strong acids as they completely dissociate when dissolved in the water. The reaction is given as-
${\text{HN}}{{\text{O}}_{\text{3}}} \rightleftharpoons {{\text{H}}^ + } + {\text{NO}}_3^ - $
${\text{HCl}}{{\text{O}}_{\text{4}}} \rightleftharpoons {{\text{H}}^{\text{ + }}}{\text{ + ClO}}_{\text{4}}^{\text{ - }}$
${{\text{H}}_{\text{3}}}{\text{B}}{{\text{O}}_3}$(Boric acid) is a weak acid as it forms meta-borate ion when dissolved in acid. The reaction is given as-
${{\text{H}}_{\text{3}}}{\text{B}}{{\text{O}}_{\text{3}}} + {{\text{H}}_2}{\text{O}} \rightleftharpoons {\text{B}}\left( {{\text{OH}}} \right)_{_{\text{4}}}^{\text{ - }}$
 Acetic acid ${\text{C}}{{\text{H}}_3}{\text{COOH}}$is also a weak acid which only dissociates to an extent when dissolved in the water.
${\text{C}}{{\text{H}}_3}{\text{COOH}} \rightleftharpoons {{\text{H}}^{\text{ + }}}{\text{ + C}}{{\text{H}}_{\text{3}}}{\text{CO}}{{\text{O}}^ - }$
But it only dissociates partially.

Answer-Hence the correct options are A and C.

Note: The pH measures the acidity or alkalinity of any substance or solution. The solution will be acidic if there are more hydrogen ions in the solution than the hydroxide ion after dissolving the substance in water. The solution will be alkaline or basic if there are more hydroxide ions in the solution than the hydrogen ions. Since strong acid dissociates completely, it increases the concentration of hydrogen ions in solution. The weak acid only partially dissociates due to which there is no increase in the concentration of hydrogen ions.