Question

The pH of $0.15M$ solution of $HOCl$ $({K_a} = 9.6 \times {10^{ - 6}})$ is:
      A. $4.42$
      B. $2.92$
      C. $3.42$
      D. None of these

Answer 1

Hint:We know that $HOCl$ is a weak acid so $HOCl$ will dissociate to give small amount of ${H_3}{O^ + }$ and ${A^ - }$ . The equilibrium constant for an acid is called the acid ionization constant, $Ka$ . First we will determine the concentration of ${H^ + }$ions present in the solution using the formula $\sqrt {KaC} $ where $Ka$ is the equilibrium constant and $C$ is the concentration of the acid. After finding the ${H^ + }$ ions we will find the pH by using the formula $ - \log [{H^ + }]$ .


Complete step by step answer:
First, we will write the equilibrium equation:
$HOCl(aq) + {H_2}O(l) \rightleftharpoons {H_3}{O^ + }(aq) + C{l^ - }(aq)$
We know that for acidic solutions
${H^ + } = \sqrt {{K_a}C} $
Where $Ka$$ = 9.6 \times {10^{ - 6}}$ and $C = 0.15M$
On putting the values of $Ka$ and $C$ in the above formula we get: -
${H^ + } = \sqrt {{K_a}C} $
        $
   = \sqrt {9.6 \times {{10}^{ - 6}} \times 0.15} \\
   = \sqrt {1.44 \times {{10}^{ - 6}}} \\
   = 0.0012M \\
 $
 We got the value of ${H^ + }$so now we can simply determine the pH of the solution by using the formula: -
$pH = - \log [{H^ + }]$
By putting the value of ${H^ + }$ in this formula we get: -
$pH = - \log [{H^ + }]$
       $
   = - \log [0.0012] \\
   = 2.920818 \\
 $
i.e., option (B) is correct.


Additional information: By determining the equilibrium constants in aqueous solutions, we can measure the relative strength of acid. The larger the $Ka$ of an acid, the larger will be the concentration of ${H_3}{O^ + }$ and ${A^ - }$ . Thus, the ionization constant increases as the strength of the acid increases. The concentration of the H3O+ ion in an aqueous solution gradually decreases and the pH of the solution increases as the solution becomes more dilute.


Note:: The two assumptions that are made in weak-acid equilibrium are as follows:
1-The dissociation of the acid is so small that the change in the concentration of the acid can be ignored.
2-The dissociation of the acid is so large that the H3O+ ion concentration can be ignored.