Question

Henderson’s equation is ${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{{\text{[salt]}}}}{{{\text{[acid]}}}}$. If the acid gets half neutralized the value of pH will be: $\left( {{\text{p}}{{\text{K}}_{\text{a}}} = 4.30} \right)$
A) 4.3
B) 2.15
C) 8.60
D) 7

Answer 1

Hint: We know that the degree of alkalinity or acidity of a solution is known as its pH. pH is the negative logarithm of the hydrogen ion concentration. We are given Henderson’s equation to calculate the pH. To solve this we have to first calculate the concentration of the salt and the acid correctly. Then simply by substituting the values we can calculate the pH of the acid.

Complete step-by-step solution:
We know that the degree of alkalinity or acidity of a solution is known as its pH. pH is the negative logarithm of the hydrogen ion concentration.
We are given Henderson’s equation as follows:
${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{{\text{[salt]}}}}{{{\text{[acid]}}}}$
Henderson’s equation is used to calculate the pH of weak acid. The acid which does not dissociate completely is known as a weak acid.
We are given that the acid gets half neutralized. The point at which half of the acid has been neutralized is known as half-neutralization point. At the half-neutralization point, the concentration of weak acid is equal to the concentration of its conjugate base or salt.
Thus, we can say that the concentration of acid and the concentration of salt is equal. Thus,
${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\left( {\text{1}} \right)$ …… ${\text{[salt]}} = {\text{[acid]}}$
We are given that ${\text{p}}{{\text{K}}_{\text{a}}} = 4.30$. Thus,
${\text{pH}} = {\text{4}}{\text{.30}} + {\text{0}}$
${\text{pH}} = {\text{4}}{\text{.3}}$
Thus, the value of pH is 4.3.

Thus, the correct answer is option ‘A’.

Note: Here, we can see that the value of pH is equal to the value of ${\text{p}}{{\text{K}}_{\text{a}}}$. ${\text{p}}{{\text{K}}_{\text{a}}}$ is the negative logarithm of the acid dissociation constant. When only half of the acid dissociates, the reaction is in equilibrium. When the reaction is in equilibrium, it is the half-neutralization point. At half-neutralization point, the value of pH is equal to the value of ${\text{p}}{{\text{K}}_{\text{a}}}$.