Question

What is the ${{K}_{a}}$ value of the citric acid + NaOH titration?

Answer 1

Hint: The titration is between citric acid and NaOH (sodium hydroxide) in which citric acid is a weak acid and sodium hydroxide is a strong base. When the titration takes place between a weak acid and a strong base then we get two equivalence points.

Complete answer:
Titration is a process in which we get the neutralization point, by adding a specific amount of base into a specific concentration of acid. When the acid and base are strong then we get a sharp equivalence. The titration is between citric acid and NaOH (sodium hydroxide) in which the citric acid is a weak acid and sodium hydroxide is a strong base. When the titration takes place between a weak acid and a strong base then we get two equivalence points, i.e., before the equivalence and after the equivalence.
When we take 0.1 M NaOH and 0.1 M citric acid, then we get 5.8 ml as the first equivalence point and 16.0 ml as the second equivalence point.
So, there will be two ${{K}_{a}}$ values for citric acid which can help to find the pH of the solution.
$7.4\text{ x 1}{{\text{0}}^{-3}}$ is the first ${{K}_{a}}$ value of citric acid and pH is nearly equal to the $p{{K}_{a}}$
$pH\approx p{{K}_{a}}=-\log (7.4\text{ x 1}{{\text{0}}^{-3}})=2.13$
$1.7\text{ x 1}{{\text{0}}^{-5}}$ is the second ${{K}_{a}}$ value of citric acid. So the pH will be:
$pH\approx p{{K}_{a}}=-\log (1.7\text{ x 1}{{\text{0}}^{-5}})=4.77$

Note:
While we plot the graph of pH and volume of the titrant of the titration between a weak acid or base and strong acid or base, then the curve is difficult to study so the equivalence points are difficult to differentiate.