Question

How would you use the Henderson-Hasselbalch equation to calculate the pH of each solution?

Answer 1

In the calculation of pH, this above equation is used for the calculation of pH of a buffer solution and the numerical acid dissociation constant ${{K}_{a}}$ of the acid is known and thus the value of the pH can be calculated for particular solution.

Complete step by step answer:
- The concept of the calculation of pH of the solution from the basic concept of chemistry and some of the related calculations are familiar to us.
Let us recall the Henderson-Hasselbalch equation which is a common equation for the calculation of pH of solution.
- The Henderson-Hasselbalch equation relates the pH, $p{{K}_{a}}$ and the molar concentration together.
- This equation is mainly used for the calculation of pH of a buffer solution. The equilibrium between the weak acid and its conjugate base allows the solution to resist the changes to pH when a small amount of strong acid or base is added and thus this buffer pH can be estimated by using this equation.
- The Henderson-Hasselbalch equation is given by,
$pH = pKa + {{\log }_{10}}\left( \dfrac{[{{A}^{-}}]}{[HA]} \right)$
where pH is the acidity of the buffer solution
$p{{K}_{a}}$ is the negative logarithm of ${{K}_{a}}$
${{K}_{a}}$ is the acid dissociation constant
$[HA]$ is the concentration of acid
$[{{A}^{-}}]$ is the concentration of conjugate base.
Consider an example of calculating pH of a buffer solution of 0.27 M formic acid and 0.5 M sodium formate.
- We know that $p{{K}_{a}}$ of formic acid is 3.75
By using the Henderson-Hasselbalch equation and substituting the values of the data, we have
$pH=3.75+\log \left( \dfrac{0.5}{0.27} \right)$
$\Rightarrow pH = 3.75 + 0.268 = 4.02$
Therefore, the pH of the buffer solution is 4.02 which is higher than that of the acid.

Note: Note that the value of the higher pH of the solution than the value of the acid that is the $p{{K}_{a}}$ value indicates that there is more of the conjugate base than the weak acid and the logarithm will have the positive value and this means that pH will actually increase.