Question

How do you calculate pH of acetic acid?

Answer 1

Hint: The answer lies in the fact that acetic acid is the weak acid and thus partially ionizes in the aqueous solution and thus the pH can be calculated by finding the solubility product and then using the formula $pH = -\log \left( \sqrt{c\times {{K}_{sp}}} \right)$

Complete step by step answer:
- We are familiar with the topics of physical chemistry, which deals with the basic concept of the solubility product and the formula used to calculate the solubility product and how that can be related to find the pH of the solution.
- Let us recall the concepts and derive the required answer.
- We need to cite an example in order to derive the pH value of acetic acid and since this is weak acid, it ionizes partially in the aqueous solution to give hydronium ions and acetate ions as shown below,
\[C{{H}_{3}}COOH(aq)+{{H}_{2}}O(l){{H}_{3}}{{O}^{+}}(aq)+C{{H}_{3}}CO{{O}^{-}}(aq)\]
The acid dissociation constant for acetic acid is given by ${{K}_{a}}=1.8\times {{10}^{-5}}$
Let us assume the concentration of acetic acid as ‘c’ and the ‘x’ as the concentration of acetic acid which ionizes the we can write the concentration terms at equilibrium accordingly as:
 \[C{{H}_{3}}COOH(aq)+{{H}_{2}}O(l){{H}_{3}}{{O}^{+}}(aq)+C{{H}_{3}}CO{{O}^{-}}(aq)\]

Initial Concentration	C(-x)	0(+x)	0(+x)
At equilibrium	c-x	x	x

The acid dissociation constant thus will be,
\[{{K}_{a}}=\dfrac{\left[ {{H}_{3}}{{O}^{+}} \right]\left[ C{{H}_{3}}CO{{O}^{-}} \right]}{C{{H}_{3}}COOH}\]
This will be equivalent to the solubility product as,
\[{{K}_{sp}}=\dfrac{x\times x}{c-x}=\dfrac{{{x}^{2}}}{c-x}\]
For the higher initial concentration of acetic acid, we have$c-x\approx c$for $c$>>>\[{{K}_{sp}}\]
Thus, the equation becomes, \[{{K}_{sp}}=\dfrac{{{x}^{2}}}{c}\]
\[\Rightarrow x\sqrt{c\times {{K}_{sp}}}\] …………..(1)
We also know that pH of the solution is given by, $pH = -\log \left( \left[ {{H}_{3}}{{O}^{+}} \right] \right)$ ……(2)
Combining equations (1) and (2),
$pH=-\log \left( \sqrt{c\times {{K}_{sp}}} \right)$
Thus, this expression gives the pH of acetic acid.

Note: Note that by changing the pH of the solution we can change the charge state of the solute and if pH is such that a particular molecule carries no net electric charge the solute has minimal solubility and thus will precipitate out of the solution.