Question

How do you solve for $Ka$ when you have only molarity of the acid and pH ?

Answer 1

Hint: First of all, write the reaction for the dissociation of the weak acid and write the Ka for the reaction . we can find the concentration of the hydrogen ions through the pH of solution and the concentration of acid through the molarity. Now with the help of this you can easily answer the given statement.

Complete step by step answer:
- First of all, let’s discuss what is pH. pH gives us the measure of acid/base strength of any solution. pH scale ranges from 0-14, 7 is neutral, below 7 it represents acidic nature i.e. the compound is acidic and above 7 it represents basic nature i.e. the compound is basic.
- Now, coming next to the $Ka$ value. The $pKa$ tells us about the strength of the acid. The $pKa$ is the negative logarithm of the dissociation constant i.e. $Ka$. Smaller value of $pKa$ indicates that it is a strong acid and it has a large $Ka$ value. On the other hand, a larger value of $pKa$ indicates that it is a weak acid and it has large $Ka$ value.
- Now Considering the given statement as:
 The dissociation of a weak acid occurs as;
$HA+{{H}_{2}}O\to {{H}_{3}}{{O}^{+}}+{{A}^{-}}$
Then, the dissociation constant of acid is as;
$Ka=\dfrac{[{{H}_{3}}{{O}^{+}}][{{A}^{-}}]}{[HA]}$ ------------(1)
The concentration of the hydronium ions can be found by using the pH as;
$[{{H}_{3}}{{O}^{+}}]={{10}^{-pH}}$
- Now, if the mole ratio between the acid and [OH] ions and between the acid and the [A] base is $1:1$, then the concentration of both i.e. the hydronium ion and the conjugate base ([A]) is same as;
$[{{A}^{-}}]=[{{H}_{3}}{{O}^{+}}]$
So, thus equation (1), can be rewritten as;
$Ka=\dfrac{{{[{{H}_{3}}{{O}^{+}}]}^{2}}}{[HA]}$
- Hence, by Knowing the molarity of the solution, we can find the concentration of the HA and we know the concentration of the hydronium ion from the pH and hence we can find the Ka of the acid.

Note: Don’t get confused in the $pKa$ and $Ka$.
$pKa$ value gives us the strength of the acid i.e. it tells whether the given acid is a strong acid or a weak acid. $pKa$ value is the negative logarithm of the $Ka$ value i.e. $pKa=-\log 10\text{ Ka}$.
- On the other hand, $Ka$ is the dissociation constant of the acid.
- Smaller value of $pKa$ indicates that it is a strong acid and it has a large $Ka$ value. On the other hand, a larger value of $pKa$ indicates that it is a weak acid and it has a large $Ka$ value.