Question

Calculate the pH of 0.1 M solution of $N{{H}_{4}}OCN$. ${{K}_{b}}$ for $N{{H}_{3}}$ is 1.75 x ${{10}^{-5}}$ and ${{K}_{a}}$ for HOCN is 3.3 x ${{10}^{-4}}$.

Answer 1

Hint: It is important to know the ions that are present in one molecule of $N{{H}_{4}}OCN$. The reaction between ammonia and cyanic acid gives ammonium cyanate. The reaction is identified as a neutralisation reaction. The pH of the solution can be determined using the dissociation constant of the acid and base.

Complete Solution :
First, we are given with the salt i.e. ammonium cyanate. We know that on dissolving it will dissociate into the weak acid and weak base.
Now, the dissociation can be represented as:
$N{{H}_{4}}OCN\to \text{ }N{{H}_{4}}^{+}+OC{{N}^{-}}$

- From the reaction we can say that it is being dissociated into the ammonium ion, and the cyanate ion.
Here, ammonium ion is a weak base, whereas cyanate ion is a weak acid.
- The dissociation constant of acid increases the concentration of hydronium ions. On the other hand, dissociation constant of base neutralises the hydronium ions reducing concentration of hydronium ions.
- We can conclude that pH increases when base is added and reduces when an acid is added. Now, the pH in terms of weak base, and weak acid can be represented as:
$pH=7+\dfrac{1}{2}\left( p{{K}_{a}}-p{{K}_{b}} \right)$
where,
pH stands for potenz of hydrogen,
$p{{K}_{a}}$ denotes negative logarithm of ${{K}_{a}}$,
$p{{K}_{b}}$ denotes negative logarithm of ${{K}_{b}}$.
- In the question, we are given with the value of ${{K}_{a}}$ is 1.75 x ${{10}^{-5}}$, and ${{K}_{b}}$ is 3.3 x ${{10}^{-4}}$.

- Let us substitute the values in the formula of pH, then
\[pH=7+\dfrac{1}{2}\left( \log \dfrac{1.75\text{ x 1}{{\text{0}}^{-5}}}{3.3\text{ x 1}{{\text{0}}^{-4}}} \right)\]
pH = 7 – 0.635
pH = 6.365
- In the last, we can say that the pH of 0.1 M solution of ammonium cyanate is 6.365 according to the given data in the question.

Note: $p{{K}_{a}}$ numerically denotes the concentration of hydrogen ions in a solution. pH stands for potenz of hydrogen and indicates the amount of ${{H}^{+}}$ ions present. It is important to know that greater the value of ionisation constant of acid, lower will be the pH of the resultant solution. So do not get confused between the two terms.