Question

The ionisation constant of a monobasic acid is $5\times {{10}^{-2}}$. The pH of 0.01M acid solution is:
1) 1.30
2) 3.30
3) 5.0
4) 1.65

Answer 1

Hint The answer lies in the basic concept of physical chemistry which tells that for a weak monobasic acid the concentration of the hydrogen ions is given by the formula, $[{{H}^{+}}]=\sqrt{{{K}_{a}}C}$ and then followed by the calculation of the hydrogen ion concentration.

Complete step – by – step answer:
The concept of the physical chemistry which deals with the calculation of the pH of the solution and also the acid dissociation constant and several related terms are known to us.
We shall now calculate the pH of the solution based on the given data.
- pH is defined as the negative logarithm of the hydrogen ion concentration and therefore, the values below the neutral value that is below pH = 7 will be the acidic solutions and that which is above 7 will be the basic solution.
- Thus, in the above given data, we have the dissociation constant of a monobasic acid given as $5\times {{10}^{-2}}$
- Monobasic acid is the one which has a single proton in it and can donate that proton to a base and the calculation of pH of 0.01M solution needs the value of hydrogen ion concentration value.
So, the hydrogen ion concentration of the monobasic acid is given as,
$[{{H}^{+}}]=\sqrt{{{K}_{a}}C}$
where, ${{K}_{a}}$is the acid dissociation constant and it is $5\times {{10}^{-2}}$
$C$ is the concentration of the solution that is 0.01M =${{10}^{-2}}M$
Substituting these values in the above equation, we get
$[{{H}^{+}}]=\sqrt{5\times {{10}^{-2}}\times {{10}^{-2}}}=2.2\times {{10}^{-2}}$
Now, to calculate the pH of the acid solution, we know the formula for the pH according to the definition as,
\[pH=-\log [{{H}^{+}}]\]
\[\Rightarrow pH=-\log \left( 2.2\times {{10}^{-2}} \right)\]
\[\Rightarrow pH=1.65\]

Therefore, the correct answer is option 4) 1.65

Note: Note that acid dissociation constant is a measure of strength of an acid in the solution and the large value of this constant indicates that the solution is strongly acidic and lower value indicates the presence of weak acid.