Question

Given that $50\%$ neutralisation of a solution of formic acid $\left( {{{\text{K}}_{\text{a}}} = 2 \times {{10}^{ - 4}}} \right)$ with ${\text{NaOH}}$ would result in a solution having a hydrogen ion concentration of:
A. ${\text{2}} \times {\text{1}}{{\text{0}}^{ - 4}}$
B. $3.69$
C. $4.0$
D. $1.85$

Answer 1

We will use the formula for buffer of acid here. Equal amount of acid and salt is present in the mixture. We will get the pH of hydrogen ions from there. Then, we can calculate the concentration of hydrogen ions.

Formula used: ${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{{\text{salt}}}}{{{\text{acid}}}}$
Here ${\text{pH}}$ is the power of hydrogen p is the operator that represent $- \log$ and ${{\text{K}}_{\text{a}}}$ is dissociation constant for acid.

Complete step by step solution:
The molecular formula for formic acid is ${\text{HCOOH}}$
The molecular formula for sodium hydroxide is ${\text{NaOH}}$
The dissociation of the formic acid occurs as:
${\text{HCOOH}} \rightleftharpoons {{\text{H}}^ + } + {\text{HCO}}{{\text{O}}^ - }$

The neutralisation of formic acid with the sodium hydroxide occurs as:
${\text{HCOOH}} + {\text{NaOH}} \to {\text{HCOONa}} + {{\text{H}}_2}{\text{O}}$
Now since it is given to us that fifty percent of the acid is neutralised that means fifty percent of the salt has been formed and fifty percent of the acid is still present in the undissociated form. In the solution there is acid and its conjugate base that will form an ideal condition for buffer formation. If the initial concentration of acid is C then the concentration of salt formed will be $\dfrac{{\text{C}}}{2}$ and the concentration of acid left will also be $\dfrac{{\text{C}}}{2}$ .

So we will apply the formula of buffer as:
${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{{\text{salt}}}}{{{\text{acid}}}}$
${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}} + {\text{log}}\dfrac{{\dfrac{{\text{C}}}{2}}}{{\dfrac{{\text{C}}}{2}}}$
The value of log 1 is zero and hence we will get:
${\text{pH}} = {\text{p}}{{\text{K}}_{\text{a}}}$
Or by removing the p operator we will get concentration of hydrogen ion become equal to the dissociation constant which is equal to the ${\text{2}} \times {\text{1}}{{\text{0}}^{ - 4}}$.

Hence, the correct option is A.

Note: The Buffer is a solution which resists change in pH value when a small amount of acid or base is added to the solution. A buffer works only under a certain pH range that depends on the nature of acid or base used to make the buffer.