Question

Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH = $6$. If ionization constant of HA is ${10^{ - 5}}$, the ratio of salt to acid concentration in the buffer solution will be:
A. $1:10$
B. $4:5$
C. $10:1$
D. $5:4$

Answer 1

Hint: We know that the pH value is generally used to describe or explain the term potential of the hydrogen atom. It generally shows the relationship with the acid dissociation constant through the equation named as Henderson-Hasselbalch Equation.

Complete step by step solution:
We have given the data as follows,
The ionization constant of weak acid ${K_{\rm{a}}} = {10^{ - 5}}$.
The pH of the buffer solution is $6$.
As we all know, the formula which is used for the ionization constant is shown below.
${\rm{p}}{K_{\rm{a}}} = - \log {K_{\rm{a}}}$
Where the constant ${\rm{p}}{K_{\rm{a}}}$ is dissociation constant of acid, and ${K_{\rm{a}}}$ is the ionization constant.
Substitute the value of ionization constant in above equation we get,
$
\Rightarrow {\rm{p}}{K_{\rm{a}}} = - \log {10^{ - 5}}\\
\Rightarrow {\rm{p}}{K_{\rm{a}}} = 5
$
The ratio of acid concentration to the buffer solution salt can be calculated by using the formula is shown below.
${\rm{pH}} = {\rm{p}}{K_{\rm{a}}} + \log \dfrac{{\left[ {{\rm{salt}}} \right]}}{{\left[ {{\rm{acid}}} \right]}}$
Where, the constant pH is the potential of hydrogen atom, ${\rm{p}}{K_{\rm{a}}}$ is dissociation constant of acid, [salt] is the concentration of buffer solution alt, and [acid] is the concentration of the weak acid.
Substitute all the respective values in above equation we get,
$
\Rightarrow {\rm{6}} = 5 + \log \dfrac{{\left[ {{\rm{salt}}} \right]}}{{\left[ {{\rm{acid}}} \right]}}\\
\Rightarrow 1 = \log \dfrac{{\left[ {{\rm{salt}}} \right]}}{{\left[ {{\rm{acid}}} \right]}}
$
Thus, the ratio of buffer solution salt and weak acid by taking the antilog is shown below.
$\Rightarrow \dfrac{{\left[ {{\rm{salt}}} \right]}}{{\left[ {{\rm{acid}}} \right]}} = \dfrac{{10}}{1}$.

Hence, the correct option for this given question is C that is $10:1$.

Note:
The pH value is usually being utilized for determining the nature of the solution. The nature of the solution can commonly be of two types one is an acid solution, and second is a basic solution. The acidic solution provides the hydrogen ion after dissociation, and basic or alkaline solution provides the hydroxide solution after dissociation.