Question

A buffer of acetic acid $\left( {{\text{p}}{{\text{K}}_{\text{a}}} = 4.8} \right)$ with sodium acetate will be, when ${\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}$ and ${\text{C}}{{\text{H}}_{\text{3}}}{\text{COONa}}$ are present in equivalent amounts has pH limits equal to:
A.$0$ to $4.8$
B.$3.8$ to $5.8$
C.$4.3$to $5.3$
D.$4.8$

Answer 1

Hint: The negative log of the acid dissociation constant ${{\text{K}}_{\text{a}}}$ is termed as ${\text{p}}{{\text{K}}_{\text{a}}}$ and its value is also used to indicate the strength of an acid.
For an acidic buffer, the pH value of the buffer is related to the${\text{p}}{{\text{K}}_{\text{a}}}$ value of the acid by the following expression:
${\text{pH = p}}{{\text{K}}_{\text{a}}} + \log \dfrac{{\left[ {{\text{salt}}} \right]}}{{\left[ {{\text{acid}}} \right]}}$
Here, $\left[ {{\text{salt}}} \right]$ and $\left[ {{\text{acid}}} \right]$ represents the concentrations of the salt and acid respectively that make up the buffer. This is called Henderson’s equation.

Complete step by step answer:
The pH can be measured on the pH scale from 0(highly acidic) to 14(highly basic). Higher the hydrogen ion concentration of a substance, lower is the pH value.
For a neutral solution, pH value is 7. If the pH value is less than 7, it represents an acidic solution and if it is higher than 7, it represents a basic solution.
An acidic buffer consists of an equimolar mixture of a weak acid and its salt with a strong base. Since acetic acid is a weak acid and sodium acetate is a salt of acetic acid with the strong base sodium hydroxide, so the equimolar mixture of acetic acid with sodium acetate is an acidic buffer.
According to the given question, the ${\text{p}}{{\text{K}}_{\text{a}}}$ value of acetic acid is $4.8$ .
So, the Henderson’s equation will be:
${\text{pH = 4}}{\text{.8}} + \log \dfrac{{\left[ {{\text{C}}{{\text{H}}_{\text{3}}}{\text{COONa}}} \right]}}{{\left[ {{\text{C}}{{\text{H}}_{\text{3}}}{\text{COOH}}} \right]}}$
Sodium acetate and acetic acid are present in equivalent amounts, so:
$
  {\text{pH = 4}}{\text{.8}} + \log 1 \\
   \Rightarrow {\text{pH = }}4.8 + 0 \\
   \Rightarrow {\text{pH = }}4.8 \\
 $
So, $3.8$ to $5.8$ is the range of the pH of the buffer.

So, the correct option is B.

Note:
A basic buffer consists of an equimolar mixture of a weak base and its salt with a strong acid.
For a basic buffer, the pH value of the buffer is related to the ${\text{p}}{{\text{K}}_{\text{b}}}$ value of the base by the following expression:
${\text{pH = p}}{{\text{K}}_{\text{b}}} + \log \dfrac{{\left[ {{\text{salt}}} \right]}}{{\left[ {{\text{base}}} \right]}}$
Here, $\left[ {{\text{salt}}} \right]$ and $\left[ {{\text{base}}} \right]$ represents the concentrations of the salt and base respectively that make up the buffer. This is Henderson's equation for basic buffer.