Question

# $p{{K}_{a}}$ value of acetic acid is 4.76 at room temperature. How do you obtain buffers of 4.4 and 5.4 pH values from acetic acid and sodium acetate?

Hint: .The pKa value is used to indicate the strength of an acid. pKa is the negative log of the acid dissociation constant or we can say Ka value. A lower pKa value indicates a stronger acid.

- pH represents the basicity or acidity of a solution on a logarithmic scale on which value 7 is neutral, higher values than 7 are basic and lower values than 7 are acidic.
The pH is equal to , $-{{\log }_{10}}c$ where, c is the concentration of hydrogen ion in moles per litre.
-We are provided with the value of acetic acid at room temperature= 4.76,
- Firstly let’s see the case to obtain the value of 4.4, we will use the formula,
$pH=p{{K}_{a}}+\log \dfrac{\left[ sodium\text{ }acetate \right]}{\left[ acetic\text{ }acid \right]}$
- Now, we will put all the given values in the equation,
\begin{align} & 4.4=4.76+\log \dfrac{sodium\text{ }acetate}{acetic\text{ }acid} \\ & \log \dfrac{sodium\text{ }acetate}{acetic\text{ }acid}=-0.36 \\ \end{align}
So, we get the ratio of sodium acetate to that of acetic acid as:
$\dfrac{sodium\text{ }acetate}{acetic\text{ }acid}=0.4365$
- Secondly we will discuss about to obtain pH of 5.4 value:

-We will solve it also in similar manner as we have solved in above question,
$pH=p{{K}_{a}}+\log \dfrac{\left[ sodium\text{ }acetate \right]}{\left[ acetic\text{ }acid \right]}$
\begin{align} & 5.4=4.76+\log \dfrac{\left[ sodium\text{ }acetate \right]}{\left[ acetic\text{ }acid \right]} \\ & 5.4=4.76+\log \dfrac{\left[ sodium\text{ }acetate \right]}{\left[ acetic\text{ }acid \right]} \\ \end{align}
- So the ratio of sodium acetate and acetic acid at a pH of 5.4 will be:
$\dfrac{sodium\text{ }acetate}{acetic\text{ }acid}=4.364$
- Hence, by this method we can obtain the buffers of 4.4 and 5.4 pH values from acetic acid and sodium acetate

Note: - Strong acids or bases will have low values $p{{K}_{a}}$, whereas weak acids and bases will have $p{{K}_{a}}$higher values. Acids are having pH values less than 7 and bases are having pH values more than 7.