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?

To prepare buffer solutions of specific pH values using acetic acid and sodium acetate, we can utilize the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the concentration of its acidic and basic components. The equation is given as follows:

\[
\text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)
\]

Where:
- \(\text{pH}\) is the desired pH of the buffer.
- \(\text{pK}_a\) is the dissociation constant of the weak acid (in this case, acetic acid), which is 4.76.
- \([\text{A}^-]\) is the concentration of the conjugate base (sodium acetate).
- \([\text{HA}]\) is the concentration of the weak acid (acetic acid).

### 1. Preparing a Buffer with pH 4.4

For a buffer with pH 4.4:

1. **Use the Henderson-Hasselbalch equation**:
\[
4.4 = 4.76 + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)
\]
Rearranging this gives:
\[
\log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) = 4.4 - 4.76 = -0.36
\]

2. **Convert the log ratio to concentration ratio**:
\[
\frac{[\text{A}^-]}{[\text{HA}]} = 10^{-0.36} \approx 0.44
\]
This means that for every 0.44 moles of sodium acetate, there is 1 mole of acetic acid.

### 2. Preparing a Buffer with pH 5.4

For a buffer with pH 5.4:

1. **Use the Henderson-Hasselbalch equation**:
\[
5.4 = 4.76 + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)
\]
Rearranging gives:
\[
\log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) = 5.4 - 4.76 = 0.64
\]

2. **Convert the log ratio to concentration ratio**:
\[
\frac{[\text{A}^-]}{[\text{HA}]} = 10^{0.64} \approx 4.37
\]
This means that for every 4.37 moles of sodium acetate, there is 1 mole of acetic acid.

### Summary

- For **pH 4.4**: Mix acetic acid and sodium acetate in a ratio of **1:0.44** (more acetic acid than sodium acetate).
- For **pH 5.4**: Mix acetic acid and sodium acetate in a ratio of **1:4.37** (more sodium acetate than acetic acid).

### Preparation Steps

1. **Calculate the required volumes** of acetic acid and sodium acetate based on your target concentrations.
2. **Mix the solutions** in the determined ratios to achieve the desired pH levels.
3. **Measure the pH** with a pH meter and adjust the concentrations if necessary.

By following these steps, you can successfully prepare buffer solutions at the desired pH values.