Question

One liter of a buffer solution contains 0.004 mole of acetic acid (pK\(_a\) = 4.76) and 0.4 mole of sodium acetate. The pH of the solution is ................. (Round off to two decimal places)

Hint:

The pH of a buffer solution can be easily calculated using the Henderson-Hasselbalch equation, which relates pH, pK\(_a\), and the concentrations of the acid and conjugate base.

Answer 1

Correct Answer: 6.66

Step 1: Understanding the buffer equation.
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation: \[ \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] where \([A^-]\) is the concentration of the base (acetate ion, \(\text{CH}_3\text{COO}^-\)) and \([HA]\) is the concentration of the acid (acetic acid, \(\text{CH}_3\text{COOH}\)).
Step 2: Substitute the given values.
- pK\(_a\) = 4.76
- \([A^-]\) = 0.4 M (sodium acetate)
- \([HA]\) = 0.004 M (acetic acid)
Substitute into the equation: \[ \text{pH} = 4.76 + \log \left( \frac{0.4}{0.004} \right) \] \[ \text{pH} = 4.76 + \log (100) \] \[ \text{pH} = 4.76 + 2 \] \[ \text{pH} = 5.04 \] Step 3: Conclusion.
The pH of the buffer solution is 5.04.