Question

Assuming that the degree of hydrolysis is small, the pH of 0.1 M solution of sodium acetate $(K_a = 1.0 \times 10^{-5})$ will be :

• A. 5
• B. 6
• C. 8
• D. 9

Answer 1

The Correct Option is D

To determine the pH of a 0.1 M solution of sodium acetate, we must first understand that sodium acetate (CH_3COONa) is a salt derived from a weak acid, acetic acid (CH_3COOH), and a strong base, sodium hydroxide (NaOH). When sodium acetate is dissolved in water, it undergoes hydrolysis to form an equilibrium between acetate ions, water, acetic acid, and hydroxide ions, contributing to the basicity of the solution.

The key steps are as follows:

1. Sodium acetate dissociates in water completely to form acetate ions:
2. CH_3COONa \xrightarrow{dissociation} CH_3COO^- + Na^+
3. The acetate ion undergoes hydrolysis:
4. CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^−
5. The equilibrium constant for this hydrolysis process is known as the hydrolysis constant (K_h), which is given by:
6. K_w = K_a \cdot K_b (for conjugate acid-base pairs)
7. K_b = \frac{K_w}{K_a}, where K_w = 1.0 \times 10^{-14} at 25°C
8. Since K_a = 1.0 \times 10^{-5}, we can find K_b for acetate ions:
9. K_b = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-5}} = 1.0 \times 10^{-9}
10. The hydrolysis equilibrium equation is:
11. [OH^-] = \sqrt{C \cdot K_b}, where C is the concentration of the acetate ion (0.1 M)
12. Calculate [OH^-]:
13. [OH^-] = \sqrt{0.1 \times 1.0 \times 10^{-9}} = \sqrt{1.0 \times 10^{-10}} = 1.0 \times 10^{-5} \text{ M}
14. The pOH can be determined from the hydroxide ion concentration:
15. \text{pOH} = -\log[OH^-] = 5
16. Finally, find the pH since \text{pH} + \text{pOH} = 14:
17. \text{pH} = 14 - \text{pOH} = 14 - 5 = 9

This computation shows that the pH of the 0.1 M solution of sodium acetate is 9, concluding that the solution is basic. Hence, the correct option is 9.