If degree of dissociation of 2M `CH_3 COOH` is 10% then degree of dissociation of this acetic acid in 3 Molar `CH_3 COONa` solution will be

Options

A. `=10%`
B. `lt 10%`
C. `gt10%`
D. Cannot be determine

Answer

To solve the problem, we need to determine the degree of dissociation of acetic acid (CH₃COOH) in a solution that contains sodium acetate (CH₃COONa). We are given that the degree of dissociation of 2M CH₃COOH is 10%.

### Step-by-Step Solution:

1. **Understanding Degree of Dissociation**:
- The degree of dissociation (α) is defined as the fraction of the total number of moles that dissociates into ions. In this case, for acetic acid, α = 0.10 (10%).

2. **Initial Concentration of Acetic Acid**:
- The initial concentration of acetic acid (CH₃COOH) is 2M. Therefore, the concentration of undissociated acetic acid is:
\[ [CH₃COOH] = 2M \times (1 - α) = 2M \times (1 - 0.10) = 2M \times 0.90 = 1.8M \]

3. **Dissociation of Acetic Acid**:
- The dissociation of acetic acid can be represented as:
\[ CH₃COOH \rightleftharpoons CH₃COO^- + H^+ \]
- At 10% dissociation, the concentration of ions produced will be:
\[ [CH₃COO^-] = [H^+] = 2M \times 0.10 = 0.2M \]

4. **Adding Sodium Acetate**:
- When we add 3M sodium acetate (CH₃COONa), it dissociates completely in solution:
\[ CH₃COONa \rightarrow CH₃COO^- + Na^+ \]
- Therefore, the concentration of acetate ions (CH₃COO^-) from sodium acetate is 3M.

5. **Total Concentration of Acetate Ions**:
- The total concentration of acetate ions in the solution will be:
\[ [CH₃COO^-]_{total} = 0.2M + 3M = 3.2M \]

6. **Common Ion Effect**:
- The presence of a common ion (CH₃COO^-) from sodium acetate will suppress the dissociation of acetic acid due to the common ion effect. This means that the degree of dissociation of acetic acid will decrease.

7. **Conclusion on Degree of Dissociation**:
- Since the degree of dissociation in the presence of a common ion is always less than that in pure solution, we conclude that the degree of dissociation of acetic acid in the presence of 3M sodium acetate will be less than 10%.

### Final Answer:
The degree of dissociation of 2M CH₃COOH in 3M CH₃COONa solution will be **less than 10%**.