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 understand the concept of degree of dissociation and how the presence of a common ion affects it. Here’s a step-by-step solution:

### Step 1: Understand the given data
We are given:
- The concentration of acetic acid (CH₃COOH) = 2 M
- The degree of dissociation (α) of acetic acid in this solution = 10% = 0.10

### Step 2: Calculate the concentration of dissociated species
The dissociation of acetic acid can be represented as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]

From the degree of dissociation, we can calculate the concentration of the dissociated species:
- Initial concentration of CH₃COOH = 2 M
- Degree of dissociation (α) = 0.10
- Concentration of dissociated CH₃COO⁻ and H⁺ ions = \( 2 \times 0.10 = 0.20 \, \text{M} \)

### Step 3: Calculate the concentration of undissociated CH₃COOH
The concentration of undissociated acetic acid after dissociation:
\[ \text{Concentration of CH}_3\text{COOH} = 2 - 0.20 = 1.80 \, \text{M} \]

### Step 4: Introduce the common ion effect
Now, we are adding this acetic acid to a solution of sodium acetate (CH₃COONa) which provides a common ion (CH₃COO⁻). The concentration of CH₃COO⁻ from the sodium acetate solution is 3 M.

### Step 5: Analyze the effect of the common ion
The presence of the common ion (CH₃COO⁻) will suppress the dissociation of acetic acid due to Le Chatelier's principle. This means the degree of dissociation will decrease when acetic acid is in a solution with a high concentration of CH₃COO⁻.

### Step 6: Conclusion
Since the degree of dissociation in the presence of a common ion is always less than that in its absence, we can conclude that the degree of dissociation of acetic acid in a 3 M CH₃COONa solution will be less than 10%. Therefore, the answer is that the degree of dissociation will be less than 10%.

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

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