Degree of dissociation of decinormal acetic acid is `3.66% ` at `25^@C`.If the equivalent conductance at infinite dilution of acetic acid at `25^@C` is `390.7 "ohm"^(-1)`,calculate the equivalent conductance at given concentration.

Answer

To solve the problem, we need to calculate the equivalent conductance at the given concentration of acetic acid using the degree of dissociation and the equivalent conductance at infinite dilution.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Degree of dissociation (α) = 3.66% = 0.0366 (as a decimal)
- Equivalent conductance at infinite dilution (λ₀) = 390.7 ohm⁻¹ cm² equiv⁻¹

2. **Use the Formula for Equivalent Conductance:**
The relationship between the degree of dissociation (α), equivalent conductance at a given concentration (λ), and equivalent conductance at infinite dilution (λ₀) is given by:
\[ \alpha = \frac{\lambda}{\lambda_0} \]

3. **Rearranging the Formula:**
We can rearrange the formula to find the equivalent conductance (λ) at the given concentration:
\[ \lambda = \alpha \cdot \lambda_0 \]

4. **Substitute the Values:**
Now, substitute the known values into the equation:
\[ \lambda = 0.0366 \cdot 390.7 \]

5. **Calculate λ:**
Performing the multiplication:
\[ \lambda = 0.0366 \times 390.7 \approx 14.299 \, \text{ohm}^{-1} \, \text{cm}^2 \, \text{equiv}^{-1} \]

6. **Final Answer:**
The equivalent conductance at the given concentration of acetic acid is approximately:
\[ \lambda \approx 14.299 \, \text{ohm}^{-1} \, \text{cm}^2 \, \text{equiv}^{-1} \]