The dissociation constant of n-butyric acid is `1.6 xx 10^(-5)` and the molar conductivity at infinite dilution is `380 xx 10^(-4) Sm^(2) mol^(-1)`. The specific conductance of the `0.01M` acid solution is

Options

A. `1.52 xx 10^(-5) Sm^(-1)`
B. `1.52 xx 10^(-2) Sm^(-1)`
C. `1.52 xx 10^(-3) Sm^(-1)`
D. none

Explanation

To find the specific conductance (κ) of a 0.01 M n-butyric acid solution, we can follow these steps:

### Step 1: Write down the given data
- Dissociation constant (Ka) of n-butyric acid = \(1.6 \times 10^{-5}\)
- Molar conductivity at infinite dilution (\( \Lambda_m^\infty \)) = \(380 \times 10^{-4} \, \text{S m}^2 \text{mol}^{-1}\)
- Concentration (C) = \(0.01 \, \text{M}\)

### Step 2: Calculate the degree of dissociation (α)
For a weak acid, the dissociation constant is given by:
\[ K_a = C \alpha^2 \]
Rearranging this gives:
\[ \alpha = \sqrt{\frac{K_a}{C}} \]
Substituting the values:
\[ \alpha = \sqrt{\frac{1.6 \times 10^{-5}}{0.01}} = \sqrt{1.6 \times 10^{-3}} = 0.04 \]

### Step 3: Calculate the molar conductivity at the given concentration (\( \Lambda_{mC} \))
The molar conductivity at the given concentration can be calculated using:
\[ \Lambda_{mC} = \alpha \cdot \Lambda_m^\infty \]
Substituting the values:
\[ \Lambda_{mC} = 0.04 \times (380 \times 10^{-4}) = 15.2 \times 10^{-4} \, \text{S m}^2 \text{mol}^{-1} \]

### Step 4: Convert the molar conductivity to specific conductance (κ)
The relationship between molar conductivity and specific conductance is given by:
\[ \Lambda_{mC} = \frac{\kappa \cdot 1000}{C} \]
Rearranging gives:
\[ \kappa = \frac{\Lambda_{mC} \cdot C}{1000} \]
Substituting the values:
\[ \kappa = \frac{15.2 \times 10^{-4} \cdot 0.01}{1000} = 1.52 \times 10^{-4} \, \text{S cm}^{-1} \]

### Step 5: Convert to S m⁻¹
To convert the specific conductance from S cm⁻¹ to S m⁻¹:
\[ \kappa = 1.52 \times 10^{-4} \, \text{S cm}^{-1} = 1.52 \times 10^{-2} \, \text{S m}^{-1} \]

### Final Answer
The specific conductance of the 0.01 M n-butyric acid solution is:
\[ \kappa = 1.52 \times 10^{-2} \, \text{S m}^{-1} \]

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