The specific conductivity of an aqueous solution of a weak monoprotic acid is `0.00033 ohm^(-1) cm^(-1)` at a concentration 0.02 M. If at this concentration the degree of dissociation is 0.043, then calculate the value of `lambda_(0) ("in" ohm^(-1)cm^(2)//eqt)`:

Options

A. 483
B. 438
C. 348
D. 384

Explanation

To solve the problem, we need to calculate the molar conductivity at infinite dilution (\( \lambda_0 \)) of a weak monoprotic acid given the specific conductivity, concentration, and degree of dissociation. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Specific conductivity (\( \kappa \)) = \( 0.00033 \, \text{ohm}^{-1} \text{cm}^{-1} \)
- Concentration (\( C \)) = \( 0.02 \, \text{M} \)
- Degree of dissociation (\( \alpha \)) = \( 0.043 \)

### Step 2: Calculate the molar conductivity at the given concentration
The molar conductivity (\( \Lambda \)) at a particular concentration can be calculated using the formula:
\[ \Lambda = \frac{\kappa \times 1000}{C} \]
Substituting the values:
\[ \Lambda = \frac{0.00033 \, \text{ohm}^{-1} \text{cm}^{-1} \times 1000}{0.02 \, \text{M}} \]
\[ \Lambda = \frac{0.33 \, \text{ohm}^{-1} \text{cm}^{-1}}{0.02} \]
\[ \Lambda = 16.5 \, \text{ohm}^{-1} \text{cm}^2/\text{eqt} \]

### Step 3: Use the degree of dissociation to find molar conductivity at infinite dilution
Using the relationship between degree of dissociation (\( \alpha \)), molar conductivity at a particular concentration (\( \Lambda \)), and molar conductivity at infinite dilution (\( \lambda_0 \)):
\[ \alpha = \frac{\Lambda}{\lambda_0} \]
Rearranging gives:
\[ \lambda_0 = \frac{\Lambda}{\alpha} \]
Substituting the values:
\[ \lambda_0 = \frac{16.5 \, \text{ohm}^{-1} \text{cm}^2/\text{eqt}}{0.043} \]
\[ \lambda_0 \approx 383.72 \, \text{ohm}^{-1} \text{cm}^2/\text{eqt} \]

### Step 4: Round off the answer
Rounding off gives:
\[ \lambda_0 \approx 384 \, \text{ohm}^{-1} \text{cm}^2/\text{eqt} \]

### Final Answer
The value of \( \lambda_0 \) is approximately \( 384 \, \text{ohm}^{-1} \text{cm}^2/\text{eqt} \).

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