The equivalent conductance of monobasic acid at infinite dilution is `438 ohm^(-1) cm^(2) eq^(-1)`. If the resistivity of the solution containing 15g of acid (Molecular weight =49) in 1L is 18.5 ohm cm. What is the degree of dissociation of acid.

Options

A. 0.459
B. 0.402
C. 0.604
D. 0.507

Explanation

To find the degree of dissociation of the monobasic acid, we can follow these steps:

### Step 1: Calculate the Normality of the Acid Solution
Given:
- Mass of the acid = 15 g
- Molecular weight of the acid = 49 g/mol

First, we calculate the number of equivalents of the acid:
\[ \text{Number of equivalents} = \frac{\text{Mass of acid}}{\text{Molecular weight}} = \frac{15 \, \text{g}}{49 \, \text{g/mol}} \approx 0.306 \, \text{eq} \]

Since the solution is 1 L, the normality (N) of the solution is:
\[ N = \text{Number of equivalents} = 0.306 \, \text{N} \]

### Step 2: Calculate the Conductivity of the Solution
Given:
- Resistivity of the solution = 18.5 ohm cm

The conductivity (\( \kappa \)) is the inverse of resistivity:
\[ \kappa = \frac{1}{\text{Resistivity}} = \frac{1}{18.5 \, \text{ohm cm}} \approx 0.05405 \, \text{S/cm} \]

### Step 3: Calculate the Equivalent Conductance of the Solution
The equivalent conductance (\( \Lambda \)) can be calculated using the formula:
\[ \Lambda = \frac{\kappa}{N} \]
Substituting the values:
\[ \Lambda = \frac{0.05405 \, \text{S/cm}}{0.306 \, \text{N}} \approx 0.176 \, \text{S cm}^2/\text{eq} \]

### Step 4: Calculate the Degree of Dissociation
The degree of dissociation (\( \alpha \)) can be calculated using the formula:
\[ \alpha = \frac{\Lambda}{\Lambda_0} \]
Where \( \Lambda_0 \) is the equivalent conductance at infinite dilution, given as 438 ohm\(^{-1}\) cm\(^{2}\) eq\(^{-1}\).

Substituting the values:
\[ \alpha = \frac{0.176 \, \text{S cm}^2/\text{eq}}{438 \, \text{S cm}^2/\text{eq}} \approx 0.0004 \]

To express this as a percentage:
\[ \alpha \times 100 \approx 0.04\% \]

### Step 5: Conclusion
The degree of dissociation of the monobasic acid is approximately 0.04%.