The resistance of `1N` solution of acetic acid is `250ohm`, when measured in a cell of cell constant `1.15 cm^(-1)`. The equivalent conductance `(` in `ohm^(-1) cm^(2)eq^(-1))` of `1N` acetic acid is

Options

A. `4.6`
B. `9.2`
C. `18.4`
D. `0.023`

Explanation

To find the equivalent conductance of a 1N solution of acetic acid, we can follow these steps:

### Step 1: Understand the relationship between resistance, cell constant, and conductance
The conductance \( G \) of the solution can be calculated using the formula:
\[ G = \frac{1}{R} \]
where \( R \) is the resistance of the solution.

### Step 2: Calculate the conductance
Given that the resistance \( R \) of the 1N acetic acid solution is \( 250 \, \Omega \):
\[ G = \frac{1}{250 \, \Omega} = 0.004 \, \text{S} \, (\text{Siemens}) \]

### Step 3: Calculate the specific conductance \( K \)
The specific conductance \( K \) can be calculated using the formula:
\[ K = G \times \text{Cell Constant} \]
Given that the cell constant is \( 1.15 \, \text{cm}^{-1} \):
\[ K = 0.004 \, \text{S} \times 1.15 \, \text{cm}^{-1} = 0.0046 \, \text{S cm}^{-1} \]

### Step 4: Calculate the equivalent conductance \( \Lambda \)
The equivalent conductance \( \Lambda \) is given by the formula:
\[ \Lambda = \frac{K}{C} \]
where \( C \) is the normality of the solution. For a 1N solution:
\[ \Lambda = \frac{0.0046 \, \text{S cm}^{-1}}{1 \, \text{N}} = 0.0046 \, \text{S cm}^{-1} \]

### Step 5: Convert to appropriate units
To express this in \( \text{ohm}^{-1} \text{cm}^2 \text{eq}^{-1} \):
\[ \Lambda = 0.0046 \, \text{S cm}^{-1} \times 1000 \, \text{cm}^2/\text{eq} = 4.6 \, \text{ohm}^{-1} \text{cm}^2 \text{eq}^{-1} \]

### Final Answer
The equivalent conductance of 1N acetic acid is:
\[ \Lambda = 4.6 \, \text{ohm}^{-1} \text{cm}^2 \text{eq}^{-1} \]