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 formula for conductivity (k)
The conductivity (k) can be calculated using the formula:
\[ k = \frac{Cell \ Constant}{Resistance} \]

### Step 2: Substitute the values for cell constant and resistance
From the question, we know:
- Cell constant = 1.15 cm\(^{-1}\)
- Resistance = 250 ohms

Substituting these values into the formula gives:
\[ k = \frac{1.15 \ cm^{-1}}{250 \ \Omega} \]

### Step 3: Calculate the conductivity (k)
Now, we perform the calculation:
\[ k = \frac{1.15}{250} = 0.0046 \ \text{S cm}^{-1} \]
(Note: 1 S = 1 Ohm\(^{-1}\))

### Step 4: Use the formula for equivalent conductance (λ_eq)
The equivalent conductance (λ_eq) can be calculated using the formula:
\[ \lambda_{eq} = \frac{1000 \cdot k}{n} \]
where \(n\) is the normality of the solution.

### Step 5: Substitute the values into the equivalent conductance formula
Given that the normality \(n\) of the acetic acid solution is 1N, we substitute the values:
\[ \lambda_{eq} = \frac{1000 \cdot 0.0046 \ \text{S cm}^{-1}}{1} \]

### Step 6: Calculate the equivalent conductance (λ_eq)
Now, we perform the calculation:
\[ \lambda_{eq} = 1000 \cdot 0.0046 = 4.6 \ \text{S cm}^2 \text{eq}^{-1} \]

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

---