The resistance of 0.01 N solution at `25^(@)C` is 200 ohm. Cell constant of the conductivity cell is unity. Calculate the equivalent conductance of the solution.

Options

A. `500 "ohm"^(-1) cm^(2) eq^(-1)`
B. `5 "ohm"^(-1) cm^(2) eq^(-1)`
C. `250 "ohm"^(-1) cm^(2) eq^(-1)`
D. None

Answer

To solve the problem, we need to calculate the equivalent conductance of a 0.01 N solution given its resistance and the cell constant. Here are the steps to find the solution:

### Step 1: Understand the Formula for Specific Conductivity
The specific conductivity (κ) can be calculated using the formula:
\[ \kappa = \frac{1}{R} \times \text{Cell Constant} \]
where \( R \) is the resistance of the solution.

### Step 2: Substitute the Given Values
From the problem, we know:
- Resistance \( R = 200 \, \Omega \)
- Cell Constant = 1

Substituting these values into the formula:
\[ \kappa = \frac{1}{200} \times 1 = \frac{1}{200} \, \text{S/cm} \]

### Step 3: Calculate the Specific Conductivity
Now, we calculate the specific conductivity:
\[ \kappa = 0.005 \, \text{S/cm} \]

### Step 4: Use the Formula for Equivalent Conductance
The equivalent conductance (\( \Lambda \)) can be calculated using the formula:
\[ \Lambda = \frac{\kappa \times 1000}{N} \]
where \( N \) is the normality of the solution.

### Step 5: Substitute the Values for Equivalent Conductance
Given:
- Normality \( N = 0.01 \)

Substituting the values into the formula:
\[ \Lambda = \frac{0.005 \times 1000}{0.01} \]

### Step 6: Perform the Calculation
Calculating the above expression:
\[ \Lambda = \frac{5}{0.01} = 500 \, \text{S cm}^2/\text{equivalent} \]

### Final Answer
The equivalent conductance of the solution is:
\[ \Lambda = 500 \, \text{S cm}^2/\text{equivalent} \]