The resistance of `0.1N` solution of formic acid is `200 ohm` and cell constant is `2.0 cm^(-1)`. The equivalent conductivity ( in `Scm^(2) eq^(-1))` of `0.1N` formic acid is `:`

Options

A. 100
B. 10
C. 1
D. None of these

Answer

To solve the problem, we need to calculate the equivalent conductivity of a 0.1N solution of formic acid given its resistance and cell constant. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the relationship between resistance, cell constant, and specific conductance
The specific conductance (K) can be calculated using the formula:
\[ K = \frac{1}{R} \times \text{Cell Constant} \]
where \( R \) is the resistance and the cell constant is given.

### Step 2: Substitute the values into the formula
Given:
- Resistance \( R = 200 \, \Omega \)
- Cell constant = \( 2.0 \, \text{cm}^{-1} \)

Substituting these values:
\[ K = \frac{1}{200} \times 2.0 \]
\[ K = \frac{2.0}{200} = 0.01 \, \text{S cm}^{-1} \]

### Step 3: Calculate the equivalent conductivity
The equivalent conductivity (\( \Lambda \)) can be calculated using the formula:
\[ \Lambda = K \times \frac{1000}{N} \]
where \( N \) is the normality of the solution.

Given:
- Normality \( N = 0.1 \, \text{N} \)

Substituting the values:
\[ \Lambda = 0.01 \times \frac{1000}{0.1} \]
\[ \Lambda = 0.01 \times 10000 = 100 \, \text{S cm}^2 \text{eq}^{-1} \]

### Final Answer
The equivalent conductivity of the 0.1N formic acid solution is:
\[ \Lambda = 100 \, \text{S cm}^2 \text{eq}^{-1} \]

---