Resistance of a decimolar solution between two electrodes 0.02 meter apart and 0.0004 `m^2` in area was found to be 50 ohm. Specific conductance (k0 is :

Options

A. `0.1Sm^(-1)`
B. `1Sm^(-)`
C. `10Sm^(-1)`
D. `4xx10^(-4)Sm^(-1)`

Answer

To find the specific conductance (k) of a decimolar solution given the resistance, distance between electrodes, and area, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Resistance (R) = 50 ohms
- Distance between electrodes (L) = 0.02 m
- Area of the electrodes (A) = 0.0004 m²

2. **Use the Formula for Resistance**:
The relationship between resistance (R), specific resistance (ρ), distance (L), and area (A) is given by the formula:
\[ R = \frac{\rho L}{A} \]

3. **Rearrange the Formula to Find Specific Resistance (ρ)**:
Rearranging the formula to solve for specific resistance (ρ):
\[ \rho = \frac{R \cdot A}{L} \]

4. **Substitute the Values into the Formula**:
Substitute the known values into the rearranged formula:
\[ \rho = \frac{50 \, \text{ohm} \cdot 0.0004 \, \text{m}^2}{0.02 \, \text{m}} \]

5. **Calculate Specific Resistance (ρ)**:
Performing the calculation:
\[ \rho = \frac{50 \cdot 0.0004}{0.02} = \frac{0.02}{0.02} = 1 \, \text{ohm meter} \]

6. **Find Specific Conductance (k)**:
The specific conductance (k) is the reciprocal of specific resistance (ρ):
\[ k = \frac{1}{\rho} \]
Substituting the value of ρ:
\[ k = \frac{1}{1 \, \text{ohm meter}} = 1 \, \text{ohm}^{-1} \text{m}^{-1} \]

7. **Convert to Siemens**:
Since \(1 \, \text{ohm}^{-1} = 1 \, \text{Siemens}\), we can express the specific conductance as:
\[ k = 1 \, \text{S/m} \]

### Final Answer:
The specific conductance (k) of the solution is \(1 \, \text{S/m}\).

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