Calculate the cell constant if the specific conductance of a Solution is 0.2 `"ohm"^(-1)cm^(-1)` and its conductance is 0.04 `"ohm"^(-1)`.

Options

A. `1 cm^(-1)`
B. `0 cm^(-1)`
C. `5 cm^(-1)`
D. `0.2 cm^(-1)`

Answer

To calculate the cell constant, we can use the relationship between specific conductance (κ), conductance (G), and the cell constant (G*). The formula we will use is:

\[ G^* = \frac{κ}{G} \]

Where:
- \( G^* \) is the cell constant (in cm\(^{-1}\))
- \( κ \) is the specific conductance (in ohm\(^{-1}\)cm\(^{-1}\))
- \( G \) is the conductance (in ohm\(^{-1}\))

### Step-by-Step Solution:

1. **Identify Given Values**:
- Specific conductance (κ) = 0.2 ohm\(^{-1}\)cm\(^{-1}\)
- Conductance (G) = 0.04 ohm\(^{-1}\)

2. **Substitute the Values into the Formula**:
\[ G^* = \frac{κ}{G} = \frac{0.2 \, \text{ohm}^{-1}\text{cm}^{-1}}{0.04 \, \text{ohm}^{-1}} \]

3. **Perform the Division**:
- The units of ohm\(^{-1}\) will cancel out:
\[ G^* = \frac{0.2}{0.04} \, \text{cm}^{-1} \]

4. **Calculate the Result**:
\[ G^* = 5 \, \text{cm}^{-1} \]

### Final Answer:
The cell constant \( G^* \) is 5 cm\(^{-1}\).

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