The resistance of 0.01N solution of an electrolyte AB at 328K is 100ohm. The specific conductance of solution is
(cell constant =`1cm^(-1)` )

Options

A. 100ohm
B. `10^(-2)ohm^(-1)`
C. `10^(-2)ohm^(-1)cm^(-1)`
D. `10^(2)ohm-cm`

Explanation

To find the specific conductance of the electrolyte AB in a 0.01N solution at 328K, we can use the following steps:

### Step 1: Understand the relationship between conductance, resistance, and specific conductance
The specific conductance (κ) is related to the conductance (G) and the cell constant (L/A) by the formula:
\[ κ = G \times \frac{L}{A} \]
Where:
- κ is the specific conductance (in S/cm)
- G is the conductance (in S)
- L/A is the cell constant (in cm⁻¹)

### Step 2: Calculate the conductance (G)
Conductance (G) is the reciprocal of resistance (R):
\[ G = \frac{1}{R} \]
Given that the resistance (R) is 100 ohms, we can calculate G:
\[ G = \frac{1}{100 \, \text{ohms}} = 0.01 \, \text{S} \]

### Step 3: Use the cell constant to find specific conductance (κ)
We know the cell constant (L/A) is given as 1 cm⁻¹. Now we can substitute the values into the specific conductance formula:
\[ κ = G \times \frac{L}{A} = 0.01 \, \text{S} \times 1 \, \text{cm}^{-1} \]
\[ κ = 0.01 \, \text{S/cm} \]

### Step 4: Convert specific conductance to appropriate units
Since specific conductance is often expressed in terms of ohm⁻¹ cm⁻¹, we can convert:
\[ 0.01 \, \text{S/cm} = 10^{-2} \, \text{ohm}^{-1} \text{cm}^{-1} \]

### Final Answer
The specific conductance of the 0.01N solution of electrolyte AB at 328K is:
\[ κ = 10^{-2} \, \text{ohm}^{-1} \text{cm}^{-1} \]

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