Resistance of an aqueous solution containing 2 "mole" `NH_(4)Cl` and is filled in between two electrodes which are 20 cm apart was found to be 100 ohm. Calcualte the `lambda_(m)(S cm6(2) mol^(-)` for `NH_(4)Cl`(aq).

Answer

To calculate the molar conductance (λm) of the aqueous solution of NH4Cl, we can follow these steps:

### Step 1: Understand the given information
- Resistance (R) of the solution = 100 ohms
- Distance (L) between the electrodes = 20 cm
- Number of moles of NH4Cl = 2 moles

### Step 2: Write the formula for molar conductance
Molar conductance (λm) can be calculated using the formula:
\[ \lambda_m = \frac{L}{R \cdot N} \]
Where:
- \(L\) = distance between the electrodes in cm
- \(R\) = resistance in ohms
- \(N\) = number of moles of the solute

### Step 3: Substitute the values into the formula
Substituting the values we have:
- \(L = 20 \, \text{cm}\)
- \(R = 100 \, \text{ohms}\)
- \(N = 2 \, \text{moles}\)

Now substituting these values into the formula:
\[ \lambda_m = \frac{20}{100 \cdot 2} \]

### Step 4: Calculate the molar conductance
Calculating the denominator:
\[ 100 \cdot 2 = 200 \]
Now substituting back into the equation:
\[ \lambda_m = \frac{20}{200} = 0.1 \, \text{S cm}^2 \text{mol}^{-1} \]

### Step 5: Final result
Thus, the molar conductance (λm) of the NH4Cl solution is:
\[ \lambda_m = 0.1 \, \text{S cm}^2 \text{mol}^{-1} \]

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