Calculate the resistance of 0.01 N solution of an electrolyte whose equivalent conductivity is 420 `ohm^(-1) cm^(2) equiv^(-1)`. (The cell constant of the cell is 0.88 `cm^(-1)` )

Explanation

To calculate the resistance of a 0.01 N solution of an electrolyte with an equivalent conductivity of 420 ohm^(-1) cm^(2) equiv^(-1) and a cell constant of 0.88 cm^(-1), we can follow these steps:

### Step 1: Understand the relationship between equivalent conductivity (λ), conductivity (κ), and concentration (C).
The formula for equivalent conductivity is given by:
\[ \lambda = \frac{\kappa \times 1000}{C} \]
where:
- \( \lambda \) = equivalent conductivity (ohm^(-1) cm^2 equiv^(-1))
- \( \kappa \) = conductivity (ohm^(-1) cm^(-1))
- \( C \) = concentration (equivalents per liter)

### Step 2: Rearrange the formula to find conductivity (κ).
From the above equation, we can rearrange it to find conductivity:
\[ \kappa = \frac{\lambda \times C}{1000} \]

### Step 3: Substitute the known values into the equation.
Given:
- \( \lambda = 420 \, \text{ohm}^{-1} \text{cm}^2 \text{equiv}^{-1} \)
- \( C = 0.01 \, \text{N} \) (which is equivalent to 0.01 equivalents per liter)

Substituting the values:
\[ \kappa = \frac{420 \times 0.01}{1000} = \frac{4.2}{1000} = 4.2 \times 10^{-3} \, \text{ohm}^{-1} \text{cm}^{-1} \]

### Step 4: Use the relationship between conductivity, resistance (R), and cell constant (X).
The relationship is given by:
\[ \kappa = \frac{1}{R} \times X \]
where:
- \( R \) = resistance (ohms)
- \( X \) = cell constant (cm^(-1))

### Step 5: Rearrange the formula to find resistance (R).
Rearranging the equation gives:
\[ R = \frac{X}{\kappa} \]

### Step 6: Substitute the known values into the equation.
Given:
- \( X = 0.88 \, \text{cm}^{-1} \)
- \( \kappa = 4.2 \times 10^{-3} \, \text{ohm}^{-1} \text{cm}^{-1} \)

Substituting the values:
\[ R = \frac{0.88}{4.2 \times 10^{-3}} = \frac{0.88}{0.0042} \approx 209.52 \, \text{ohms} \]

### Conclusion:
The resistance of the 0.01 N solution of the electrolyte is approximately **209.52 ohms**.

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