Read the passage given below and answer the question:
The cell constant is usually determined by measuring the resistance of the cell containing a solution whose conductivity is already known. For this purpose, we generally use KCl solutions whose conductivity is known accurately at various concentrations and at different temperatures. consider the resistance of a conductivity cell filled with 0.1 M KCl solution is 200 Ohm. if the resistance of the same cell when filled with 0.02 M KCl solution is 420 Ohm.
(Conductivity of 0.1 M KCl solution is 1.29 S `m^(-1)`).
Q. Which of the following is not true ?
The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to

Options

A. size of the ions in which they dissociate
B. concentration of ions
C. charge of the ions in which they dissociate
D. is independent of ions movement under a potential gradient

Explanation

To solve the problem, we need to analyze the information provided and determine which statement about the conductivity of solutions of different electrolytes is not true.

### Step 1: Understand the Concept of Conductivity
Conductivity (κ) is a measure of a solution's ability to conduct electricity, which depends on the concentration of ions in the solution, the charge of the ions, and the mobility of the ions.

### Step 2: Analyze the Given Data
We have two KCl solutions:
- 0.1 M KCl with a resistance of 200 Ohm and a known conductivity of 1.29 S/m.
- 0.02 M KCl with a resistance of 420 Ohm.

### Step 3: Calculate the Cell Constant (K)
The cell constant (K) can be calculated using the formula:
\[ K = \frac{\kappa \cdot R}{1} \]
Where:
- \( \kappa \) = conductivity of the solution
- \( R \) = resistance of the cell

For the 0.1 M KCl solution:
\[ K = \kappa \cdot R = 1.29 \, \text{S/m} \cdot 200 \, \Omega = 258 \, \text{S/m} \cdot \Omega \]

### Step 4: Calculate the Conductivity of the 0.02 M KCl Solution
Using the cell constant calculated from the 0.1 M solution, we can find the conductivity of the 0.02 M KCl solution:
\[ \kappa = \frac{K}{R} = \frac{258}{420} \approx 0.614 \, \text{S/m} \]

### Step 5: Evaluate the Statements
Now we need to evaluate the statements regarding the conductivity of solutions of different electrolytes. The options likely relate to factors affecting conductivity, such as:
1. The size of the ion
2. The charge of the ion
3. The degree of dissociation
4. The temperature of the solution

### Step 6: Identify the Incorrect Statement
- The size of the ion: Larger ions typically have lower mobility, which can affect conductivity.
- The charge of the ion: Higher charges generally lead to higher conductivity.
- The degree of dissociation: More dissociation means more ions in solution, leading to higher conductivity.
- The temperature of the solution: Higher temperatures usually increase conductivity due to increased ion mobility.

Based on this analysis, if any statement incorrectly attributes the cause of conductivity differences to a factor that does not significantly affect it, that would be the answer.

### Conclusion
The statement that is not true is likely related to the size of the ion being the primary factor affecting conductivity, as it is more complex and involves multiple factors including charge and mobility.