Which of the following statements is/are correct?

Options

A. The conductance of one `cm^3` (or 1 `unit^3`) of a solution is called specific conductance
B. Specific conductance increases while molar conductivity decreases on progressive dilution
C. The limiting equivalent conductivity of weak electrolyte cannot be determined exactly by extraplotation of the plot of `wedge_(eq)` against `sqrtc`
D. The conductance of metals is due to the movement of free electrons

Answer

To solve the question regarding which statements are correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1: The conductance of 1 cm³ or 1 unit cube of a solution is called specific conductance.**
- **Analysis:** This statement is correct. Specific conductance (or conductivity) is defined as the conductance of a solution when the dimensions of the sample are 1 cm³ (or 1 unit cube). Therefore, this statement is true.

2. **Statement 2: Specific conductance increases while molar conductivity decreases on progressive dilution.**
- **Analysis:** This statement is incorrect. Molar conductivity (Λ) is given by the formula:
\[ \Lambda = \frac{\kappa \times 1000}{C} \]
where \( \kappa \) is the specific conductance and \( C \) is the concentration. When a solution is diluted, the concentration \( C \) decreases, which causes molar conductivity \( \Lambda \) to increase (since it is inversely proportional to concentration). On the other hand, specific conductance \( \kappa \) decreases with dilution because it is directly proportional to concentration. Thus, the statement is false.

3. **Statement 3: The limiting equivalent conductivity of a weak electrolyte cannot be determined exactly by extrapolation of the plot of equivalent conductivity against \(\sqrt{C}\).**
- **Analysis:** This statement is correct. The relationship for equivalent conductivity (\( \Lambda \)) for weak electrolytes does not follow the same linear extrapolation as strong electrolytes. Therefore, the limiting equivalent conductivity cannot be determined exactly for weak electrolytes using this method. Thus, this statement is true.

4. **Statement 4: The conductance of matter is due to the movement of free electrons.**
- **Analysis:** This statement is also correct. In metals, conductance is primarily due to the movement of free electrons. When an electric field is applied, these free electrons move, resulting in electric current. Therefore, this statement is true.

### Conclusion:
Based on the analysis:
- **Correct Statements:** 1st, 3rd, and 4th.
- **Incorrect Statement:** 2nd.

### Final Answer:
The correct statements are 1st, 3rd, and 4th.

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