Let `C_(NaCl) and C_(BaSO_(4))` be the conductances (in S) measured for saturated aqueous solutions of NaCl and BaSO4, respectively, at a temperature T.
Which of the following is false?

Options

A. `C_(NaCl)(T_(2))gtC_(NaCl)(T_(1))" for "T_(2) gt T_(1)`
B. `C_(BaSO_(4))(T_(2))gtC_(BaSO_(4))(T_(1))" for "T_(2) gt T_(1))`
C. Ionic mobilities of ions form both salts increase with T.
D. `C_(NaCl)gt gt C_(BaSO_(4))` at a given T

Explanation

To solve the problem, we need to analyze the conductance of saturated aqueous solutions of NaCl and BaSO4 and determine which statement is false based on the information provided.

### Step-by-Step Solution:

1. **Understanding Conductance**: Conductance (C) is a measure of how well a solution can conduct electricity. It depends on the concentration and mobility of the ions in the solution.

2. **Dissociation of Compounds**:
- NaCl dissociates into Na⁺ and Cl⁻ ions in solution.
- BaSO₄ dissociates into Ba²⁺ and SO₄²⁻ ions in solution.

3. **Ionic Size and Mobility**:
- Na⁺ is a smaller ion compared to Ba²⁺. Smaller ions typically have higher mobility in solution because they can move more freely.
- However, the mobility of ions is also affected by the solvation process, where water molecules surround the ions.

4. **Effect of Solvation**:
- In aqueous solutions, smaller ions like Na⁺ can form a more extensive solvation shell due to their charge density, which can hinder their movement.
- Larger ions like Ba²⁺ may not form as extensive a solvation shell and can move more freely, resulting in higher conductance.

5. **Comparison of Conductance**:
- At a given temperature, the conductance of NaCl (C_NaCl) can be less than that of BaSO₄ (C_BaSO₄) due to the reasons discussed.
- However, in a molten state, the conductance of NaCl is higher than that of BaSO₄ because the ions are not solvated and can move freely.

6. **Identifying the False Statement**:
- The statement that "the conductance of NaCl is less than the conductance of BaSO₄ in aqueous solution" is true.
- The statement that "the conductance of NaCl is greater than that of BaSO₄ in molten state" is also true.
- Therefore, if any statement claims that the conductance of NaCl is greater than BaSO₄ in aqueous solution, that would be false.

### Conclusion:
The false statement is that the conductance of NaCl is greater than that of BaSO₄ in saturated aqueous solutions.