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 the two salts, NaCl and BaSO₄, at different temperatures and determine which statement is false among the given options.

### Step-by-Step Solution:

1. **Understanding Conductance**:
Conductance (C) of an electrolyte solution is influenced by the concentration of ions and their mobility. Higher mobility and concentration lead to higher conductance.

2. **Analyzing NaCl**:
- NaCl is a strong electrolyte that completely dissociates into Na⁺ and Cl⁻ ions in solution.
- As temperature increases (from T1 to T2), the mobility of ions increases due to decreased intermolecular forces. This results in increased conductance.
- Therefore, the statement that "conductance of NaCl at T2 is more than at T1" is **true**.

3. **Analyzing BaSO₄**:
- BaSO₄ is a sparingly soluble salt, meaning it does not completely dissociate in water. Its solubility increases with temperature.
- As temperature increases, more Ba²⁺ and SO₄²⁻ ions will dissolve, increasing the number of ions in solution and thus increasing conductance.
- Therefore, the statement that "conductance of BaSO₄ at T2 is more than at T1" is also **true**.

4. **Ionic Mobility**:
- The mobility of ions increases with temperature due to reduced forces of attraction between them. This is a general property of ionic solutions.
- Thus, the statement "ionic mobility increases with temperature" is **true**.

5. **Comparing Conductance of NaCl and BaSO₄**:
- NaCl, being highly soluble, will produce a larger number of ions compared to the limited dissociation of BaSO₄.
- Therefore, the statement "the conductance of sodium chloride is very high compared to barium sulfate" is **true**.

6. **Conclusion**:
- All the statements analyzed are true based on the properties of the salts and the effects of temperature on their conductance.

### Final Answer:
None of the statements are false; all provided statements are true.