To determine the conditions under which the dissociation of ClF3(g) is favored, we need to analyze the given reaction and apply the principles of chemical equilibrium, particularly Le Chatelier's principle.
### Step-by-Step Solution:
1. **Understand the Reaction**:
The reaction given is:
\[
\text{ClF}_2(g) + 3\text{F}_2(g) \rightleftharpoons 2\text{ClF}_3(g)
\]
The enthalpy change (ΔH) for the forward reaction (formation of ClF3) is -329 kJ, indicating that it is an exothermic reaction.
**Hint**: Identify the direction of the reaction and the sign of ΔH to understand whether heat is released or absorbed.
2. **Identify the Backward Reaction**:
The backward reaction, which is the dissociation of ClF3, can be written as:
\[
2\text{ClF}_3(g) \rightleftharpoons \text{ClF}_2(g) + 3\text{F}_2(g)
\]
Since the forward reaction is exothermic, the backward reaction (dissociation) is endothermic, meaning it requires heat.
**Hint**: Recognize that the reverse of an exothermic reaction is endothermic.
3. **Apply Le Chatelier's Principle**:
According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in temperature, pressure, or concentration, the equilibrium will shift in a direction that counteracts the change.
4. **Evaluate the Options**:
- **Increasing Temperature**: Since the backward reaction is endothermic, increasing the temperature will favor the dissociation of ClF3.
- **Conclusion**: This option is correct.
- **Increasing Volume**: Increasing the volume of the container will favor the side with more gaseous moles. The forward reaction has 4 moles of gas (1 ClF2 + 3 F2) and the backward reaction has 2 moles of gas (2 ClF3). Thus, increasing the volume will favor the backward reaction.
- **Conclusion**: This option is correct.
- **Adding Fluorine Gas**: Adding more F2 increases the concentration of reactants, which will shift the equilibrium to the right (forward direction), favoring the formation of ClF3, not its dissociation.
- **Conclusion**: This option is incorrect.
- **Adding Inert Gas at Constant Pressure**: Adding an inert gas at constant pressure increases the volume, which, as established, will favor the side with more moles of gas (the backward reaction).
- **Conclusion**: This option is correct.
5. **Final Answer**:
The dissociation of ClF3(g) will be favored by:
- Increasing the temperature
- Increasing the volume of the container
- Adding an inert gas at constant pressure
Thus, the correct options are A, B, and D.