Answer :

To write the systemic name of the chemical compound [tex]\( LiI \cdot 3 H_2O \)[/tex], follow these steps:

1. Identify the anhydrous compound:
- [tex]\( LiI \)[/tex] is the chemical formula for lithium iodide. It is composed of lithium (Li) and iodide (I), an ionic compound.

2. Recognize the hydrate notation:
- The notation [tex]\( \cdot 3 H_2O \)[/tex] means the compound includes three water molecules. These are called water of hydration and are integral to the compound's structure.

3. Name the anhydrous part:
- The name of [tex]\( LiI \)[/tex] is lithium iodide.

4. Combine the two components:
- Since there are three water molecules associated with each formula unit of lithium iodide, we use the prefix "tri-" for three.
- The general naming convention for hydrates is to append "hydrate" with the proper numerical prefix indicating the number of water molecules.

5. Final systemic name:
- Combining the name of the anhydrous component and the hydrate component, we get the systemic name: lithium iodide trihydrate.

Therefore, the systemic name of [tex]\( LiI \cdot 3 H_2O \)[/tex] is lithium iodide trihydrate.