The IUPAC name of the compound `[CuCl_2(CH_3NH_2)_2]` is

Explanation

To determine the IUPAC name of the compound \([CuCl_2(CH_3NH_2)_2]\), we will follow these steps:

### Step 1: Identify the central metal atom
The central metal atom in the compound is copper (Cu).

**Hint:** Look for the metal that is surrounded by ligands in the coordination compound.

### Step 2: Determine the oxidation state of the central metal
In this compound, we have two chloride ions (Cl) and two methylamine ligands (CH₃NH₂). Each chloride ion has a charge of -1. Therefore, the total charge contributed by the two chloride ions is -2. The methylamine ligands are neutral.

Let \( x \) be the oxidation state of copper. The overall charge of the compound is neutral (0). Thus, we can set up the equation:

\[ x + (-2) + 0 = 0 \implies x = +2 \]

**Hint:** Remember that the sum of the oxidation states in a neutral compound must equal zero.

### Step 3: Identify the ligands and their names
The ligands in this compound are:
- Two chloride ions (Cl⁻), which are named "chloro".
- Two methylamine ligands (CH₃NH₂), which are named "methylamine".

Since there are two of each type of ligand, we will use the prefixes "di-" for both.

**Hint:** Use the appropriate prefixes to indicate the number of each type of ligand present.

### Step 4: Arrange the ligands in alphabetical order
When naming coordination compounds, ligands are listed in alphabetical order regardless of their prefixes.
- "Chloro" comes before "methylamine" alphabetically.

Thus, we will name the ligands as follows:
- "di-chloro" for the two chloride ligands.
- "bis-methylamine" for the two methylamine ligands (the prefix "bis" is used for ligands with names that start with a vowel).

**Hint:** Alphabetize the ligands based on their names, not their prefixes.

### Step 5: Combine the names and add the oxidation state of the metal
Now we combine the names of the ligands with the name of the metal and its oxidation state. The name will be structured as follows:

\[ \text{di-chloro} \, \text{bis-methylamine} \, \text{copper(II)} \]

**Hint:** Ensure to include the oxidation state of the metal in parentheses after its name.

### Final Answer
The IUPAC name of the compound \([CuCl_2(CH_3NH_2)_2]\) is:

**Di-chloro bis(methylamine) copper(II)**