The `IUPAC` name of the coordination compound `[CuCI_(2)(CH_(3)NH_(2))_(2)]` is
(a) Dimethylamine copper(II)chloride
(b) Bis(dimehtylamine copper(II) chloride
(c ) Dichloridobis(methylamine)copper(II)
(d) Dichlorobis(dimethylamine) copper(II) .

Answer

To determine the IUPAC name of the coordination compound \([CuCl_2(CH_3NH_2)_2]\), we will follow the systematic nomenclature rules for coordination compounds. Here’s a step-by-step breakdown of the process:

### Step 1: Identify the Ligands
The coordination compound consists of:
- Two chloride ions \((Cl^-)\)
- Two methylamine ligands \((CH_3NH_2)\)

The name of the chloride ligand in coordination chemistry is "chlorido," and the name for the methylamine ligand is "methylamine."

### Step 2: Determine the Oxidation State of the Central Metal
Let the oxidation state of copper be \(x\). The charges from the ligands are:
- Chlorido: Each chloride ion has a charge of \(-1\), and there are 2 chloride ions, contributing \(-2\) total.
- Methylamine: It is a neutral ligand, contributing \(0\).

The overall charge of the complex is neutral (0). Therefore, we can set up the equation:
\[ x + (-2) + 0 = 0 \]
Solving for \(x\):
\[ x - 2 = 0 \implies x = +2 \]
Thus, the oxidation state of copper is \(+2\).

### Step 3: Naming the Ligands
According to IUPAC nomenclature:
- The ligands are named in alphabetical order, regardless of the number of ligands.
- Since we have two chlorido ligands, we use the prefix "di" for two.
- For the two methylamine ligands, we use the prefix "bis" since it is a complex ligand.

So, we have:
- Chlorido (for \(Cl^-\))
- Bis(methylamine) (for \(2\) methylamine ligands)

### Step 4: Combine the Names
Now, we combine the names of the ligands with the name of the central metal:
- The name of the central metal is "copper," and since its oxidation state is \(+2\), we denote it as "copper(II)."

### Step 5: Final Assembly of the Name
Putting it all together, we write the name as:
\[ \text{dichloridobis(methylamine)copper(II)} \]

### Conclusion
Thus, the IUPAC name of the coordination compound \([CuCl_2(CH_3NH_2)_2]\) is:
**Dichloridobis(methylamine)copper(II)**

### Answer Selection
Among the given options, this matches with:
(c) Dichloridobis(methylamine)copper(II)

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