Tetrammine diaqua copper (II) hydroxide is given by the formula

Options

A. `[Cu(NH_(3))_(4)](OH)_(2).2H_(2)O`
B. `[Cu(NH_(3))_(4)(OH)_(2)].2H_(2)O`
C. `[Cu(NH_(3))_(4)(H_(2)O)_(2)](OH)_(2)`
D. `[Cu(NH_(3))_(4)(H_(2)O)(OH)_(2)]`

Explanation

To determine the formula for tetrammine diaqua copper(II) hydroxide, we will break down the components of the name step by step.

### Step 1: Identify the components
The name "tetrammine diaqua copper(II) hydroxide" indicates the following:
- **Tetrammine**: This means there are 4 amine (NH₃) ligands.
- **Diaqua**: This indicates there are 2 water (H₂O) molecules.
- **Copper(II)**: This tells us that copper is in the +2 oxidation state.
- **Hydroxide**: This indicates the presence of hydroxide ions (OH⁻).

### Step 2: Write the coordination complex
The coordination complex will consist of the copper ion surrounded by the ligands:
- The copper ion (Cu²⁺) will be at the center.
- The 4 amine ligands (NH₃) will be coordinated to copper.
- The 2 water molecules (H₂O) will also be coordinated to copper.
- The hydroxide ions (OH⁻) will be outside the coordination sphere.

### Step 3: Determine the charge balance
- The charge from copper is +2.
- Each amine (NH₃) is neutral, contributing 0 charge.
- Each water (H₂O) is also neutral, contributing 0 charge.
- The hydroxide ions (OH⁻) are outside the coordination sphere and will contribute -2 charge in total (since there are 2 OH⁻).

### Step 4: Write the final formula
Putting this all together, we have:
- Inside the coordination sphere: Cu(NH₃)₄(H₂O)₂
- Outside the coordination sphere: (OH)₂

Thus, the complete formula for tetrammine diaqua copper(II) hydroxide is:
\[ \text{[Cu(NH}_3\text{)}_4\text{(H}_2\text{O)}_2\text{]}(\text{OH})_2 \]

### Final Answer:
The formula for tetrammine diaqua copper(II) hydroxide is:
\[ \text{[Cu(NH}_3\text{)}_4\text{(H}_2\text{O)}_2\text{]}(\text{OH})_2 \]

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