The appropriate formula of dichloridobis(ethane-1, 2-diamine)platinum(IV) nitrate is :

Options

A. `[PtCl_(2)(en)_(2)](NO_(3))_(2)`
B. `[Pt(en)_(2)Cl_(2)](NO_(3))_(2)`
C. `[Pt(en)_(2)Cl_(2)]NO_(3)`
D. `[PtCl_(2)(en)_(2)]NO_(3)`

Answer

To derive the appropriate formula for dichloridobis(ethane-1,2-diamine)platinum(IV) nitrate, we will follow these steps:

### Step 1: Identify the Components of the Compound
The name "dichloridobis(ethane-1,2-diamine)platinum(IV) nitrate" indicates the following components:
- **Cation**: dichloridobis(ethane-1,2-diamine)platinum(IV)
- **Anion**: nitrate (NO3)

### Step 2: Determine the Anion
The anion is clearly stated as nitrate, which has the formula NO3⁻.

### Step 3: Analyze the Cation
The cation consists of:
- **Chloride ligands**: "dichloro" indicates there are 2 chloride ions (Cl⁻).
- **Ethylene-diamine ligand**: "bis(ethane-1,2-diamine)" indicates there are 2 ethylene-diamine (en) ligands. Ethylene-diamine is a neutral ligand.

### Step 4: Write the Cation Formula
The cation can be represented as:
- Platinum (Pt) is the central metal.
- The overall charge of the cation must be calculated considering the oxidation state of platinum (IV) and the charges of the ligands.

### Step 5: Calculate the Charge on the Cation
- The oxidation state of platinum (Pt) is +4.
- Each chloride ion (Cl) contributes -1 charge, and there are 2 of them, contributing a total of -2.
- Ethylene-diamine (en) is neutral, contributing 0 charge.

Thus, the charge on the cation can be calculated as follows:
\[ \text{Charge on cation} = +4 - 2 = +2 \]

### Step 6: Combine Cation and Anion
The cation has a charge of +2 and the anion (nitrate) has a charge of -1. To balance the charges and ensure the compound is neutral:
- We need 2 nitrate ions to balance the +2 charge from the cation.

### Step 7: Write the Final Formula
The final formula can be constructed as:
\[ \text{[PtCl}_2\text{(en)}_2]^{2+} \text{(NO}_3\text{)}_2^{-} \]

This results in the overall formula:
\[ \text{[PtCl}_2\text{(en)}_2\text{](NO}_3\text{)}_2} \]

### Final Answer
The appropriate formula of dichloridobis(ethane-1,2-diamine)platinum(IV) nitrate is:
\[ \text{[PtCl}_2\text{(en)}_2\text{](NO}_3\text{)}_2} \]

---