Which of the following statements is not true about the complex ion `[CrCl(NO_(2))(en)_(2)]^(+)` ?

Options

A. It has two geometrical isomers cis and trans
B. cis and trans forms are not diastereomers to each other
C. only the cis isomer displays optical activity
D. it has three optically active isomers: `d,l` and trans forms

Explanation

To determine which statement is not true about the complex ion \([CrCl(NO_2)(en)_2]^+\), we will analyze each statement step by step.

### Step 1: Identify the Coordination Number
The complex consists of:
- 1 Chlorine (Cl)
- 1 Nitrite (NO2)
- 2 Ethylenediamine (en) ligands (each en is bidentate)

Calculating the coordination number:
- Chlorine contributes 1
- Nitrite contributes 1
- Each ethylenediamine contributes 2 (since it is bidentate, it binds through two sites)

Thus, the total coordination number is:
\[ 1 (Cl) + 1 (NO_2) + 2 \times 2 (en) = 1 + 1 + 4 = 6 \]

### Step 2: Determine the Geometry
With a coordination number of 6, the geometry of the complex is octahedral.

### Step 3: Analyze Geometrical Isomers
In an octahedral complex, we can have geometrical isomers, specifically cis and trans forms.

- **Cis form**: The two ethylenediamine ligands are adjacent to each other.
- **Trans form**: The two ethylenediamine ligands are opposite each other.

Thus, the first statement claiming that it has two geometrical isomers (cis and trans) is **true**.

### Step 4: Analyze Diastereomers
Diastereomers are non-superimposable and not mirror images of each other. The cis and trans forms of this complex are indeed non-superimposable and not mirror images. Therefore, the second statement claiming that cis and trans forms are not diastereomers is **not true**.

### Step 5: Optical Activity
The cis isomer can exhibit optical activity because it lacks a plane of symmetry, while the trans isomer has a plane of symmetry and does not exhibit optical activity. Thus, the third statement claiming that only the cis isomer displays optical activity is **true**.

### Step 6: Optical Isomers
The fourth statement claims that it has three optically active isomers: D, L, and trans. However, while D and L refer to the optical isomers, the trans form is a geometrical isomer and does not count as an optically active isomer. Therefore, this statement is also **not true**.

### Conclusion
The statements that are not true about the complex ion \([CrCl(NO_2)(en)_2]^+\) are:
- **Second Statement**: Cis and trans forms are not diastereomers to each other.
- **Fourth Statement**: It has three optically active isomers D, L, and trans.

### Final Answer
The incorrect statements are 2 and 4.

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