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 can analyze the properties and characteristics of the complex step by step.

### Step 1: Identify the Geometry of the Complex
The complex ion \([CrCl(NO_2)(en)_2]^+\) consists of a chromium (Cr) center coordinated to two bidentate ethylenediamine (en) ligands, one nitro (NO₂) ligand, and one chloro (Cl) ligand. Since it has six ligands, the geometry of the complex is octahedral.

**Hint:** Remember that octahedral complexes can have different geometrical isomers due to the arrangement of ligands.

### Step 2: Determine Possible Geometrical Isomers
In an octahedral complex with two bidentate ligands and two monodentate ligands, we can have geometrical isomers. The two types of isomers that can arise are cis and trans isomers.

- **Cis Isomer:** The two monodentate ligands (Cl and NO₂) are adjacent to each other.
- **Trans Isomer:** The two monodentate ligands are opposite each other.

**Hint:** Visualize the arrangement of ligands in the octahedral geometry to identify cis and trans forms.

### Step 3: Analyze Optical Activity
- The **cis isomer** is optically active because it does not have a plane of symmetry, meaning it has non-superimposable mirror images.
- The **trans isomer**, on the other hand, is optically inactive because it has a plane of symmetry, making its mirror image superimposable.

**Hint:** Recall that optical activity is determined by the presence or absence of symmetry in the molecular structure.

### Step 4: Identify Diastereomers
Diastereomers are stereoisomers that are not mirror images of each other. In this case, the cis and trans forms of the complex are indeed diastereomers because they have different spatial arrangements and are not superimposable.

**Hint:** Understand the difference between enantiomers (which are mirror images) and diastereomers (which are not).

### Step 5: Evaluate the Statements
Now, we need to evaluate the statements provided regarding the complex ion:

1. **Cis and trans forms are diastereomers.** (True)
2. **Only the cis isomer displays optical activity.** (True)
3. **Cis and trans forms are not diastereomers.** (Not True)
4. **There are three optically active isomers: D, L, and trans form.** (Not True, as the trans form is not optically active)

### Conclusion
The statements that are not true about the complex ion \([CrCl(NO_2)(en)_2]^+\) are:
- "Cis and trans forms are not diastereomers."
- "There are three optically active isomers: D, L, and trans form."

Thus, the answer to the question is that the statement "Cis and trans forms are not diastereomers" is not true.