How many geometrical isomers are possible for `[Zn(NH_(3))ClBrPPh_(3)]^(-)` ?

Answer

To determine how many geometrical isomers are possible for the complex \([Zn(NH_3)ClBrPPh_3]^-\), we will analyze the structure and the ligands involved.

### Step 1: Identify the Coordination Number and Geometry
The central metal ion in this complex is zinc (Zn), which typically has a coordination number of 4 when it forms complexes. Given the ligands \((NH_3, Cl, Br, PPh_3)\), we can infer that the geometry of the complex will be tetrahedral.

**Hint:** Remember that the coordination number indicates how many ligands are bonded to the central metal ion, which helps determine the geometry.

### Step 2: Understand Geometrical Isomerism
Geometrical isomerism, also known as cis-trans isomerism, occurs when there are different spatial arrangements of the same ligands around the central metal ion. For tetrahedral complexes, geometrical isomerism is not typically observed because all bond angles are approximately 109.5 degrees, which does not allow for distinct cis or trans arrangements.

**Hint:** Geometrical isomers require specific arrangements that are not possible in tetrahedral geometries.

### Step 3: Analyze the Ligands
In the given complex, we have four different ligands: \(NH_3\), \(Cl\), \(Br\), and \(PPh_3\). Since all four ligands are different, there are no identical pairs that could lead to cis or trans configurations.

**Hint:** Look for identical ligands to determine if geometrical isomerism is possible. Different ligands do not create isomerism.

### Step 4: Conclusion on Geometrical Isomers
Since the complex is tetrahedral and contains four different ligands, it does not exhibit geometrical isomerism. Therefore, there is only one geometrical isomer possible, which is the complex itself.

**Final Answer:** Only one geometrical isomer is possible for the complex \([Zn(NH_3)ClBrPPh_3]^-\).

### Summary of Steps:
1. Identify the coordination number and geometry (tetrahedral).
2. Understand that geometrical isomerism requires specific arrangements that tetrahedral complexes do not provide.
3. Analyze the ligands to confirm there are no identical pairs.
4. Conclude that only one geometrical isomer exists.