If in the mixed carbonyl the other ligand is also `pi` acceptor it would compete with the ligand `CO` for gaining the metal `d_(pi)` electron charge The higher is the extent of back donation in `CO` , the lesser will be the stretching vibration frequency for `C-O` bond If `PP_(3)` is better pi-acceptor than `CO` then answer the following
Select the correct order of `C-O` bond length in the following molecules .
(I) `[Mo(CO)_(3)(PF_(3))_(3)]` (II) `[Mo(CO)_(3)(PCI_(3))_(3)]`
(III) `[Mo(CO)_(3)(P(Me)_(3))]`
(a) `IgtIIgtIII`
(b) `IIIgtIgtII`
(c) `IIgtIIIgtI`
(d) `IltIIltIII`

Answer

To solve the problem, we need to determine the order of C-O bond lengths in the given mixed carbonyl complexes based on the pi-acceptor abilities of the ligands. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Relationship Between Bond Order and Bond Length
- The bond length of a molecule is inversely related to its bond order. Higher bond order means shorter bond length, while lower bond order means longer bond length.

### Step 2: Identify the Ligands and Their Pi-Acceptor Strengths
- We have three complexes:
1. \([Mo(CO)_{3}(PF_{3})_{3}]\)
2. \([Mo(CO)_{3}(PCl_{3})_{3}]\)
3. \([Mo(CO)_{3}(PMe_{3})]\)

- The ligands in question are \(PF_{3}\), \(PCl_{3}\), and \(PMe_{3}\). We need to compare their abilities as pi-acceptors:
- **PF3**: Strongest pi-acceptor due to the high electronegativity of fluorine.
- **PCl3**: Moderate pi-acceptor, less than PF3 but more than PMe3.
- **PMe3**: Weakest pi-acceptor due to the presence of methyl groups which are less electronegative.

### Step 3: Establish the Order of Pi-Acceptor Strength
- The order of pi-acceptor strength is:
- \(PF_{3} > PCl_{3} > PMe_{3}\)

### Step 4: Relate Pi-Acceptor Strength to Bond Order
- Since the pi-acceptor strength affects the back-donation from the metal to the ligand, we can conclude:
- The stronger the pi-acceptor, the higher the bond order of the C-O bond.
- Thus, the order of bond order will be:
- \(PF_{3} > PCl_{3} > PMe_{3}\)

### Step 5: Determine the Order of C-O Bond Lengths
- Since bond length is inversely related to bond order, we can now establish the order of C-O bond lengths:
- The longest bond length corresponds to the lowest bond order, which is for \(PMe_{3}\), followed by \(PCl_{3}\), and the shortest bond length corresponds to the highest bond order, which is for \(PF_{3}\).

- Therefore, the order of C-O bond lengths is:
- \(PMe_{3} > PCl_{3} > PF_{3}\)

### Step 6: Match with Given Options
- The correct order of C-O bond lengths in the complexes is:
- \([Mo(CO)_{3}(PMe_{3})] > [Mo(CO)_{3}(PCl_{3})] > [Mo(CO)_{3}(PF_{3})]\)

- This corresponds to option (d): \(I < II < III\).

### Final Answer
- The correct answer is (d) \(I < II < III\).