Consider the following complexes
`(P) [Cr(CO)_(x)]" "(Q) [Cr(CO)_(x-1)PF_(3)]`
If `PF_(3)` is better `pi` acceptor than `CO, what will be the order of bond length of CO in complexes (P) and (Q) :

Options

A. `PgtQ`
B. `QgtP`
C. `P=Q`
D. can not be compared

Explanation

To determine the order of bond lengths of CO in the complexes (P) \([Cr(CO)_{x}]\) and (Q) \([Cr(CO)_{x-1}PF_{3}]\), we need to analyze the effect of the ligands on the bond order of CO in each complex.

### Step-by-Step Solution:

1. **Understanding the Ligands:**
- In complex (P), the ligand is CO (carbon monoxide), which is a good π-acceptor.
- In complex (Q), the ligand is PF₃ (phosphorus trifluoride), which is given to be a better π-acceptor than CO.

2. **Effect of π-Acceptors on Bonding:**
- When a ligand acts as a π-acceptor, it can accept electron density from the metal through back-bonding. This back-bonding increases the bond order of the metal-ligand bond.
- In complex (P), CO will participate in π-backbonding with the chromium center, leading to a certain bond order for the C≡O bond.

3. **Analyzing Complex (Q):**
- In complex (Q), since PF₃ is a better π-acceptor than CO, it will compete for the back-bonding with the chromium metal.
- The presence of PF₃ will reduce the extent of π-backbonding with CO because the electron density will be preferentially donated to PF₃.

4. **Bond Order and Bond Length Relationship:**
- The bond order is inversely related to bond length; that is, a higher bond order corresponds to a shorter bond length.
- In complex (P), the bond order of CO is higher due to effective π-backbonding with CO.
- In complex (Q), the bond order of CO is lower because the π-backbonding is diminished due to PF₃ being a better π-acceptor.

5. **Conclusion on Bond Lengths:**
- Since the bond order of CO in complex (P) is higher than in complex (Q), it follows that:
- The bond length of CO in complex (P) will be shorter than in complex (Q).
- Therefore, the order of bond lengths is:
\[ \text{Bond Length of CO in (P)} > \text{Bond Length of CO in (Q)} \]
- This can be written as:
\[ \text{Bond Length (P)} > \text{Bond Length (Q)} \]

### Final Answer:
The order of bond lengths of CO in complexes (P) and (Q) is:
\[ \text{Bond Length (P)} > \text{Bond Length (Q)} \]