Among the following complexes, the one showing the highest rate of substitution of a CO ligand on heating with one equivalent of PPh₃ in decalin, is

contributes Concept:

Substitution reaction:

• A substitution reaction is a type of chemical reaction, in which one functional group is replaced by another functional group.
• A ligand substitution reaction involves the exchange of one ligand for another, with no change in the oxidation state of the metal.
• The incoming and outgoing ligands may be of L- or X- type.
• 
• Ligand substitution reaction can be of type (a) Associative mechanism and (b) Dissociative mechanism.
• An Associative mechanism is common for 16e^- complex and a Dissociative mechanism is common for 18e^- complex. 

Explanation:

• All the metal complexes contain the metal atom Mn and 3 CO ligands.
• The number of valence electrons contributed by a metal atom to the total electron count in a zero-oxidation state is equal to the group number. In each metal complex, Mn has a 0 oxidation state and Mn belongs to group 7. Thus, Mn contributes 7 electrons to the total electrons count. 3 CO present in the complex contributes a total of 6 electrons as CO act as a 2 electron donor.
• C5H5, C5Ph5, C5Me5, and indenyl ligand act as a 5 electron donor species.  
• The total electrons present in each metal complex is 
  =5+7+6 = 18 electrons.
  So, each metal complex follows the 18-electron rule.

• Now, in case of a ligand substitution reaction, a ligand containing a double ring undergo an easy or fast substitution reaction.
• Out of C5H5, C5Ph5, C5Me5, and indenyl ligand, the indenyl ligand contains a double ring. Thus it will undergo an easy ligand substitution reaction.
• Among the following complexes, the one showing the highest rate of substitution of a CO ligand on heating with one equivalent of PPh3 in decalin is (η5 - indenyl) Mn(CO)3.​

Conclusion:

Among the following complexes, the one showing the highest rate of substitution of a CO ligand on heating with one equivalent of PPh3 in decalin is (η5 - indenyl) Mn(CO)3.