Explanation:

The given compound is [Re2Cl4(PPhMe2)4], which contains two rhenium atoms, four chloride ions, and eight phosphine ligands. The metal-metal bond refers to the bond between the two rhenium atoms.

1. Determining the oxidation state of rhenium

Each chloride ion has a -1 charge, and each phosphine ligand has a neutral charge. Let x be the oxidation state of rhenium. Then:

2(-1) + 4(0) + 4(0) + 2x = 0
-2 + 2x = 0
2x = 2
x = +1

Therefore, each rhenium atom has a +1 oxidation state.

2. Determining the electronic configuration of rhenium

The electronic configuration of rhenium in the +1 oxidation state is [Xe] 4f14 5d5. Each rhenium atom has one unpaired electron in the 5d orbital.

3. Determining the bonding in [Re2Cl4(PPhMe2)4]

The compound has a dimeric structure, with each rhenium atom bonded to four phosphine ligands and two chloride ions. The chloride ions bridge the two rhenium atoms, forming a Re-Cl-Re bridge. The phosphine ligands are coordinated to each rhenium atom, forming a tetrahedral geometry.

The metal-metal bond arises from the overlap of the 5d orbitals on the two rhenium atoms. The two unpaired electrons in the 5d orbital of each rhenium atom can form a bond, resulting in a quadruple bond between the two rhenium atoms.

Therefore, there are three metal-metal bonds in [Re2Cl4(PPhMe2)4].