\({}^{31}\mathrm{P}-\{{}^{1}\mathrm{H}\}\) spectrum of diamagnetic complex mer–RhCl3 (PEt3)3 would show (\({}^{103}\mathrm{Rh}\), \({}^{31}\mathrm{P}\); I = \(\frac{1}{2}\))
doublet of doublet and doublet of triplet
In the meridional isomer of octahedral RhCl3(PEt3)3 two phosphines are trans to each other (Pa, chemically equivalent) and the third is trans to chloride (Pb). Proton decoupling removes all couplings to the ethyl hydrogens.
Both \({}^{103}\mathrm{Rh}\) (100% abundant) and \({}^{31}\mathrm{P}\) have I = 1/2, so each coupled nucleus splits a signal by the n + 1 rule.
Pa (2 equivalent nuclei) couples to 1 Rh and to 1 Pb: a doublet (\(^{1}J_{\mathrm{RhP}}\)) of doublets (\(^{2}J_{\mathrm{PP}}\)).
Pb (1 nucleus) couples to 1 Rh and to 2 equivalent Pa: a doublet (\(^{1}J_{\mathrm{RhP}}\)) of triplets (\(^{2}J_{\mathrm{PP}}\)).
A single doublet would require all three P atoms to be equivalent, as in the fac isomer; a lone triplet fits no isomer, and the reverse multiplicities do not match the 2 : 1 set of phosphorus environments. The intensity of the doublet of doublets to the doublet of triplets is 2 : 1.
Hence, doublet of doublet and doublet of triplet.
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