How to show that ["Co"("CN")_6]^(3-) (a yellow complex) has a larger Delta_o than ["CoF"_6]^(3-) (a blue complex) using knowledge of sigma donor, pi donor, and pi acceptor behavior, and spin-only magnetic moment?

1 Answer
Feb 8, 2017

First of all, it is crucial to recognize the following:

  • The crystal field splitting energy (i.e. the Delta_o for these octahedral complexes) corresponds to the energy of the light absorbed.
  • The color of the complexes is due to light reflected, so the complementary color is absorbed and its wavelength is what we should compare.

PI DONORS, SIGMA DONORS, AND PI ACCEPTORS

Now, recall what it means to be a bbpi donor, bbsigma donor, and bbpi acceptor.

  • pi donors donate electron density into the metal's bonding pi orbitals. This somewhat raises the energy of the bb(t_(2g)) orbitals.
  • sigma donors donate electron density into the metal's antibonding sigma^"*" orbitals. This raises the energy of the bb(e_g) orbitals.
    Inorganic Chemistry, Miessler et al.Inorganic Chemistry, Miessler et al.
  • pi acceptors accept electron density from the metal bonding pi orbitals. This lowers the energy of the bb(t_(2g)) orbitals.
    Inorganic Chemistry, Miessler et al.Inorganic Chemistry, Miessler et al.
    The pi donation depiction is similar, but in reverse.

These energy alterations are summarized below, using ["CrF"_6]^(3-) and ["Cr"("CN")_6]^(3-) as examples of a strong-field and weak-field splitting, respectively:

Inorganic Chemistry, Miessler et al.Inorganic Chemistry, Miessler et al.

From left to right you can see Delta_o decreasing.

Therefore, pi acceptors are the strongest-field ligands (large crystal field splitting energy, promotes low-spin), and pi donors are the weakest-field ligands (small crystal field splitting energy, promotes high-spin).

WAVELENGTH CONCLUSIONS

As it turns out, "CN"^(-) is a great pi acceptor AND sigma donor, so its Delta_o should be large, compared to that from "F"^(-), a pi donor.

From this, it follows that the Delta_o for ["CoF"_6]^(3-) is smaller than that for ["Co"("CN")_6]^(3-), and thus corresponds to a smaller frequency and longer wavelength.

Given that...

  • blue reflected light corresponds to orange absorbed light,
  • and yellow reflected light corresponds to violet absorbed light,

...we have that violet light is lower wavelength, violet is higher frequency and thus the yellow complex should have a larger Delta_o and stronger-field ligand... and it does!

SPIN-ONLY MAGNETIC MOMENT?

Lastly, the exact spin-only magnetic moment equation is not important for this purpose. All it really gives us for this situation is that higher mu_S corresponds to more unpaired electrons.

The point is to realize that that strong-field ligands give rise to low-spin complexes (more electron pairing), and vice versa.

Therefore, we expect that ["Co"("CN")_6]^(3-) has a lower mu_S than ["CoF"_6]^(3-), as the former has less unpaired electrons than the latter. This would experimentally demonstrate that "CN"^(-) is strong-field and "F"^(-) is weak-field.