Three complex ions of cobalt(iii), [co(cn)6] 3-, [co(nh3)6] 3+, and [cof6] 3-, absorb light at wavelengths of (in no particular order) 290 nm, 440 nm, and 770 nm. match each complex ion to the appropriate wavelength absorbed. what color would you expect each solution to be?

The [Co(CN)₆]³⁻ would absorb light of wavelength 290nm

             The [Co(NH₃)₆]³⁺ would absorb light of wavelength 440nm

             The [Co(F)₆]³⁻ would absorb light of wavelength 770nm

Explanation:

All the metal complexes of Cobalt given here are octahedral complexes.

They would follow the crystal field splitting pattern of normal octahedral complexes.

The crystal field splitting pattern for octahedral complexes gives us the information that  under the influence of an octahedral ligand field a degenrate d-orbital splits in to two sets of orbitals t₂g and eg.

The t₂g orbital is stabilized and is lower in energy than the energy of degenrate d-orbital .

The eg orbital is destabilised and hence its higher in energy than the degenerate d-orbital.

The t₂g orbital is triply degenerate and eg is doubly degenrate.

The energy gap between the the t₂g and eg is Δo, known as the crystal field splitting constant.

So greater is the energy gap between the t₂g and eg orbitals greater will be the energy required to cause a transition from  t₂g to eg.

There are two types of ligands, strong field ligands and weak field ligands.

The strong field ligand complexes have  more energy gap between t₂g and eg and hence the more stabilize the t₂g set of orbitals  and  more destabilize the eg set of orbitals.

so the energy gap for a strong field ligand complex would be  more as compared  to that in a weak field ligand complex.

CN⁻ is a strong field ligand.

NH₃ is a moderate field ligand.

F⁻ is a weak field ligand .

The ligand field strength is following :

CN⁻>NH₃>F⁻

So the energy gap between the t₂g and eg orbitals would be highest for CN- then for NH3 and would be least for F-.

So more energy is required for CN⁻ followed by NH₃ and least energy would be required for F⁻.

E=hv

E=hc/λ

Energy is inversely related with λ. So Greater the energy lesser would be λ. Or Greater will be the λ lesser would be the energy.

So the following wavelegth would be absorbed by the complexes:]

             The [Co(CN)₆]³⁻ would absorb light of wavelength 290nm.

             The [Co(NH₃)₆]³⁺ would absorb light of wavelength 440nm  

             The [Co(F)₆]³⁻ would absorb light of wavelength 770nm.

The color of a complex compound is complementary to the color which the comoplex would have observed.

So , The [Co(CN)₆]³⁻ would absorb light of wavelength 290nm which is in UV region and so the complementary color in this wavelength would be pale yellow.

so,The [Co(NH₃)₆]³⁺ would absorb light of wavelength 440nm  which can be considered corresponding to wavelength of blue light and hence it would show complementary color to blue which is orange.

The [Co(F)₆]³⁻ would absorb light of wavelength 770nm which can be considered corresponding to wavelength of red light and hence it would show complementary color to red which is green.(usually red light occurs till 700nm)

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