The [Cr(H₂O)₆]³⁺ ion is violet, and [Cr(CN)₆]^3- is yellow. Explain this difference using crystal field theory. Use the colors to order H₂O and CN^- in the spectrochemical series.

Video transcript

Alright. Hi, everyone. So this question says that the colors of the complex ions cocn 63 minus and cof 63 minus are orange and green respectively, explain the difference and identify the order of cyanide and fluoride in the spectra chemical series. So here we have four different entry choices comparing the crystal field splitting energies of both ligands proposing whether one is smaller or larger. Also each entero is comparing whether or not cyanide and fluoride are strong field or weak field ligands. So let's go ahead and begin by talking about what the crystal field splitting energy tells us about a given ligand, right? Recall that the crystal field splitting energy is represented by the symbol delta and delta essentially describes the energy required to transition from lower energy D orbitals to higher energy D orbitals. Right. So the energy required for this transition from the lower energy to higher energy D orbitals is described as delta and it is this energy transition or electronic transition that determines the color of a given complex because the value for delta is heavily dependent on the nature of the leg in itself. Now, when lien is considered strong field, right, the delta value is going to be higher by comparison. Whereas a weak field ligand will subsequently have a relatively low delta valley. And it's also worth noting that energy in this case, delta is proportional to the wavelength of light absorbed by a particular ligand because recall it E which stands for energy is equal to H multiplied by C divided by LAMBDA. Right H is planks constant C is the speed of light and lambda is the wavelength of light absorbed. So essentially, right, the more energy is absorbed or required for the electronic transition, the shorter the wavelength of light absorbed will be because it just so happens that energy and wavelength or lambda are inversely proportional. So as one increases the other decreases, so let's consider our different ligands. We have co three and six three minus and we also have C oops co F 63 minus. Now, the complex with cyanide appears to be orange and the one with fluoride appears to be green. And if we recall for a second, the visible light spectrum or Roy G biv, so to speak, red is going to have the higher wavelength whereas violet is going to have the lowest wavelength. So as we can see the wavelength of the color orange is greater than the wavelength for the color green. So we have to recall also that the appearance of a given compound is dependent on what color is reflected, not absorbed, right. So because orange is the color that's reflected, that means that the wavelength absorbed is going to be shorter because the ligand that contains cyanide must have absorbed the complementary color of orange, which had a shorter wavelength because recall that the complementary color of orange is blue. So that means that the ligand that contains cyanide has absorbed blue light and therefore reflected the complementary color which is orange. So therefore, the lambda absorbed is going to be shorter for cyanide than it is for fluoride. This means that our answer, if I scroll up one more time is going to be option C in the multiple choice, right, the crystal field splitting of cocn 63 minus is larger than the crystal field splitting of cof 63 minus cyanide is a strong field ligand while fluoride is a weak field ligand. And the reason why the crystal field splitting energy of the ligand containing cyanide is larger is because the wavelength absorbed is smaller. And with that being said, thank you so very much for watching. And I hope you found this helpful.