Understanding Color and Light Absorption in Coordination Complexes

Coordination complexes often exhibit color because they absorb light in the visible region of the electromagnetic spectrum. This absorption is typically due to electronic transitions within the metal ion, specifically d-d transitions. When a coordination complex absorbs light of a particular wavelength (\(\lambda\)), the light of the complementary color is transmitted or reflected, which is what we perceive as the color of the complex.

The energy (\(E\)) of the absorbed light corresponds to the energy difference between the d orbitals, which are split in the presence of ligands. In octahedral complexes like the ones listed, the d orbitals split into two sets: the lower energy \(t_{2g}\) set and the higher energy \(e_g\) set. The energy difference between these sets is called the crystal field splitting energy (\(\Delta_o\)).

The relationship between the absorbed energy (\(E\)), Planck's constant (\(h\)), the speed of light (\(c\)), and the wavelength of absorbed light (\(\lambda\)) is given by the equation:

$$E = \frac{hc}{\lambda}$$

This equation shows that energy is inversely proportional to wavelength. Therefore, a larger crystal field splitting energy (\(\Delta_o\)) corresponds to the absorption of higher energy light, which means absorption at a shorter wavelength (\(\lambda\)).

Impact of Ligands on Crystal Field Splitting (\(\Delta_o\))

The magnitude of the crystal field splitting energy (\(\Delta_o\)) is highly dependent on the nature of the ligands surrounding the metal ion. Ligands are arranged in a series called the spectrochemical series, which orders them based on their ability to cause crystal field splitting. Strong field ligands cause a large splitting (\(\Delta_o\)), while weak field ligands cause a small splitting.

For the ligands present in the given complexes (\(\text{Cl}^-\), \(\text{H}_2\text{O}\), \(\text{NH}_3\), and \(\text{CN}^-\)), their relative positions in the spectrochemical series (from weak field to strong field) are:

\(\text{Cl}^- < \text{H}_2\text{O} < \text{NH}_3 < \text{CN}^-\)

Thus, complexes with stronger field ligands will have larger \(\Delta_o\) values and absorb shorter wavelengths of light compared to complexes with weaker field ligands.

Analyzing Complex Ions and Expected Absorption Wavelengths

Let's analyze each complex ion provided in List I and predict the relative strength of the ligand field, the magnitude of \(\Delta_o\), and consequently, the expected absorbed wavelength (\(\lambda\)). All complexes involve the \(\text{Co}\) metal ion, specifically \(\text{Co}^{2+}\) in complex A and \(\text{Co}^{3+}\) in complexes B, C, and D. For a given metal ion, the ligand field strength is the primary factor determining \(\Delta_o\).

• A. \([\text{CoCl}_3(\text{NH}_3)_5]^{2+}\): This complex contains \(\text{Cl}^-\) (weak field ligand) and \(\text{NH}_3\) (medium field ligand). The presence of chloride ions suggests a relatively weaker overall ligand field compared to complexes with only \(\text{NH}_3\) or \(\text{CN}^-\). We expect a relatively small \(\Delta_o\) and thus absorption at a relatively long wavelength.
• B. \([\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]^{3+}\): This complex contains \(\text{NH}_3\) (medium field) and \(\text{H}_2\text{O}\) (slightly weaker than \(\text{NH}_3\)). The overall ligand field strength will be slightly weaker than a complex with only \(\text{NH}_3\) due to the presence of \(\text{H}_2\text{O}\). We expect a moderate \(\Delta_o\) and absorption at a moderate wavelength.
• C. \([\text{Co}(\text{NH}_3)_6]^{3+}\): This complex contains only \(\text{NH}_3\) (medium field). This represents the splitting caused purely by \(\text{NH}_3\). We expect a moderate \(\Delta_o\) and absorption at a moderate wavelength, likely shorter than complex B due to the absence of the weaker \(\text{H}_2\text{O}\).
• D. \([\text{Co}(\text{CN})_6]^{3-}\): This complex contains only \(\text{CN}^-\) (very strong field ligand). This ligand causes a very large crystal field splitting (\(\Delta_o\)). We expect a large \(\Delta_o\) and thus absorption at a very short wavelength.

Based on the spectrochemical series (\(\text{Cl}^- < \text{H}_2\text{O} < \text{NH}_3 < \text{CN}^-\)) and considering the dominant ligands, we can order the complexes by increasing expected \(\Delta_o\) (and thus decreasing absorbed \(\lambda\)):

\([\text{CoCl}_3(\text{NH}_3)_5]^{2+}\) < \([\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]^{3+}\) < \([\text{Co}(\text{NH}_3)_6]^{3+}\) < \([\text{Co}(\text{CN})_6]^{3-}\)

Therefore, the order of absorbed wavelength (\(\lambda\)) from longest to shortest is:

\([\text{CoCl}_3(\text{NH}_3)_5]^{2+}\) > \([\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]^{3+}\) > \([\text{Co}(\text{NH}_3)_6]^{3+}\) > \([\text{Co}(\text{CN})_6]^{3-}\)

Matching Complex Ions with Wavelengths

Now let's look at the given wavelengths in List II and order them from longest to shortest:

1. 535 nm
2. 500 nm
3. 475 nm
4. 310 nm

Based on our expected order of absorbed wavelengths for the complex ions (A > B > C > D), we can match them to the ordered wavelengths:

• Complex A (\([\text{CoCl}_3(\text{NH}_3)_5]^{2+}\)) is expected to absorb the longest wavelength. The longest wavelength in List II is 535 nm (II). So, A matches II.
• Complex B (\([\text{Co}(\text{NH}_3)_5(\text{H}_2\text{O})]^{3+}\)) is expected to absorb the next longest wavelength. The next longest is 500 nm (I). So, B matches I.
• Complex C (\([\text{Co}(\text{NH}_3)_6]^{3+}\)) is expected to absorb the next shortest wavelength. The next shortest is 475 nm (III). So, C matches III.
• Complex D (\([\text{Co}(\text{CN})_6]^{3-}\)) is expected to absorb the shortest wavelength. The shortest is 310 nm (IV). So, D matches IV.

The resulting matching is A-II, B-I, C-III, D-IV.

Final Matching Conclusion

Based on the analysis of the complex ions and the spectrochemical series, the correct matching is A-II, B-I, C-III, D-IV. This corresponds to one of the provided options.

Revision Table: Ligand Field Strength and Absorption

Additional Information: Spectrochemical Series and Complex Color

The spectrochemical series is an experimentally determined list that ranks ligands based on the magnitude of \(\Delta_o\) they produce with a given metal ion. A portion of the common spectrochemical series is:

\(\text{I}^- < \text{Br}^- < \text{SCN}^- < \text{Cl}^- < \text{S}^{2-} < \text{F}^- < \text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{H}_2\text{O} < \text{NCS}^- < \text{EDTA}^{4-} < \text{NH}_3 < \text{en} < \text{NO}_2^- < \text{CN}^- < \text{CO}\)

Note that the specific order can vary slightly depending on the metal ion and its oxidation state, but the general trend is consistent. Ligands on the left are weak field, and those on the right are strong field.

The color observed for a complex is the complementary color to the color of light absorbed. For example, if a complex absorbs strongly in the blue region (around 450-495 nm), it will appear orange (the complementary color). If it absorbs in the green region (around 495-570 nm), it will appear red-purple.

In this problem, \([\text{Co}(\text{CN})_6]^{3-}\) absorbs at 310 nm, which is in the UV region (not visible light). This means it wouldn't absorb visible light and might appear colorless or white, or its observed color would be due to other transitions like ligand-to-metal charge transfer (LMCT) or metal-to-ligand charge transfer (MLCT) if those occur in the visible region. However, for this type of matching question based on simple d-d transitions and the spectrochemical series, we focus on the relationship between \(\Delta_o\) and the *potential* absorption wavelength for d-d transitions, even if it falls outside the easily visible range for strong-field ligands.