Molar Extinction Coefficient Explained

The molar extinction coefficient ($\epsilon$) is a measure of how strongly a chemical species absorbs light at a particular wavelength. It is related to the probability of an electronic transition occurring when light interacts with the substance. Higher values of $\epsilon$ indicate stronger absorption and often result in more intensely colored solutions.

Several factors influence the value of the molar extinction coefficient, including:

• The nature of the electronic transition (e.g., $\pi \rightarrow \pi^*$, d-d, charge transfer).
• The symmetry of the molecule or complex (e.g., Laporte selection rule).
• Spin selection rules.

Absorption Characteristics of Given Species

Let's examine the types of electronic transitions expected for each species:

• Chlorophyll: This is a large organic molecule with an extensive conjugated $\pi$ system (porphyrin ring). The absorption bands in the visible region are primarily due to strong $\pi \rightarrow \pi^*$ transitions. These transitions are generally very intense, leading to high molar extinction coefficients.
• [NiCl4]2−: This is a tetrahedral Ni(II) complex. Ni(II) is a d⁸ ion. In tetrahedral complexes, d-d transitions are formally Laporte forbidden (like in octahedral complexes) but the absence of a center of symmetry allows for significant mixing of d and p orbitals, relaxing the Laporte rule more effectively than vibronic coupling in octahedral complexes. This leads to relatively higher intensity d-d bands compared to typical octahedral complexes.
• [Cr(H2O)6]2+: This is an octahedral Cr(II) complex. Cr(II) is a d⁴ ion. The absorption bands in the visible region are due to d-d transitions. These transitions are Laporte forbidden but gain intensity through vibronic coupling. For d⁴, spin-allowed transitions are possible. Octahedral d-d transitions generally have lower $\epsilon$ values than tetrahedral d-d transitions or $\pi \rightarrow \pi^*$ transitions.
• [Mn(H2O)6]2+: This is an octahedral Mn(II) complex. Mn(II) is a d⁵ ion. In high-spin octahedral complexes, all d-d transitions are both Laporte forbidden and spin forbidden (since all d electrons are paired or unpaired with parallel spins in the ground state, and transitions involve changing spin multiplicity). Spin-forbidden transitions are very weak, resulting in very low molar extinction coefficients. This is why aqueous Mn(II) solutions are typically very pale pink or almost colorless.

Comparing Molar Extinction Coefficient Values

Based on the types of transitions and selection rules:

• $\pi \rightarrow \pi^*$ transitions (Chlorophyll) are the most intense.
• Tetrahedral d-d transitions ([NiCl₄]²⁻) are generally more intense than octahedral d-d transitions due to better relaxation of the Laporte rule.
• Octahedral d-d spin-allowed transitions ([Cr(H₂O)₆]²⁺) are weaker than tetrahedral d-d transitions.
• Octahedral d-d spin-forbidden transitions ([Mn(H₂O)₆]²⁺) are the weakest.

Therefore, the expected order of molar extinction coefficient values from highest to lowest is:

Chlorophyll > [NiCl₄]²⁻ > [Cr(H₂O)₆]²⁺ > [Mn(H₂O)₆]²⁺

Final Order

The correct order of molar extinction coefficient values for the visible absorption bands is:

\text{Chlorophyll} > \text{[NiCl}_4\text{]}^{2-} > \text{[Cr(H}_2\text{O)}_6\text{]}^{2+} > \text{[Mn(H}_2\text{O)}_6\text{]}^{2+}