In \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3},\) the \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) ion absorbs visible light in the blue-violet range, and the compound is yellow- orange. In \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{3}\), the \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) ion absorbs visible light in the red range, and the compound is blue-gray. Explain these differences in light absorbed and compound color.

Color absorption in transition metal complexes is a result of the interaction between light and the electrons in the d-orbitals of the metal ion. When light hits these complexes, certain wavelengths are absorbed, promoting electrons from lower energy d-orbitals to higher energy d-orbitals. This process is known as d-d transitions. The specific wavelength that is absorbed depends on the difference in energy between these orbitals, which is influenced by the ligands surrounding the metal ion.

The term 'visible light' refers to the range of electromagnetic radiation that can be detected by the human eye, spanning wavelengths from about 400 to 700 nm. For example, in the complex \(\begin{bmatrix}Cr(NH_3)_6\begin{bmatrix} ^{3+}\begin{bmatrix}\right)\right\right\), blue-violet light is absorbed, which corresponds to higher energy. Meanwhile, in \(\begin{bmatrix}Cr(H_2O)_6\begin{bmatrix} ^{3+}\right)\right\), red light is absorbed, corresponding to lower energy.

This absorption of specific wavelengths directly influences the color we perceive, due to the phenomenon of complementary colors.

Complementary colors are pairs of colors that, when combined, cancel each other out. This means they produce a grayscale color like white or black. In the context of light absorption in complexes, the color we see is the complementary color of the light absorbed. For instance, if a complex absorbs blue-violet light, the color we see is yellow-orange.

To find the complementary color, one must look at a color wheel where opposite colors are complementary. For \(\begin{bmatrix}Cr(NH_3)_6\begin{bmatrix} ^{3+}\right)\right\), since it absorbs blue-violet light, its complementary color is yellow-orange, making the compound appear yellow-orange. Conversely, for \(\begin{bmatrix}Cr(H_2O)_6\begin{bmatrix} ^{3+}\right)\right\), absorbing red light means the complementary color is blue-gray, making the compound appear blue-gray.

Understanding complementary colors helps to predict and explain the colors observed in different chemical compounds.

The strength of the field created by ligands around a metal ion significantly influences the color absorption of metal complexes. Ligand Field Strength (also known as Ligand Field Splitting) refers to the difference in energy between the d-orbitals of the metal ion caused by the presence of ligands.

The ability of a ligand to split the d-orbital energy levels of a metal ion is influenced by the nature of the ligand itself. Strong field ligands, such as NH3 (ammonia), cause a large energy splitting, resulting in the absorption of light at higher energy (shorter wavelengths, like blue-violet). On the other hand, weaker field ligands, such as H2O (water), cause smaller energy splitting, resulting in the absorption of light at lower energy (longer wavelengths, like red).

In summary, the field strength of ligands is a crucial factor in determining the specific light wavelength absorbed, and thus, the observed color of the metal complex.

Complex ions are formed when a central metal ion is surrounded by molecules or ions called ligands. These ligands can either be neutral molecules like water and ammonia or ions like chloride or cyanide.

The nature of these ligands significantly affects the properties of the complex ion, including its color. For instance, in the complexes \(\begin{bmatrix}Cr(NH_3)_6\begin{bmatrix} ^{3+}\right)\right\) and \(\begin{bmatrix}Cr(H_2O)_6\begin{bmatrix} ^{3+}\right)\right\), NH3 and H2O act as ligands. The type of ligands and their arrangement around the central metal ion lead to different energy splittings in the d-orbitals, directly influencing which wavelengths of light are absorbed.

Complex ions are a fundamental concept in understanding the chemistry of transition metals and their interactions with light. By studying these ions, one can predict and explain a wide range of chemical behaviors and properties, especially related to color and spectroscopy.