The complex ion \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) has an absorption maximum at around \(800 \mathrm{nm} .\) When four ammonias replace water, \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+},\) the absorption maximum shifts to around \(600 \mathrm{nm} .\) What do these results signify in terms of the relative field splittings of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) ? Explain.

In coordination chemistry and ligand field theory, field splitting refers to the splitting of degenerate energy levels of a metal ion in the presence of ligands. The energy gap between the higher and lower energy levels correlates to the wavelength of light that can be absorbed by the complex ion. Larger field splitting means larger energy difference, resulting in the absorption of shorter wavelengths (higher energy).

We are given the absorption maximum wavelengths for the two complex ions: - \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) absorbs light at around \(800 \mathrm{nm}\) - \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+}\) absorbs light at around \(600 \mathrm{nm}\) Since the absorption maximum wavelength of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+}\) (600 nm) is shorter than that of \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) (800 nm), we can infer that the field splitting for the complex ion with ammonia ligands is larger.

We have established that the field splitting for \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+}\) is larger than that for \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\). From this, we can conclude that ammonia ligands (\(\mathrm{NH}_{3}\)) cause a larger field splitting than water ligands (\(\mathrm{H}_{2} \mathrm{O}\)). In summary, the results signify that the field splitting caused by \(\mathrm{NH}_{3}\) is larger than that caused by \(\mathrm{H}_{2} \mathrm{O}\). This is indicated by the shorter absorption maximum wavelength of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}^{2+}\) compared to \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\).