WEB Indicate whether each of the following is true or false. If the statement is false, correct it. (a) The coordination number of iron(III) in \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\) is 5 . (b) \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) is expected to absorb at a longer wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{ }^{2+}\)

The coordination number of a metal ion in a complex is determined by the number of ligand donor atoms directly bonded to it. In the complex \(\mathrm{Fe}\left(\mathrm{NH}_{3}\right)_{4}(\mathrm{en})^{3+}\), there are 4 ammonia ligands (\(\mathrm{NH}_{3}\)) and 1 ethylenediamine ligand (en). Each ammonia ligand provides 1 donor atom (N), while the ethylenediamine ligand (en) provides 2 donor atoms (2 N). To find the coordination number, sum up the number of donor atoms provided by all ligands: \(\text{Coordination number} = 4(\text{from } \mathrm{NH}_{3}s) + 2(\text{from } \mathrm{en}) = 6\) Thus, the statement is false, since the actual coordination number of iron(III) ion in the complex is 6.

To determine which complex has a longer absorption wavelength, we need to understand crystal field theory. The magnitude of the crystal field splitting parameter, \(\Delta_{o}\), affects the wavelength of light absorbed in a d-d transition. Complexes with stronger ligands (ligands that cause a larger splitting) will have a higher \(\Delta_{o}\) and will, therefore, absorb light at a lower wavelength according to the approximate relation \(\Delta_{o} = h\frac{c}{\lambda}\). Hence, the complex with a larger \(\Delta_{o}\) will have a shorter wavelength of absorption. The spectrochemical series orders ligands depending on their ability to split the d orbitals of a transition metal. Based on the spectrochemical series, the cyanide ligand (CN-) is a stronger field ligand compared to ammonia (NH3). Thus, the \(\Delta_{o}\) for \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) will be larger than that of \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{ }^{2+}\), resulting in the \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) complex absorbing light at a shorter wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{ }^{2+}\). The statement is false. The correct statement is: \(\mathrm{Ni}(\mathrm{CN})_{6}^{4-}\) is expected to absorb at a shorter wavelength than \(\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}{ }^{2+}\).