Which of the following statement(s) is(are) true? a. The coordination number of a metal ion in an octahedral complex ion is \(8 .\) b. All tetrahedral complex ions are low-spin. c. The formula for triaquatriamminechromium(III) sulfate is \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_ 3}\) d. The electron configuration of \(\mathrm{Hf}^{2+}\) is \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\) e. Hemoglobin contains \(\mathrm{Fe}^{3+}\).

The coordination number refers to the number of ligands attached to a central metal ion in a coordination complex. Octahedral complexes have six ligand atoms that surround the metal ion, and therefore, their coordination number is 6. The given statement a is false because the coordination number of a metal ion in an octahedral complex ion is not 8 but 6.

Tetrahedral complex ions have four ligands surrounding a central metal ion. Low-spin complexes are formed when electrons preferentially enter the low-energy orbitals before pairing up. Tetrahedral complexes do not exhibit the "splitting of d orbitals" phenomenon, as is the case with octahedral and square planar complexes. Because there is no splitting of d orbitals, these complexes have only one possible arrangement for the d-electron configuration. By definition, this makes all tetrahedral complex ions low-spin complexes. Hence, statement b is true.

The formula for triaquatriamminechromium(III) sulfate should have three aqua ligands (\(\mathrm{H}_{2}\mathrm{O}\)) and three ammine ligands (\(\mathrm{NH}_{3}\)) attached to chromium(III). Also, there will be sulfate counterions to balance the charge. Let's analyze the given formula: \(\left[\mathrm{Cr}\left(\mathrm{H}_{2}\mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]_{2}\left(\mathrm{SO}_{4}\right)_{3}\) The formula has the correct chromium(III) complex with three aqua and three ammine ligands. The charge on the chromium(III) complex ion is \(3+\) (as there are three positive charges from the chromium ion). Since there are two complex ions, the total positive charge is \(2\times3=6+\). The charge on sulfate ions is \(2-\), and there are three of them, resulting in a total negative charge of \(2\times3=6-\). Balance in charge makes the given formula correct. Therefore, statement c is true.

To determine the electron configuration of \(\mathrm{Hf}^{2+}\), first, find the electron configuration for the neutral Hf atom and then remove two electrons. The neutral Hf atom has 72 electrons, and its configuration is \([\mathrm{Xe}] 4 f^{14} 5 d^{2} 6 s^{2}\). By removing two electrons, we get the electron configuration of \(\mathrm{Hf}^{2+}\), which is \([\mathrm{Xe}] 4 f^{14} 5 d^{1} 6 s^{1}\). Statement d is false because the given electron configuration (\([\mathrm{Xe}] 4 f^{12} 6 s^{2}\)) does not match the actual electron configuration we determined for \(\mathrm{Hf}^{2+}\).

Hemoglobin is a protein responsible for transport of oxygen in blood cells and contains a heme group with an iron ion. In deoxygenated hemoglobin, the iron ion has the +2 oxidation state and is coordinated to the nitrogen atom of the imidazole side chain of histidine. When hemoglobin binds to oxygen, the Fe(II) is partially oxidized to Fe(III), but the overall charge of the iron ion remains +2 due to charge sharing between the iron and oxygen. Therefore, statement e is false because hemoglobin does not contain \(\mathrm{Fe}^{3+}\), but instead has \(\mathrm{Fe}^{2+}\). Final verdict: The true statement(s) among the given options are: (b) and (c).