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 \(\mathrm{Fe}^{3+}\).

#tag_title# Statement analysis: Tetrahedral complexes and low-spin #tag_content# Tetrahedral complex ions are formed when four ligands are attached to a central metal ion. The term low-spin refers to the electron spin configuration in a coordination compound where electrons are paired in the lower energy orbitals before they begin to populate the higher energy orbitals. Tetrahedral complexes are associated with high-spin configurations due to the significantly lower crystal field splitting energy compared to the octahedral complexes. Since the statement b states that all tetrahedral complexes are low-spin and that's incorrect, b is false. #tag_title# Statement analysis: Molecular formula #tag_content# The name triaquatriamminechromium(III) sulfate consists of the following parts: - triaqua: indicating 3 water molecules (H₂O) - triammine: indicating 3 ammonia molecules (NH₃) - chromium(III): Chromium with a +3 oxidation state (Cr³⁺) - sulfate: sulfate ion (SO₄²⁻) Based on the name, the correct formula should be \(\left[\mathrm{Cr}\left(\mathrm{H}_{2}\mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]\left(\mathrm{SO}_{4}\right)_{2}\), because the overall charge balance must be conserved. So statement c is false. #tag_title# Statement analysis: Electron configuration #tag_content# Hafnium (Hf) has an atomic number of 72. The electron configuration of a neutral Hf atom is \([\mathrm{Xe}] 4 f^{14} 5 d^{2} 6 s^{2}\). In losing two electrons to form Hf²⁺, its electron configuration will become \([\mathrm{Xe}] 4 f^{14} 5 d^{1}\), which differs from the statement d that claims it to be \([\mathrm{Xe}] 4 f^{12} 6 s^{2}\). Therefore, statement d is false. #tag_title# Statement analysis: Hemoglobin and iron #tag_content# Hemoglobin is a protein responsible for transporting oxygen in the blood. It contains iron (Fe) in its heme group, coordinated to a porphyrin ring. The iron in hemoglobin is predominantly in the +2 oxidation state (Fe²⁺) when binding to oxygen, not in the +3 state (Fe³⁺) as stated in statement e. Therefore, statement e is false. #Short_Answer# All given statements (a, b, c, d, and e) are false.