Which of the following ions is(are) expected to form colored octahedral aqueous complex ions? a. \(Z n^{2+}\) b. \(C u^{2+}\) c. \(M n^{3+}\) d. \(T i^{4+}\)

To determine whether a given ion has a partially filled d-orbital, we need to know its electronic configuration. For this, we will first find the atomic numbers and electronic configurations of the neutral atoms of the given elements and then remove appropriate electrons to obtain the configuration of the ions. a. \(Zn^{2+}\): Zn has an atomic number of 30. The electronic configuration of Zn is \([Ar]3d^{10}4s^2\). When Zn loses 2 electrons to form the \(Zn^{2+}\) ion, its configuration becomes \([Ar]3d^{10}\). b. \(Cu^{2+}\): Cu has an atomic number of 29. The electronic configuration of Cu is \([Ar]3d^{10}4s^1\). When Cu loses 2 electrons to form the \(Cu^{2+}\) ion, its configuration is \([Ar]3d^9\). c. \(Mn^{3+}\): Mn has an atomic number of 25. The electronic configuration of Mn is \([Ar]3d^5 4s^2\). When Mn loses 3 electrons to form the \(Mn^{3+}\) ion, its configuration becomes \([Ar]3d^4\). d. \(Ti^{4+}\): Ti has an atomic number of 22. The electronic configuration of Ti is \([Ar]3d^2 4s^2\). When Ti loses 4 electrons to form the \(Ti^{4+}\) ion, its configuration is \([Ar]3d^0\).

Now, we will check which of the ions have partially filled d-orbitals (i.e., having d-electrons but not completely filled, which is 10 electrons). a. \(Zn^{2+}\): The configuration of \(Zn^{2+}\) is \([Ar]3d^{10}\), which has no partially filled d-orbitals, so it is not expected to form colored octahedral aqueous complex ions. b. \(Cu^{2+}\): The configuration of \(Cu^{2+}\) is \([Ar]3d^9\), which has partially filled 3d-orbitals, so it is expected to form colored octahedral aqueous complex ions. c. \(Mn^{3+}\): The configuration of \(Mn^{3+}\) is \([Ar]3d^4\), which has partially filled 3d-orbitals, so it is expected to form colored octahedral aqueous complex ions. d. \(Ti^{4+}\): The configuration of \(Ti^{4+}\) is \([Ar]3d^0\), which has no partially filled d-orbitals, so it is not expected to form colored octahedral aqueous complex ions.

Based on our analysis, the ions expected to form colored octahedral aqueous complex ions are: - \(Cu^{2+}\) (b) - \(Mn^{3+}\) (c) Thus, the correct answer is: b and c.