\(\mathrm{CoCl}_{4}^{2-}\) forms a tetrahedral complex ion and \(\mathrm{Co}(\mathrm{CN})_{6}^{3-}\) forms an octahedral complex ion. What is wrong about the following statements concerning each complex ion and the \(d\) orbital splitting diagrams? a. \(\mathrm{CoCl}_{4}^{2-}\) is an example of a strong-field case having two unpaired electrons. b. Because \(\mathrm{CN}^{-}\) is a weak-field ligand, \(\mathrm{Co}(\mathrm{CN})_{6}^{3-}\) will be a low-spin case having four unpaired electrons.

First, let's determine the oxidation state of cobalt in CoCl4^{2-}: \[\mathrm{Co} + 4(\mathrm{Cl}) = -2 \rightarrow \mathrm{Co} = \text{+2}\] The d electron configuration of Co(II) is d^7. In a tetrahedral complex, the d orbitals are split into two groups \(e\) (d_xy, d_xz, d_yz) and \(t_2\) (d_z^2, d_x^2 - d_y^2). Tetrahedral complexes don't cause significant splitting, so they will always be high-spin. In this case, three orbitals are at a lower energy level and two orbitals are at a higher energy level. The filling will be as follows, considering that each electron will be unpaired before pairing starts: ↓, ↓, ↓, ↑, ↑. So, CoCl4^{2-} is actually a high-spin case having three unpaired electrons, not a strong-field case having two unpaired electrons. Therefore, statement a is incorrect.

We start by determining the oxidation state of cobalt in Co(CN)6^{3-}: \[\mathrm{Co} + 6(\mathrm{CN}) = -3 \rightarrow \mathrm{Co} = \text{+3}\] The d electron configuration of Co(III) is d^6. In an octahedral complex, the d orbitals are split into two groups \(t_{2g}\) (d_xy, d_xz, d_yz) and \(e_g\) (d_z^2, d_x^2 - d_y^2). The CN^{-} ligand is actually a strong-field ligand, causing a larger splitting between the \(t_{2g}\) and \(e_g\) orbitals. This results in a low-spin complex, as the electrons will prefer to pair up in the \(t_{2g}\) orbitals before occupying the higher \(e_g\) orbitals. The electron filling for Co(CN)6^{3-} will be ↓↓, ↓↓, ↓↑, ↑, ↑ which results in only one unpaired electron. Statement b is incorrect because CN^{-} is a strong-field ligand, and Co(CN)6^{3-} is a low-spin case with one unpaired electron.