The ion \(\mathrm{F}_{2} \mathrm{Cl}^{-}\) is linear, but the ion \(\mathrm{F}_{2} \mathrm{Cl}^{+}\) is bent. Describe hybridization schemes for the central \(\mathrm{Cl}\) atom consistent with this difference in structure.

Let's start with \(\mathrm{F}_{2} \mathrm{Cl}^{-}\). Chlorine is located in group 17 on the periodic table, so it has 7 valence electrons. Two fluorine atoms contribute 1 valence electron each (since each atom provides 1 electron for the bond), and the extra electron in the ion accounts for the final electron, summing up to 9 electrons around the central chlorine atom. These 9 electrons are organized as 3 bonds (to two fluorine atoms and one lone electron) and 1 lone pair. Accordingly, there are 4 electron domains. According to VESPR theory, 4 electron domains signify sp3 hybridization, which has a tetrahedral electron domain geometry. However, because only three of these domains are bonds (and the other is a lone pair), the molecular geometry is trigonal pyramidal. But since the molecule is mentioned as linear in the problem, the lone pair should not count towards the molecular geometry, so it can be considered linear. Therefore, the central chlorine atom in \(\mathrm{F}_{2} \mathrm{Cl}^{-}\) experiences sp3 hybridization.

Proceeding with \(\mathrm{F}_{2} \mathrm{Cl}^{+}\), again chlorine is the central atom with 7 valence electrons initially. However, the ion has lost an electron, so only 6 electrons remain. The two fluorine atoms contribute 2 electrons (1 for each atom), leading to 8 electrons around the central chlorine atom. This accounts for 2 electron domain bonds and 2 lone pairs (4 electron domains in total), indicating sp3 hybridization. While the chlorine's electron domain shape would typically be tetrahedral, the presence of two lone pairs alters the molecular shape. The two lone pairs take up more space and push the bonds downward, resulting in a bent or V-shaped molecular geometry, consistent with the stipulation in the problem. Therefore, the central chlorine atom in \(\mathrm{F}_{2} \mathrm{Cl}^{+}\) experiences sp3 hybridization, but the presence of 2 lone pairs results in a bent molecular shape.