The complex \( [\text{Co(en)}_2\text{Cl}_2]^+ \) involves a coordination compound with cobalt(III) at the center, where \( \text{en} \) is ethylenediamine, a bidentate ligand, and \( \text{Cl}^- \) is a monodentate ligand. Since ethylenediamine is bidentate, it can form chelate rings, and the position of the chloride ions relative to the chelate rings gives rise to stereoisomers.
The number of stereoisomers can be determined based on the possible geometric arrangements of the chloride ions and the ethylenediamine ligands. For a complex like \( [\text{Co(en)}_2\text{Cl}_2]^+ \), there are two possible isomers:
Cis-isomer : Both chloride ions are adjacent to each other.
Trans-isomer : Chloride ions are opposite each other. Additionally, since the two ethylenediamine ligands can occupy two positions (cis and trans), this leads to three stereoisomers in total.
Thus, the complex exhibits 3 stereoisomers.
The correct option is (A) : 3
The complex \([Co(en)_2Cl_2]^+\) contains two types of ligands: ethylenediamine (en) and chloride ions. Ethylenediamine is a bidentate ligand, and when two such ligands coordinate with the central cobalt ion, they can form a chelate ring. This leads to different possible stereoisomers based on the spatial arrangement of the ligands.
For this complex, the possible stereoisomers are:
1. Cis isomer: The two chloride ions are adjacent to each other.
2. Trans isomer: The two chloride ions are opposite to each other.
3. Optically active isomer: The cis form can have non-superimposable mirror images, making it optically active.
Thus, \([Co(en)_2Cl_2]^+\) exhibits 3 stereoisomers: one trans isomer, one cis isomer, and the optically active cis isomer.\\
Thus, the correct number of stereoisomers is 3.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).