Q. Among the complex ions,

Co(NH₂CH₂CH₂NH₂)₂Cl₂⁺, CrCl₂(C₂O₄)₃⁻, [Fe(H₂O)₄(OH)₂]⁺,

Fe(NH₃)₂(CN)₄, Co(NH₂-CH₂-NH₂)₂(NH₃)Cl²⁺, and Co(NH₃)₄(H₂O)Cl²⁺,

the number of complex ion(s) that show(s) cis-trans isomerism is:

We are tasked with determining the number of complex ions that exhibit cis-trans isomerism among the given compounds.

Step 1: Recall the conditions for cis-trans isomerism

Cis-trans isomerism is possible in:

1. Square planar complexes (when there are two identical ligands in a square planar geometry).
2. Octahedral complexes (when there are two or more identical ligands that can occupy adjacent or opposite positions).

Step 2: Analyze each complex ion

1. Co(NH₂CH₂CH₂NH₂)₂Cl₂⁺:
   • This is an octahedral complex with two bidentate ethylenediamine (NH₂CH₂CH₂NH₂) ligands and two chlorides.
   • Cis-trans isomerism is possible due to the positions of the two chloride ligands (either adjacent or opposite).
   • Exhibits cis-trans isomerism.
2. CrCl₂(C₂O₄)₃⁻:
   • This is a complex with oxalate (C₂O₄²⁻) as bidentate ligands and two chloride ions.
   • The geometry of the complex is octahedral, and cis-trans isomerism is possible due to the positions of the chloride ions.
   • Exhibits cis-trans isomerism.
3. [Fe(H₂O)₄(OH)₂]⁺:
   • This is an octahedral complex with four water molecules and two hydroxide ions.
   • The two hydroxide ions can occupy adjacent (cis) or opposite (trans) positions.
   • Exhibits cis-trans isomerism.
4. Fe(NH₃)₂(CN)₄:
   • This is a square planar complex with two ammonia (NH₃) and four cyanide (CN⁻) ligands.
   • Cis-trans isomerism is possible due to the positions of the two ammonia ligands.
   • Exhibits cis-trans isomerism.
5. Co(NH₂-CH₂-NH₂)₂(NH₃)Cl²⁺:
   • This is an octahedral complex with two bidentate ethylenediamine (NH₂-CH₂-NH₂) ligands, one ammonia, and one chloride ion.
   • Cis-trans isomerism is not possible because there is only one chloride ion, and all other ligands are fixed in their geometry.
   • Does not exhibit cis-trans isomerism.
6. Co(NH₃)₄(H₂O)Cl²⁺:
   • This is an octahedral complex with four ammonia ligands, one water, and one chloride ion.
   • Cis-trans isomerism is not possible because there is only one chloride ion, and the water ligand does not have enough symmetry to create cis-trans isomers.
   • Does not exhibit cis-trans isomerism.

Step 3: Count the complexes that show cis-trans isomerism

• Complexes that exhibit cis-trans isomerism:
  1. Co(NH₂CH₂CH₂NH₂)₂Cl₂⁺
  2. CrCl₂(C₂O₄)₃⁻
  3. [Fe(H₂O)₄(OH)₂]⁺
  4. Fe(NH₃)₂(CN)₄
• Total: 6 complexes.

Final Answer:

The number of complexes that show cis-trans isomerism is 6.