Tell how many diastereoisomers are possible for each of the following complexes, and draw their structures. 
(c) [Cu(H₂O)₄Cl₂]⁺
(d) Ru(NH₃)₃I₃

Verified step by step guidance

1. <strong>Step 1:</strong> Understand the concept of diastereoisomers.</p><p>Diastereoisomers are stereoisomers that are not mirror images of each other. In coordination complexes, they arise when there are multiple chiral centers or when the ligands can be arranged in different spatial configurations.
2. <strong>Step 2:</strong> Analyze the complex [Cu(H₂O)₄Cl₂]⁺.</p><p>This complex has a coordination number of 6, typically forming an octahedral geometry. The ligands are four water molecules and two chloride ions. Consider the possible arrangements of these ligands around the central copper ion.
3. <strong>Step 3:</strong> Determine the possible diastereoisomers for [Cu(H₂O)₄Cl₂]⁺.</p><p>In an octahedral complex with two identical ligands (Cl^-), the ligands can be arranged in either a cis or trans configuration. The cis configuration has the two chloride ions adjacent to each other, while the trans configuration has them opposite each other.
4. <strong>Step 4:</strong> Analyze the complex Ru(NH₃)₃I₃.</p><p>This complex also has a coordination number of 6, suggesting an octahedral geometry. The ligands are three ammonia molecules and three iodide ions. Consider the possible spatial arrangements of these ligands.
5. <strong>Step 5:</strong> Determine the possible diastereoisomers for Ru(NH₃)₃I₃.</p><p>With three identical ligands (NH₃) and three identical ligands (I^-), the complex can form facial (fac) and meridional (mer) isomers. In the fac isomer, the three identical ligands are adjacent, forming a face of the octahedron. In the mer isomer, the three identical ligands form a meridian, spanning the octahedron.

Key Concepts

Diastereoisomers

Diastereoisomers are a type of stereoisomer that are not mirror images of each other. They occur in molecules with multiple chiral centers or in coordination complexes where different arrangements of ligands can lead to distinct spatial configurations. Understanding diastereoisomers is crucial for determining the number of possible isomers for a given complex.

Coordination Complexes

Coordination complexes consist of a central metal atom bonded to surrounding ligands, which can be neutral molecules or ions. The geometry of these complexes, such as octahedral or tetrahedral arrangements, influences the types of isomers that can form. Recognizing the coordination number and geometry is essential for predicting the number of diastereoisomers.

Ligand Types and Their Influence

Ligands can be classified as monodentate, bidentate, or polydentate based on the number of donor atoms they use to bond to the metal center. The nature and arrangement of these ligands significantly affect the stereochemistry of the complex. For example, the presence of bidentate ligands can lead to more complex isomerism, including diastereoisomers.