Coordination number of Cr is six. A complex with C₂O₄²⁻, en and superoxide O₂⁻ will be in the ratio to make complex [Cr(C₂O₄)ₓ(en)ᵧ(O₂)𝓏]⁻

• x = 1, y = 1, z = 1
• x = 1, y = 1, z = 2
• x = 1, y = 2, z = 2
• x = 2, y = 1, z = 1

The coordination chemistry of chromium (Cr) is quite fascinating, especially when we consider its ability to form complexes with various ligands. In your question, you're looking at a chromium complex with a coordination number of six, which is typical for Cr(III) complexes. The ligands involved are oxalate (C₂O₄²⁻), ethylenediamine (en), and superoxide (O₂⁻). Let's break down how to determine the possible ratios of these ligands in the complex [Cr(C₂O₄)ₓ(en)ᵧ(O₂)𝓏]⁻.

Understanding Coordination Numbers and Ligands

Coordination number refers to the number of ligand atoms that are bonded to a central metal atom in a complex. For chromium, particularly in the +3 oxidation state, a coordination number of six is common. This means that a total of six donor atoms from ligands can coordinate to the chromium ion.

Analyzing the Ligands

Each of the ligands you mentioned has a different number of donor atoms:

• Oxalate (C₂O₄²⁻): This is a bidentate ligand, meaning it can donate two pairs of electrons (or two donor atoms) to the metal center.
• Ethylenediamine (en): This is also a bidentate ligand, contributing two donor atoms as well.
• Superoxide (O₂⁻): This is a monodentate ligand, contributing one donor atom.

Formulating the Complex

Given that the total coordination number must equal six, we can set up an equation based on the contributions from each ligand:

2x (from C₂O₄²⁻) + 2y (from en) + z (from O₂⁻) = 6

Now, let's explore the possible combinations of x, y, and z that satisfy this equation.

Exploring the Ratios

We can analyze the options provided:

• x = 1, y = 1, z = 1: This gives us 2(1) + 2(1) + 1 = 5, which does not satisfy the coordination number of six.
• x = 1, y = 1, z = 2: This results in 2(1) + 2(1) + 2 = 6, which is valid.
• x = 1, y = 2, z = 2: Here, we have 2(1) + 2(2) + 2 = 8, exceeding the coordination number.
• x = 2, y = 1, z = 1: This gives us 2(2) + 2(1) + 1 = 7, also exceeding the coordination number.

Conclusion on Valid Combinations

From this analysis, the only valid combination that satisfies the coordination number of six is:

• x = 1, y = 1, z = 2

This means that in the complex [Cr(C₂O₄)₁(en)₁(O₂)₂]⁻, there is one oxalate ligand, one ethylenediamine ligand, and two superoxide ligands coordinating to the chromium ion. This combination effectively utilizes the available coordination sites while adhering to the rules of coordination chemistry.