In acidic aqueous solution, the complex trans-[Co(en)₂Cl₁]²⁺(aq) undergoes the following substitution reaction:
trans-[Co(en)₂Cl₁]⁺(aq) + H₂O(l) → trans-[Co(en)₂(H₂O)Cl]²⁺(aq) + Cl^–(aq)
The reaction is first order in trans-[Co(en)₂Cl₂]⁺(aq), and the rate constant at 25°C is 3.2×10^–5 s^–1.
e. Draw a crystal field energy-level diagram for trans-[Co(en)₂Cl₂]⁺ that takes account of the fact that Cl^– is a weaker-field ligand than ethylenediamine.

검증된 단계별 안내

Identify the metal center and its oxidation state in the complex trans-[Co(en)_2Cl_2]^+.

Recognize that Cl^- is a weaker-field ligand compared to ethylenediamine (en), which affects the splitting of the d-orbitals.

Draw the octahedral crystal field splitting diagram, noting that the presence of weaker-field ligands like Cl^- results in a smaller splitting energy (Δ).

Label the d-orbitals in the diagram as t_2g (lower energy) and e_g (higher energy) levels, considering the octahedral geometry.

Populate the d-orbitals with electrons according to the electron configuration of Co^3+ (d^6), considering the weak-field nature of Cl^- which may lead to high-spin configuration.

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주요 개념

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Crystal Field Theory

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes by considering the effect of ligands on the d-orbitals of the metal ion. In an octahedral field, the d-orbitals split into two energy levels: the lower-energy t2g and the higher-energy eg orbitals. The extent of this splitting depends on the nature of the ligands, with stronger field ligands causing greater splitting. Understanding this concept is crucial for predicting the electronic transitions and colors of complexes.

Ligand Field Strength

Ligand field strength refers to the ability of a ligand to split the d-orbitals of a central metal ion in a coordination complex. Ligands are classified as strong or weak field based on their ability to cause d-orbital splitting. Ethylenediamine (en) is a strong field ligand, leading to significant splitting, while chloride (Cl-) is a weak field ligand, resulting in less splitting. This concept is essential for understanding the stability and reactivity of metal complexes.

First-Order Reaction Kinetics

First-order reaction kinetics describes a reaction where the rate is directly proportional to the concentration of one reactant. In this case, the substitution reaction involving trans-[Co(en)2Cl2]+ is first-order with respect to the complex, meaning that as its concentration decreases, the rate of reaction also decreases. The rate constant, given as 3.2×10–5 s–1, allows for the calculation of reaction rates and is fundamental for understanding the dynamics of the substitution process.