Effective Atomic Number (EAN)
Effective Atomic Number (EAN)
The Effective Atomic Number (EAN) concept is a theoretical construct used in coordination chemistry to predict the stability of metal complexes. It is based on the assumption that a stable complex has an EAN equal to the atomic number of the nearest noble gas to the metal in the periodic table. This concept was originally proposed by the Danish chemist Niels Bjerrum and later developed by the British chemist Sir Nevil Sidgwick.
Understanding EAN
The EAN of a metal in a complex is calculated by adding the number of its valence electrons to the number of electrons donated by the ligands (coordinating atoms or molecules). The idea is that metal complexes tend to be more stable when the central metal atom achieves an electron configuration similar to that of a noble gas.
The formula for calculating EAN is:
$$ \text{EAN} = Z + \text{No. of electrons donated by ligands} $$
where ( Z ) is the atomic number of the central metal atom.
Calculation of EAN
To calculate the EAN for a metal in a complex, follow these steps:
- Determine the atomic number of the metal.
- Count the number of electrons the metal has in its valence shell.
- Add the number of electrons donated by each ligand. For this, you need to know the nature of the ligand (whether it is a mono-, di-, or polydentate ligand) and its donating capacity.
Table of Differences and Important Points
| Feature | Atomic Number | Effective Atomic Number (EAN) |
|---|---|---|
| Definition | The number of protons in the nucleus of an atom. | The total number of protons and electrons that a central metal atom appears to have when forming a complex. |
| Purpose | Identifies the element and its position in the periodic table. | Predicts the stability of metal complexes. |
| Calculation | Fixed for each element. | Depends on the metal and the ligands in the complex. |
| Stability | Not directly related to the stability of atoms or ions. | A metal complex is considered stable if its EAN is equal to the atomic number of the nearest noble gas. |
Examples
Let's calculate the EAN for a few metal complexes:
Example 1: [Fe(CN)₆]⁴⁻
- Atomic number of Fe: ( Z = 26 )
- Fe is in the +2 oxidation state, so it has 24 valence electrons.
- Each CN⁻ ligand donates 2 electrons, and there are 6 ligands, so ( 6 \times 2 = 12 ) electrons are donated.
- EAN = 26 (atomic number) + 12 (donated electrons) = 38
The nearest noble gas to iron is krypton, with an atomic number of 36. The EAN of this complex is higher than that of krypton, suggesting it is a stable complex.
Example 2: [Co(NH₃)₆]³⁺
- Atomic number of Co: ( Z = 27 )
- Co is in the +3 oxidation state, so it has 24 valence electrons.
- Each NH₃ ligand donates 2 electrons, and there are 6 ligands, so ( 6 \times 2 = 12 ) electrons are donated.
- EAN = 27 (atomic number) + 12 (donated electrons) = 39
The nearest noble gas to cobalt is krypton, with an atomic number of 36. The EAN of this complex is higher than that of krypton, suggesting it is a stable complex.
Example 3: [Ni(CO)₄]
- Atomic number of Ni: ( Z = 28 )
- Ni is in the 0 oxidation state, so it has 28 valence electrons.
- Each CO ligand donates 2 electrons, and there are 4 ligands, so ( 4 \times 2 = 8 ) electrons are donated.
- EAN = 28 (atomic number) + 8 (donated electrons) = 36
The nearest noble gas to nickel is krypton, with an atomic number of 36. The EAN of this complex is equal to that of krypton, suggesting it is a stable complex.
Conclusion
The EAN rule is a useful guideline for predicting the stability of metal complexes, although it has its limitations. It works well for many complexes, especially those of the first-row transition metals. However, it does not take into account factors such as the 18-electron rule, ligand field stabilization, or the Jahn-Teller effect, which can also influence the stability of metal complexes. Despite these limitations, EAN remains a valuable tool in the chemist's arsenal for understanding coordination compounds.