Effective Atomic Number – Definition, Formula, Examples

“Effective Atomic Number,” or “EAN,” is a theoretical concept used to explain electronic structure and stability of coordination compounds. It is the total number of electrons that an atom or ion in a compound appears to have in theory, taking into account both the electrons it actually possesses as valence and the electrons that are donated by nearby ligands.

The concept of Effective Atomic Number (EAN) is essential in chemistry to understand complex coordination compounds and their behaviors. This article explores the concept of effective atomic number, including its application to coordination compounds, the development of the Sidgwick EAN Rule, and real-world examples.

What is Effective Atomic Number?

Effective atomic number is the idea of electron counting, in which ligands surrounding a central metal ion contribute electron pairs to form coordinate covalent bonds. The effective atomic number is obtained by adding this cumulative electron count to the central atom’s valence electrons.

Definition

Effective atomic number represents the total number of electrons around the nucleus of central metal atom in a metal coordination complex.

Effective Atomic Number in Coordination Compounds

A coordination compound is a type of chemical compound composed of a central metal ion or atom bonded to surrounding molecules or ions called ligands. Transition metals frequently form complexes with ligands through coordinate bonds in coordination compounds. The effective atomic number of a central metal ion in a coordination compound represents the total number of electrons contributed by both the metal ion and the surrounding ligands in the coordination sphere.

The effective atomic number is calculated by summing the number of valence electrons of the central metal ion and the electrons contributed by the surrounding ligands, taking into account their charges and the nature of their bonding interactions with the metal ion.

The atomic number of various transition metals that form metal complex are mentioned below:

• Scandium – 21
• Titanium – 22
• Vanadium – 23
• Chromium – 24
• Manganese – 25
• Iron – 26
• Cobalt – 27
• Nickel – 28
• Copper – 29
• Zinc – 30

Effective Atomic Number Rule

To understand the rules for effective atomic number we need to understand the following concepts:

Coordination Complexes

Coordination complexes are ions or molecules that are created when ligands are arranged in a specific way around a central metal atom. Usually, these ligands are ions or molecules that have one or more electron pairs that are available for bonding. One of the central metal atoms or ions in a coordination complex serves as the nucleus around which the ligands coordinate. The complex receives electrons from this central metal.

Ligands

To form coordinate bonds, ligands are molecules or ions that give electron pairs to the central metal atom or ion. The central metal atom/ion is surrounded by these ligands, which affect its characteristics.

Electron Counting

Counting the total electrons contributed by the surrounding ligands and the central metal atom/ion is necessary to determine the Effective Atomic Number.

Contributions from Central Metal Atom/Ion

The valence shell of the central metal atom/ion donates electrons to the coordination complex. The amount of electrons contributed depends on the metal’s position in the periodic table and degree of oxidation.

Contributions from Ligands

The coordination complex receives electron pairs from ligands. Each ligand contributes a different number of electrons based on the kind of bond it forms with the central metal atom or ion and its nature.

Method of Calculation

The electrons contributed by the surrounding ligands and the central metal atom/ion are added up to determine the Effective Atomic Number. Mathematically the calculation of effective atomic number is done by Sidgwick formula which is give below:

Sidgwick EAN Rule Formula

An easier way to determine the Effective Atomic Number of a coordination complex is by using the Sidgwick EAN Rule. According to this rule, effective atomic number is calculated by the following formula:

EAN = Atomic Number(Z) – Oxidation Number(X) + 2 × Coordination Number(Y)

Also, EAN is equal to the charge on the metal ion less the sum of the ligand-donated electrons and the valence electrons of the metal. We can express it as

EAN = VE + (L – X)

where

• VE represents valence electrons,
• L denotes ligand electrons,
• X signifies the charge on the metal ion.

This can be understood from an example given below:

Example: Find Effective atomic number of Copper in [Cu(NH₃)₄]²⁺

Solution:

From Sidgwick rule, EAN = Atomic Number(Z) – Oxidation Number(X) + 2 × Coordination Number(Y)

For Copper,

Atomic Number(Z) = 29

Oxidation Number(X) = +2

Since, four ligands are there, hence, Coordination Number(Y) = 4

Hence, EAN = Z – X + 2Y = 29 – 2 + 2 × 4 = 29 + 6 = 35

Significance of Effective Atomic Number

The significance of effective atomic number is mentioned below:

• Understanding the Effective Atomic Number helps in predicting the coordination geometry and stability of transition metal complexes.
• It makes it easier to interpret experimental results, including spectroscopic characteristics and magnetic susceptibility.
• The reactivity and catalytic behavior can be realized with the help of EAN.

Effective Atomic Number Conclusion

Effective Atomic Number stands as a fundamental concept in coordination chemistry, offering insights into the structure, stability, and reactivity of complex compounds. Its application extends across various fields, enriching our understanding of chemical phenomena.

EAN Rule Examples

Example 1: Find the effective atomic number of Fe in the complex [Fe(CN)₆]³⁺

Solution:

The valence electron count of iron (Fe) is 8 (d⁶s²).

There are six electrons total because each cyanide ion (CN⁻) contributes one electron.

The EAN formula is as follows: EAN = 8 + (6 – 3) = 11

Effective atomic number of Fe is 11

Example 2: Find Cobalt’s Effective Atomic Number (EAN) in [Co(NH₃)₆]³⁺

Solution:

Cobalt (Co) has nine valence electrons (d⁷S²)

Six electrons are present when one electron is donated by each ammonia

Using the formula for EAN, we get EAN = 9 + (6 – 3) = 12

Thus, 12 is the Effective Atomic Number of Cobalt is 12.

Effective Atomic Number FAQs

What is meaning of effective atomic number?

Effective atomic number means the total number of electrons donated by the surrounding ligands to the central metal atom in metal complex

What is Effective Atomic Number Formula?

The formula for effective atomic number is given as EAN = Z – X + 2Y where Z is atomic number, X is oxidation state and Y is Coordination Number

How does Effective Atomic Number play role in determining magnetic behavior of coordination molecules?

EAN is a useful tool for determining if a chemical is paramagnetic or diamagnetic by evaluating the presence of unpaired electrons.

What is the relationship between an effective atomic number and the coordination geometry of a complex?

Symmetric geometries like octahedral or tetrahedral geometries are preferable when the Effective Atomic Number (EAN) is greater.

Is there exception to Sidgwick EAN Rule?

Absolutely, there are examples where EAN predictions are not accurate due to high oxidation states or unusual ligand interactions.