Effective Atomic Number: Definition, Formula, Examples

Effective Atomic Number: Effective Atomic Number can be represented as EAN in chemistry. We know that the atomic number of an element represents the total number of electrons and protons present in an atom. Similarly, metal complexes have atomic numbers representing the total number of electrons present around the central metal atom, and it is known as an Effective Atomic Number. 

The EAN rule was coined by English chemist Nevil V. Sidgwick, who observed that in a number of metal complexes, the metal atom tends to surround itself with enough ligands that the resulting effective atomic number is numerically equal to the atomic number of the noble-gas element found in the same period as the metal. In this article, we will discuss the Effective Atomic Number rule, Effective Atomic Number in coordination compounds, Formula, Rule, Examples, etc. Continue reading to know more.

Explain Effective Atomic Number

Effective atomic number or EAN is a number that represents the sum of the total number of electrons surrounding the nucleus of an atom in a metal complex. The effective atomic number is abbreviated as Z_eff. It is composed of electrons of the metal atom and the bonding electrons from the surrounding electron-donating atoms and molecules.

The effective atomic number of a metal complex has two different aspects: 

1. It represents the effective nuclear charge of an atom and, 
2. It calculates the average atomic number for a compound or mixture of materials.

Effective Atomic Number Rule

In the \(1920\)s, N.V. Sidgwick recognized that the metal atom in a simple metal carbonyl, such as \(\left[ {{\text{Ni}}{{({\text{CO}})}_4}} \right]\), has the same valence electron count \((18)\) as the noble gas that terminates the long period to which the metal belongs. Sidgwick coined the term ‘inert gas rule’ to indicate stability, but it is now usually referred to as the \(18\)–electron rule or EAN Rule. Zeff of an atom represents it. It represents the number of protons that an electron in the element effectively ‘sees’ due to screening by the inner-shell electrons. Generally, the EAN of the central metal is numerically equal to the atomic number of the noble gas element found in the same period in which the central metal atom is located. The noble gases that are under consideration are \(36\) (Krypton), \(54\) (Xenon), and \(86\) (Radon).

Coordination Number & Geometry of Complexes

These inert gas elements belong to the \({{\text{3}}^{{\text{rd}}}}{\text{,}}\,{{\text{4}}^{{\text{th}}}}\), and \({{\text{5}}^{{\text{th}}}}\) periods respectively. As the \({{\text{3}}^{{\text{rd}}}}{\text{,}}\,{{\text{4}}^{{\text{th}}}}\), and \({{\text{5}}^{{\text{th}}}}\) periods of the Periodic Table mainly comprise transition elements, the central metal atom or ion that forms metal complexes is mainly a transition element.

The central metal atom mostly belongs to the \({\text{3d,}}\,{\text{4d}}\), and \({\text{5d}}\) series of the d-block elements.

Formula

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{C}}.{\text{N}} \times 2)\)

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)

\({\text{Z}}\) represents the atomic number of the central metal ion.

\({\text{X}}\) represents the oxidation number of the central metal ion.

\({\text{L}}\) represents the total number of ligands bound to the central metal atom.

\({\text{D}}\) represents the denticity of the ligand.

Significance of Effective Atomic Number

1. Effective atomic numbers help understand why electrons are weakly bound to the nucleus when located farther from it.
2. It explains the stability of coordination compounds.
3.  The EAN rule is more valid for non-classical complexes, especially carbonyl compounds; hence, this rule is used to determine the stability, oxidising and reducing character of carbonyl compounds.
   (1) The EAN rule is generally found to be invalid in most complexes, but in the case of metal carbonyls, this rule is found to be valid in all cases.
   (2) No ligand is found to act as a three electron donor.

Examples

1. Effective Atomic Number of \({\text{Fe}}\) in \({\text{Fe}}{({\text{CO}})_5}\)

The oxidation state of \({\text{Fe}}\) in \({\text{Fe(CO}}{{\text{)}}_{\text{5}}}{\text{,}}\,{\text{X=0}}\)

Atomic number of \({\text{Fe}}({\text{Z}}) = 26\)

Carbonyl \(\left( {{\text{CO}}} \right)\) is a monodentate ligand \(\left( {{\text{D=1}}} \right)\)

Number of ligands, \({\text{L=5}}\)

\({\text{EAN}} = \left( {{\text{Z}} – {\text{X}}}\right) + \left({{\text{L}} \times {\text{D}} \times 2} \right)\)

\({\text{EAN}} = (26 – 0) + (5 \times 1 \times 2) = 26 + 10 = 36\)

\(36\) is the electronic configuration of Krypton \(\left( {{\text{Kr}}} \right)\), hence, it obeys the EAN rule.

2. Effective Atomic Number of \({\text{Fe}}\) in \({{\text{K}}_{\text{3}}}\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{6}}}} \right]\)

In \({{\text{K}}_{\text{3}}}\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{6}}}}\right]\), the anionic part \({\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{6}}}} \right]^{{\text{3-}}}}\) forms the metal complex. Oxidation state of \({\text{Fe}}\):

\({\text{X}} + 6\left({{\text{C}}{{\text{N}}^ – }} \right) =  – 3\)

\({\text{X}} + 6\left({ – 1} \right) =  – 3\)

\({\text{X}} + \left({ – 6} \right) =  – 3\)

\(X=-3+6=3\)

Atomic number of \({\text{Fe}}({\text{Z}}) = 26\)

Cyanide \(\left({{\text{CN}}}\right)\) is a unidentate ligand \(\left({{\text{D}} = 1} \right)\)

Number of ligands, \({\text{L}} = 6\)

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)

\({\text{EAN}} = (26 – 3) + (6 \times 1 \times 2) = 23 + 12 = 35\)

As EAN is \(35\), \({{\text{K}}_{\text{3}}}\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{6}}}} \right]\) does not follow the EAN rule.

3. Effective Atomic Number of \({\text{Cr}}\) in \({\text{Cr}}{({\text{CO}})_6}\)

The oxidation state of \({\text{Cr}}\) in \(\operatorname{Cr} {({\text{CO}})_5},{\text{x}} = 0\)

Atomic number of \(\operatorname{Cr} ({\text{Z}}) = 24\)

Carbonyl \(\left( {{\text{CO}}} \right)\) is a monodentate ligand \(\left({{\text{D}} – 1} \right)\)

Number of ligands, \({\text{L}} = 6\)

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)

\({\text{EAN}} = (24 – 0) + (6 \times 1 \times 2) = 24 + 12 = 36\)

\(36\) is the electronic configuration of Krypton \(\left( {{\text{Kr}}} \right)\).

As EAN is \(36\), \(\operatorname{Cr} {({\text{CO}})_6}\) follows the EAN rule.

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4. Effective Atomic Number of \({\text{Co}}\) in \(\left[{{\text{Co}}{{\left({{\text{N}}{{\text{H}}_3}} \right)}_6}} \right]{\text{C}}{{\text{l}}_3}\)

In \(\left[{{\text{Co}}{{\left({{\text{N}}{{\text{H}}_3}} \right)}_6}} \right]{\text{C}}{{\text{l}}_3}\) the cationic part \({\left[ {{\text{Co}}{{\left( {{\text{N}}{{\text{H}}_3}} \right)}_6}} \right]^{3 + }}\) forms the metal complex.

Oxidation state of \({\text{Co}}\):

\({\text{X}} + 6\left({{\text{N}}{{\text{H}}_3}} \right) =  + 3\)

\({\text{X}} + 6(0) =  + 3\)

\({\text{X}} =  + 3\)

Atomic number of \({\text{Co (Z)=27}}\)

Ammonia \(\left( {{\text{N}}{{\text{H}}_{\text{3}}}} \right)\) is a monodentate ligand \(\left({{\text{D}} = 1} \right)\)

Number of ligands, \({\text{L}} = 6\)

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)

\({\text{EAN}} = (27 – 3) + (6 \times 1 \times 2) = 24 + 12 = 36\)

As EAN is \(36\), \(\left[{{\text{Co}}{{\left({{\text{N}}{{\text{H}}_3}} \right)}_6}} \right]{\text{C}}{{\text{l}}_3}\) follows the EAN rule.

5. Effective Atomic Number of \({\text{Co}}\) in \({\left[ {{\text{Co}}{{({\text{CO}})}_4}} \right]^{2 – }}\)

The oxidation state of \({\text{Co}}\) in \({\left[ {{\text{Co}}{{({\text{CO}})}_4}} \right]^{2 – }}\) is-

\({\text{X}} + 4({\text{CO}}) =  – 2\)

\({\text{X}} + 4({\text{-1}}) =  – 2\)

\({\text{X}} + ({\text{-4}}) =  – 2\)

\(X=-2+4=2\)

Atomic number of \({\text{Co (Z)=27}}\)

Carbonyl \(\left( {{\text{CO}}} \right)\) is a monodentate ligand \(\left({{\text{D}} = 1} \right)\)

Number of ligands, \({\text{L}} = 4\)

\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)

\({\text{EAN}} = (27 – 2) + (4 \times 1 \times 2) = 25 + 8 = 33\)

\(33\) is not the electronic configuration of Krypton \(\left({{\text{Kr}}} \right)\).

As EAN is \(33\), \(\operatorname{Cr} {({\text{CO}})_4}\) does not follow the EAN rule.

Summary

In this article, we learned the effective atomic number definition and rule that governs the stability of metal complexes and the method to calculate it. We also learned about its significance and its role in imparting stability to the metal complexes.

FAQs

We have provided some frequently asked questions about

Q.1. What is the effective atomic number of water?
Ans: The effective atomic number of water \(\left({{{\text{H}}_{\text{2}}}{\text{O}}} \right)\) is \(10\).
The total number of electrons in oxygen is \(8\).
The total number of electrons in hydrogen is \(1\).
Hence, the effective atomic number of water is \(8 +1 + 1 = 10\).

Q.2. What is EAN? Give an example.
Ans: The effective atomic number includes the electrons possessed by the central metal atom and the electrons donated by the surrounding ligands. Example- The effective atomic number of water \(\left({{{\text{H}}_{\text{2}}}{\text{O}}} \right)\) is \(10\).

Q.3. What is the atomic number of oxygen?
Ans: Oxygen belongs to group \(16\) and the second period of the Periodic Table. Hence, it contains two energy shells and eight electrons are distributed in these two energy shells. As it belongs to group \(16\) of the Periodic table, it contains six valence electrons. Hence, the atomic number of oxygen is \(8\).

Q.4. What is the effective atomic number rule?
Ans: The effective atomic number rule states that the total electrons donated by the ligands to a metal in a metal complex should be equal to the nearest noble gas present in that period. 

Q.5. How do you find the effective atomic number?
Ans: The given formula calculates the effective atomic number of a metal ion in metal complexes-
\({\text{EAN}} = ({\text{Z}} – {\text{X}}) + ({\text{L}} \times {\text{D}} \times 2)\)
Here, \({\text{Z}}\) represents the atomic number of the central metal ion.
\({\text{X}}\) represents the oxidation number of the central metal ion.
\({\text{L}}\) represents the total number of ligand bound to the central metal atom.
\({\text{D}}\) represents the denticity of the ligand.

Q.6. What is the difference between atomic number and effective atomic number?
Ans: Atomic number represents the total number of electrons or protons present in an atom. In contrast, an effective atomic number represents the total number of electrons surrounding metal in a metal complex. The effective atomic number includes the electrons possessed by the central metal atom and the electrons donated by the surrounding ligands. The atomic number is represented by \({\text{Z}}\), whereas \({{\rm{z}}_{{\rm{eff}}}}\) represents the effective atomic number.

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