Effective Atomic Number rule formula calculation and examples
The effective atomic number is a very common term used in the coordination chemistry branch. The effective atomic number can be represented as EAN chemistry in short. Effective atomic number theory was the first theory that explained the concept behind the complex compound formation. This theory was given by Sidgwick. Therefore, this theory is known as the Sidgwick rule.
EAN in chemistry is used for complex compound formation. Let’s come to the main question. What is an effective atomic number? The effective atomic number is the number that tells about the total number of electrons present around the central metal in a complex compound.
The Effective Atomic Number Rule
In the 1920s, N.V. Sidgwick observed that the metal present in a complex like metal carbonyl, for example [Ni(CO4)] has the same valence electron count as that of noble gas that terminates the periodic table, of which the metal is a part. Though “the inert gas” rule was coined by the scientist to indicate stability, it is now referred to as the 18 –electron rule or EAN Rule.
The representation of the atom is done as Zeff. It indicates the number of protons that the electron in a metal effectively sees due to the screening by the inner-shell electrons. Generally, the EAN of the given central atom is numerically equal to the atomic number of the noble gas that is present in the same period to which the given central metal atom belongs. 36 (Krypton), 54 (Xenon), and 86 (Radon) are noble gases that generally fall under the consideration of the EAN rule.
The noble gases that belong to the 3rd, 4th and 5th periods are generally considered for the EAN rule. The elements that generally belong to the 3rd, 4th and 5th periods are the transition metals, hence, the central atom of the complex formed is generally composed of the transition element. Thus, the central metal atom of the complex generally belongs to the 3rd, 4th and 5th periods of the d-block element.
Effective Atomic Number in Coordination Compounds
In the above definition, we explain the effective atomic number concept. This concept explains the stability and the possibility of complex compound formation. According to this concept, only that complex compound can be formed that will attain the noble gas configuration.
D-block element atomic number
Scandium (Sc)- 21
Titanium (Ti)- 22
Vanadium (V)- 23
Chromium (Cr)-24
Manganese (Mn)- 25
Iron (Fe)- 26
Cobalt (Co)- 27
Nickel (Ni)- 28
Copper (Cu)- 29
Zinc (Zn)- 30
Krypton (Kr)- 36
The Nobel gas close to this series is 36. All these elements are less stable than the krypton. Therefore, all these above-mentioned elements will try to attain this electronic configuration. For this noble gas configuration, these elements will form a complex compound with different types of ligand.
The Formula of Sidgwick EAN Rule
EAN = Atomic number (Z) – Oxidation number + 2 × Coordination number
EAN= Z – x + 2nL
Z= Atomic number of the metal in the complex
x = Oxidation state of the metal in complex
n= Number of the ligands
L = Number of coordinate bonds formed by ligand
Sidgwick EAN Rule Tells about:
Stability of coordination compound.
The metal ion in a coordination complex will continue accepting the electrons till the total number of electrons in the metal ion becomes equal to the atomic number of the noble gas of that series.
Significance of the Effective Atomic Number
The major significance of the effective atomic number are listed below:-
The effective atomic number helps us in understanding why electrons, when further apart from the nucleus, are weakly bound to it.
The stability of the coordinate compound is explained with the help of the effective atomic number.
In the case of the non-classic complexes like that of the metal carbonyl complex, the effective atomic number is more valid. Hence this rule explains the stability, oxidising and reducing character of carbonyl compounds. Though it is found to be invalid for most of the complexes, it is seen to be valid for all the cases of the carbonyl complexes. No ligands act as a three electron donor.
EAN Rule Examples
1. Explain Effective Atomic Number for Iron (Fe) in Fe (CO)5.
Ans. The oxidation state of iron is zero.
The atomic number of iron is 26.
Carbonyl (CO) is a monodentate ligand.
EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.
EAN of iron (Fe) = 26 + 5 *2
EAN of iron (Fe) = 26 + 10
EAN of iron (Fe) = 36.
36 is the noble gas electronic configuration.
2. Explain Effective Atomic Number for Iron (Fe) in [Fe (NH3)6]+2
Ans. The oxidation state of iron is + 2.
The atomic number of iron is 26.
Number of electrons in Fe+2 = 24
Ammonia (NH3) is a monodentate ligand.
EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.
EAN of iron (Fe) = 24 + 6 *2
EAN of iron (Fe) = 24 + 12
EAN of iron (Fe) = 36.
36 is the noble gas electronic configuration.
3. Explain Effective Atomic Number for Iron (Fe) in K3 [Fe (CN)6]
Ans. The oxidation state of iron is + 3.
The atomic number of iron is 26.
Number of electrons in Fe+3 = 23
Cyanide (CN) is a monodentate ligand.
EAN for the iron will be = an Atomic number of iron + the total number of electrons donated by the ligand.
EAN of iron (Fe) = 23 + 6 * 2
EAN of iron (Fe) = 23 + 12
EAN of iron (Fe) = 35.
35 is not the noble gas electronic configuration.
Not satisfying EAN rule. To attain thirty-six electronic configurations, the iron in this compound will accept an electron. Therefore, it will act as an oxidizing agent.
Did You Know?
The 18 electron rule follows the noble gas configuration concept but still it is different from the EAN rule.
Not every coordination species follow this rule.
FAQs on Effective Atomic Number in Coordination Chemistry
1. What is effective atomic number (EAN)?
Effective atomic number (EAN) is the total number of electrons surrounding a central metal atom in a coordination compound, including its own electrons and those donated by ligands.
It is mainly used in coordination chemistry to explain the stability of metal complexes. According to the EAN rule, many stable complexes have an EAN equal to the atomic number of the nearest noble gas.
General expression:
EAN = (Atomic number of metal − oxidation state) + electrons donated by ligands
2. What is the EAN rule in coordination chemistry?
The EAN rule states that a metal complex is especially stable when the effective atomic number of the central metal equals the atomic number of the nearest noble gas.
This means the metal attains a stable noble gas configuration after:
- Losing electrons to form a cation (oxidation state)
- Gaining electron pairs donated by ligands
For many transition metal complexes, this corresponds to 18 electrons, also called the 18-electron rule.
3. How do you calculate the effective atomic number of a complex?
To calculate the effective atomic number (EAN), use the formula: EAN = (Z − oxidation state) + electrons donated by ligands.
Steps:
- 1. Write the atomic number (Z) of the metal.
- 2. Subtract its oxidation state.
- 3. Add the total electrons donated by all ligands (usually 2 electrons per monodentate ligand).
Example: For [Co(NH3)6]3+
- Z of Co = 27
- Oxidation state = +3
- Electrons from 6 NH3 ligands = 6 × 2 = 12
EAN = (27 − 3) + 12 = 36 (same as noble gas Kr).
4. What is the difference between atomic number and effective atomic number?
The atomic number is the number of protons in a neutral atom, while the effective atomic number (EAN) is the total number of electrons around a metal atom in a complex.
Key differences:
- Atomic number (Z): Fixed property of an element.
- EAN: Depends on oxidation state and ligands.
- Atomic number applies to isolated atoms.
- EAN applies mainly to coordination compounds.
For example, cobalt has Z = 27, but in [Co(NH3)6]3+, its EAN is 36.
5. What is the 18-electron rule and how is it related to EAN?
The 18-electron rule states that many stable transition metal complexes have 18 valence electrons around the metal center, corresponding to a noble gas configuration.
This is directly related to the EAN rule because when EAN equals the atomic number of the nearest noble gas, the metal effectively has 18 valence electrons in its outer shell.
Thus, for many transition metals:
- EAN equal to noble gas number
- Total valence electrons = 18
6. Can you give an example of EAN calculation for Ni(CO)4?
The effective atomic number of Ni(CO)4 is 36, which equals the atomic number of krypton.
Calculation:
- Z of Ni = 28
- Oxidation state of Ni = 0
- Each CO donates 2 electrons
- Total ligand electrons = 4 × 2 = 8
EAN = (28 − 0) + 8 = 36
This satisfies the EAN rule and corresponds to 18 valence electrons.
7. Why is the effective atomic number important in coordination compounds?
The effective atomic number (EAN) is important because it helps predict the stability of coordination complexes.
It is useful for:
- Explaining why certain complexes are stable
- Applying the 18-electron rule
- Understanding bonding in transition metal complexes
Complexes that achieve a noble gas EAN are often more stable, although there are exceptions.
8. Does every coordination compound obey the EAN rule?
No, not all coordination compounds obey the EAN rule.
Many stable complexes have EAN values different from the nearest noble gas due to:
- Steric hindrance
- Electronic factors
- Metal–metal bonding
- High or low oxidation states
Thus, the EAN rule is a useful guideline, but it is not universally applicable.
9. How many electrons does a ligand donate when calculating EAN?
In EAN calculations, a typical monodentate ligand donates 2 electrons to the central metal atom.
Examples:
- NH3 donates 2 electrons
- H2O donates 2 electrons
- Cl− donates 2 electrons
- CO donates 2 electrons
Bidentate ligands donate 4 electrons, and polydentate ligands donate more depending on the number of donor atoms.
10. What are the limitations of the effective atomic number rule?
The main limitation of the effective atomic number (EAN) rule is that it does not accurately predict stability for all transition metal complexes.
Limitations include:
- Does not apply well to early transition metals
- Fails for complexes with fewer or more than 18 electrons
- Does not account for ligand field effects
- Ignores molecular orbital considerations
Therefore, EAN is a helpful guideline but must be used along with modern bonding theories such as crystal field theory and molecular orbital theory.
