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Before we discussed the effective atomic number or EAN and how to calculate it, it’s very important to understand Singwick’s electronic concept of coordination.

In 1916, Lewis introduced the concept of a covalent bond between two atoms in a molecule. According to the lewis concept, a covalent bond is formed by the mutual sharing of two atoms. In 1927, Sidgwick extended lewis’s concept of the covalent bond and introduced a new concept of coordinate covalent bond which is also sometimes called a dative bond or polar bond.

According to Sidgwick’s concept, a coordinate covalent bond is formed when the ligands donate the electron pair to the central metal atom ion, which shows that the ligands have donated an electron pair to the metal ion. This concept is based that all the ligands contain at least one lone pair of electrons. On the basis of Sidgwick’s concept, the structure of complex ion [Co(NH)3]3+ is given below:

The net charge on the complex ion is equal to the algebraic sum of the oxidation state of the central metal atom and the charge on the ligands. For example, the net charge on the above complex ion is +3 because C03+ possesses a +3 oxidation state and NH3 is a neutral molecule so, 3+0 is equal to 3.

## Sidgwick’s Effective Atomic Number Rule (EAN Rule)

The effective atomic number (EAN) is the total number of electrons present in the central metal atom after the formation of the complex. Sidgwick’s suggested that the central metal ion will continue to accept the electron pair till it achieves the next inert gas electronic configuration. This is known as the effective atomic number rule. For example, after the formation of complex K4[Fe(CN)6], (the central metal atom is Fe) how many electrons are present in Fe?

Now we calculate the EAN of hexamine cobalt (|||) ion, [Co(NH3)6]3+. The atomic number of Cobalt is 27. It has 27 electrons. The number of electrons in Co (|||) or Co3+ is 27 – 3 is equal to 24. The number of electrons contributed by 6 Ammonia molecules is 12. EAN of Co3+ in the complex ion [Co(NH3)6]3+ is 24+12=36 which is the electronic configuration of inert gas i.e. krypton.

## How To Calculate EAN

The EAN can be calculated by using this formula:

EAN = Z-n + 2 × C.N

Where,

• Z = atomic number of the central metal atom
• n = oxidation state of the metal
• C.N = coordination number of the metal ion

## Complexes Obeying Effective Atomic Number Rule

### 1. Calculate the EAN of Nickel in [Ni(CO)4]complex?

EAN = Z-n + 2×C.N

• Atomic number of Nikel is 28.
• Oxidation state of Nikel is 0.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 28-0 + 2×4

EAN = 28+ 8

EAN = 36

The EAN of Ni is 36, which is the electronic configuration of inert gas krypton.

### 2. Calculate the effective atomic number of Chromium in [Cr(CO)6]complex?

EAN = Z-n + 2×C.N

• Atomic number of Chromium is 24.
• Oxidation state of Chromium is 0.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 24-0 + 2×6

EAN = 24+ 12

EAN = 36

The EAN of Cr is 36, which is the electronic configuration of inert gas krypton.

### 3. Calculate the EAN of Iron in [Fe(CO)5]complex?

EAN = Z-n + 2×C.N

• Atomic number of Iron is 26.
• Oxidation state of Iron is 0.
• Five ligands are attached to the central metal atom so, the coordination number is 5.

EAN = 26-0 + 2×5

EAN = 26+ 10

EAN = 36

The EAN of Fe is 36, which is the electronic configuration of inert gas krypton.

### 4. Calculate the EAN of Copper in [Cu(CN)4]3- complex?

EAN = Z-n + 2×C.N

• Atomic number of Cupper is 29.
• Oxidation state of Cupper is 1.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 29-1 + 2×4

EAN = 28+ 8

EAN = 36

The EAN of Cu is 36, which is the electronic configuration of inert gas krypton.

### 5. Calculate the EAN of Iron in [Fe(CN)6]4- complex?

EAN = Z-n + 2×C.N

• Atomic number of Iron is 26.
• Oxidation state of Iron is 2.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 26-2 + 2×6

EAN = 24+ 12

EAN = 36

The EAN of Fe is 36, which is the electronic configuration of inert gas krypton.

### 6. Calculate the effective atomic number of Molybdenum in [Mo(CO)6]complex?

EAN = Z-n + 2×C.N

• Atomic number of Molybdenum is 42.
• Oxidation state of Molybdenum is 0.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 42-0 + 2×6

EAN = 42+ 12

EAN = 54

The EAN of Mo is 54, which is the electronic configuration of inert gas Xenon.

### 7. Calculate the EAN of Platinum in [PtCl6]2- complex?

EAN = Z-n + 2×C.N

• Atomic number of Platinum is 78.
• Oxidation state of Platinum is 4.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 78-4 + 2×6

EAN =74+ 12

EAN = 86

The EAN of Pt is 86, which is the electronic configuration of inert gas Radon.

### 8. Calculate the EAN of Palladium in [Pd(NH3)6]4+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Palladium is 46.
• Oxidation state of Palladium is 4.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 46-4 + 2×6

EAN =42+ 12

EAN = 54

The EAN of Pd is 54, which is the electronic configuration of inert gas Xenon.

## Complexes Which Do Not Obey Effective Atomic Number Rule

There are many exceptions to the EAN rule. Many stable complexes are known in which the EAN rule is not obeyed.

### 1. Calculate the EAN of Nickel in [Ni(CN)4]2- complex?

EAN = Z-n + 2×C.N

• Atomic number of Nickel is 28.
• Oxidation state of Nickel is 2.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 28-2 + 2×4

EAN =26+ 8

EAN = 34

### 2. Calculate the EAN of Nickel in [Ni(NH3)6]2+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Nickel is 28.
• Oxidation state of Nickel is 2.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 28-2 + 2×6

EAN =26+ 12

EAN = 38

### 3. Calculate the EAN of Chromium in [Cr(NH3)6]3+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Chromium is 24.
• Oxidation state of Chromium is 3.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 24-3 + 2×6

EAN =21+ 12

EAN = 33

### 4. Calculate the EAN of Cobalt in [CoCl4]2- complex?

EAN = Z-n + 2×C.N

• Atomic number of Cobalt is 27.
• Oxidation state of Cobalt is 2.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 27-2 + 2×4

EAN =25+ 8

EAN = 33

### 5. Calculate the effective atomic number of Cupper in [Cu(NH3)4]2+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Cupper is 29.
• Oxidation state of Cupper is 2.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 29-2 + 2×4

EAN =27+ 8

EAN = 35

### 6. Calculate the EAN of Manganese in [Mn(CN)6]4- complex?

EAN = Z-n + 2×C.N

• Atomic number of Manganese is 25.
• Oxidation state of Manganese is 2.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 25-2 + 2×6

EAN =23+ 12

EAN = 35

### 7. Calculate the EAN of Iron in [Fe(CN)6]3- complex?

EAN = Z-n + 2×C.N

• Atomic number of Iron is 26.
• Oxidation state of Iron is 3.
• Six ligands are attached to the central metal atom so, the coordination number is 6.

EAN = 26-3 + 2×6

EAN =23+ 12

EAN = 35

### 8. Calculate the EAN of Silver in [Ag(NH3)2]+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Silver is 47.
• Oxidation state of Silver is 1.
• Two ligands are attached to the central metal atom so, the coordination number is 2.

EAN = 47-1 + 2×2

EAN =46+ 4

EAN = 50

### 9. Calculate the EAN of Palladium in [PdCl4]2- complex?

EAN = Z-n + 2×C.N

• Atomic number of Palladium is 46.
• Oxidation state of Silver is 2.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 46-2 + 2×4

EAN =44+ 8

EAN = 52

### 10. Calculate the effective atomic number of Platinum in [Pt(NH3)4]2+ complex?

EAN = Z-n + 2×C.N

• Atomic number of Platinum is 78.
• Oxidation state of Platinum is 2.
• Four ligands are attached to the central metal atom so, the coordination number is 4.

EAN = 78-2 + 2×4

EAN =76+ 8

EAN = 84

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