Question

What is an effective atomic number (EAN)? Calculate EAN of cobalt (Z=27) in\[\;{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{ + 3}}\] and the zinc (Z=30) in\[\;\left[ {Zn{{\left( {N{H_3}} \right)}_4}} \right]S{O_4}\]?

Answer 1

Hint: we must remember that the oxidation number of cobalt (Co) is +3 and for Zn is +2.

Formula Required:
We must know that the mathematical expression of effective atomic (EAN) is = \[\;Z{\text{ }}-{\text{ }}ON{\text{ }} + {\text{ }}2\left( {CN} \right)\]
Where,
Z is the atomic number of the central metal atom
ON is the oxidation number of the central metal atom
CN is the coordination number of the central metal atom

Complete step by step answer:
We can define that the effective atomic number (EAN) is the total number of electrons surrounding the nucleus of a metal ion in a metal complex. So, it is composed of both the metal ion electron and the bonding electron that the surrounding ion is donating to form a complex. It is calculated to check the stability of the complex formed. More the EAN closer to the atomic number of the next noble gas, more stable is the complex formed.
We can calculate the effective Atomic number by using the below formula.
\[\left( {EAN} \right){\text{ = }}\;Z{\text{ }}-{\text{ }}ON{\text{ }} + {\text{ }}2\left( {CN} \right)\]
Now, we have to understand that what EAN is so, let’s calculate the EAN of \[\;{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{ + 3}}\]
We have \[\;{\left[ {Co{{\left( {N{H_3}} \right)}_6}} \right]^{ + 3}}\] in this complex, the central metal ion is Co3+ and the atomic number of Co is 27 which means Z=27. Each of the NH3 molecules donates 2 electrons each for bonding, so 6 molecules of NH3 will donate a total of 12. Also the oxidation state of Co3+ is 3+. Hence, the EAN = Z – ON + 2(CN)
\[\begin{array}{*{20}{l}}
  {EAN = {\text{ }}27{\text{ }}-{\text{ }}3 + 12} \\
  {EAN{\text{ }} = {\text{ }}36}
\end{array}\]
So the EAN for is 36.
Similarly, solving for we have,
The atomic no. of the central metal atom is 30 and the oxidation number (ON) is 2. Also, each of the NH3 will donate a total of 2 electrons and there are 4 NH3, hence a total of 8 electrons.
Now,
\[
  EAN{\text{ }} = {\text{ }}30 - 2 + 8 \\
  EAN{\text{ }} = {\text{ }}36 \\
 \]

So the EAN for is 36.

Note: We must know that the effective atomic number in a complex should be equal to \[{\mathbf{36}}\left( {{\mathbf{Kr}}} \right),{\text{ }}{\mathbf{54}}\left( {{\mathbf{Xe}}} \right){\text{ }}{\mathbf{or}}{\text{ }}{\mathbf{86}}\left( {{\text{ }}{\mathbf{Rn}}{\text{ }}} \right)\]. We can find that in many cases ligands are added until the central metal ion gets the same number of electrons as are present in the next noble gas.