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The coordination number of a central metal atom in a complex is determined by:
A.The number of ligands around a metal ion bonded by sigma bonds.
B.The number of ligands around a metal ion bonded by pi bonds.
C.The number of ligands around a metal ion bonded by sigma and pi bonds both.
D.The number of only anionic ligands bonded to the metal ion.

Answer
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Hint: A coordination complex consists of a central atom which is usually a metal atom and is called the coordination center, and is surrounded by an array of bounded molecules or ions (non-metals), these are known as ligands or complexing agents. The metal center and the ligands are bonded together through a coordination bond.

Complete step by step answer:
In chemistry, we have three types of bonds:
Ionic bond: It is the complete transfer of valence electron(s) between the atoms.
Covalent bond: In it, the electrons are not completely transferred by sharing between the atoms.
Coordination bond: It is also known as a dative covalent bond. It is a kind of covalent bond but both the electrons are given by a single atom.
Now, a covalent bond can be of two kinds:
Sigma-bonds: These bonds are formed by head-on overlapping between atomic orbitals.
Pi-bonds: These bonds are formed by side-by-side overlapping of atomic orbitals.
Sigma bonds are stronger than pi bonds.
 In a coordination complex, the bond between the metal center and the ligands is a sigma bond, but both the electrons are given by the ligand.

Therefore, the correct answer is option A.

Note:
A major application of coordination complexes is as catalysts. They come under the category of organometallic compounds. The coordination compounds are very vital for the biological systems, some of the key biological components are coordination complexes, for example, Vitamin B12, Hemoglobin, chlorophyll, etc.