What is the hybridization of the central atom in ##ClF_5##?

The hybridization of the chlorine atom in ##ClF_5## is ##sp^3d^2##.

Chlorine pentafluoride, ##ClF_5##, has a total number of 42 : 7 from the chlorine atom and 7 from each of the five fluorine atoms.
The of the chlorine pentafluoride molecule looks like this

The five fluorine atoms will be bonded to the central chlorine atom via single bonds. Thsi will account for 10 of the 42 .
Each fluorine atom will have three lone pairs of electrons, which will account for 30 out of the remaining 32 .
The last 2 valence electrons will be placed as lone pairs on the chlorine atom.
As you can see, the chlorine atom is surrounded by 6 regions of electron – five single bonds and one lone pair.
This means that its steric number, which is the number that also determines the of the atom, will be equal to 6.
In order to be able to form six hybrid orbitals, the chlorine atom will use
one s-orbital;
three p-orbitals;
two d-orbitals.
Therefore, the central chlorine atom is ##sp^(3)d^(2)## hybridized. The of the molecule will be square pyamidal.

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