how do we know that an element has a vacant d-orbital??

Covalency of an element for example hydrogen, nitrogen, oxygen, fluorine is the total number of unpaired electrons in s or p orbitals.

Hydrogen for example (H®1s¹) has only one unpaired electron and shows a covalency of one.

N atom (N→2s²2p_x¹2p_y¹2p_z¹) has three unpaired electrons and shows a covalency of three.

O atom (O→2s²2p_x²2p_y¹2p_z¹) has two unpaired electrons and shows a covalency of two.

F atom (F→2s²2p_x²2p_y²2p_z¹) has one unpaired electrons and shows a covalency of one.

If you observe these elements given above have only s and p orbitals in their valence shells and do not contain vacant d orbitals.

However elements like P, S, and Cl contain vacant d-orbitals and show different values of covalency in different covalent compounds.

It is called variable covalency and is due to the presence of vacant d-orbitals in the valency shell of these elements.

Some examples of elements showing different covalencies in compounds.

Elements	Different covalencies	Examples of Compounds
Halogens(Other than fluorine)	1 3 5 7	ICl ICl3 ICl5 ICl7
Sulphur	2 4 6	SCl2 SF4 SF6
Phosphorus	3 5	PCl3 PCl5

 

Variable covalency of phosphorus of P atom (3,5)

P in Ground state : 3s² 3p_x¹ 3p_y¹ 3p_z¹

 

 

Phosphorus in its excited state: 3s¹ 3p_x¹ 3p_y¹ 3p_z¹3d¹