Question

Why is it that in the compound ClF3, the 2 lone pair of electrons are placed on the equatorial position and not on the axial position?

Answer 1

Lone pairs have a bigger volume compared to bonds as a result the lone pairs line where they could get maximum space for their shape to fit in the structure. This is my suggestion for the structure of ClF3.

Check this example:
www.chemtube3d.com/images/ClF3.png

Answer 2

this is partially due to the fact that the chlorine trifluoride is a hypervalent compound.
Remember, if you apply VSEPER theory here, what does it tell you about valence electrons and repulsion...