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Q. In $BrF _3$ molecule, the lone pairs occupy equatorial positions to minimize

Chemical Bonding and Molecular Structure

Solution:

It is to minimize lone pair - bond pair repulsions only. The three possible structures of $BrF _3$ molecule are:
I. One $l p-l p$ repulsion at $\sim 120^{\circ}$
Two $l p-b p$ repulsions at $\sim 120^{\circ}$
Four $l p-b p$ repulsions at $90^{\circ}$
Two $b p-b p$ repulsions at $90^{\circ}$ and
One $b p-b p$ repulsion at $180^{\circ}$
image
II. One $l p-l p$ repulsion at $90^{\circ}$
Three $l p-b p$ repulsions at $90^{\circ}$
Two $l p-b p$ repulsions at $\sim 120^{\circ}$
One $l p-b p$ repulsions at $180^{\circ}$
Two $b p-b p$ repulsions at $90^{\circ}$ and
One $b p-b p$ repulsion at $\sim 120^{\circ}$
image
III. One $l p-l p$ repulsion at $180^{\circ}$
Six $l p-b p$ repulsions at $90^{\circ}$ and
Three $b p-b p$ repulsions at $120^{\circ}$
image
Now, it is given that the $Br _3$ molecule prefers structure(I). In this structure, (a) $l p-l p$ repulsions are not minimum; it is minimum in structure (III). (b) $l p-b p$ repulsions are less than structure (III). (c) $b p-b p$ repulsions are more than structure (III).