In which of the following the repulsion is least?
Lets look at all the options here.
This is a trigonal bipyramidal geometry having 3 bond pairs and 2 lone pairs.
Now, first we will take repulsions on the smallest angle (which is 90∘)
Lets take 1st structure,
If we take upper pyramid, the repulsions are:
1bp - bp, 2lp - bp, 0lp - lp
In the lower pyramide,
1bp - bp, 2lp - bp, 0lp - bp
Total = 2bp - bp, 4lp - bp and 0lp - bp
In II structure,
Upper pyramid,
3lp - bp, 0bp - bp, 0lp - lp
Lower pyramid,
3lp - bp, 0bp - bp, 0lp - lp
Total = 0bp - bp, 6lp - bp, 0lp - lp
In III structure, Upper pyramid,
2lp - bp, 0bp - bp, 1lp - lp
Lower pyramid,
2bp - bp, 1lp - bp, 0lp - lp
Total → 2bp - bp, 3lp - bp, 1lp - lp
Now, we know that
lp−lp>lp−bp>bp−bp
Now, as III structure contains 1lp - lp and other two does not. Therefore structure III will be least stable.
From I and II, we can see lp - bp repulsions are more I structure II.
Therefore structure I will be most stable.