(Polar molecules, Non-polar molecules, etc.)
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The seesaw shape is more favorable, since the most stable structure would be the one with the least electron repulsions. The only way to accomplish this on a structure with 4 bonding pairs and 1 non bonding pair would be to position the electrons in such manner.
Imagine an AX5 shape. You have five equally spaced atoms bonded to the A. In an AX4E shape, it's the same situation except the lone pair repels the bonding pairs more than a bonding pair would repel others. So, to be most stable, the molecule wants the least amount of repulsion (the reason why we space the bonds equally in AX5), you most remove one of the equatorial bonds which only have two bonding pairs being affected by their repulsion as opposed to the axial pairs which have three electron pairs being affected. This gives the least amount of repulsion and results in the seesaw shape that we know.
When you pick a lone pair position, you want to look for the least amount of electron repulsions. If you pick one of the three equatorial atoms for the positioning of a lone pair, we only have two electron repulsions happening. If you pick one of the two axial atoms for this positioning though, we will have three electron repulsions occurring, which makes for a less stable structure.
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