(Polar molecules, Non-polar molecules, etc.)
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When drawing the Lewis structure for XeF2, Xe has three lone pairs around it, but why is its molecular shape linear with a bond angle of 180 degrees instead of the lone pairs pushing down on the bonded atoms? Why isn't this shape similar to a bent molecule, like H2O, where it has two lone pairs around the central atom?
The lone pairs *are* pushing the bonded atoms, it's just that they do so in a way that the resulting electron arrangement shape is trigonal bipyramidal. This is possible because there are three electron pairs and two bonded atoms. If it had only two electron pairs and two bonded atoms, then the shape would be bent. The molecular shape is linear because only the position of the bonded atoms are considered when naming the molecular geometry.
The lone pair electrons spread out equidistant around the equatorial plane and the atoms, as a result, go to either end of the axial plane, as far away from each other as possible. The electron arrangement would appear trigonal bipyramidal while the molecular shape is linear. This is only possible with three lone pairs of electrons because just one or two lone pairs would result in a bent shape as you said.
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