(Polar molecules, Non-polar molecules, etc.)
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When determining the shape of a molecule, all the regions of electron density need to be taken into account. They must be spread as far apart as possible in order to make the structure more stable (close together causes e- repulsion and therefore instability). Since lone pairs are regions of e- density, you must treat them like another atom attached to the central atom.
Lone pairs affect the shape of a molecule because electrons have negative and repulsive energy. They are constantly being tugged at and pushing each other away. When they are sitting as a lone pair, they have more freedom to buzz about near their home base atom. When the electrons are engaged in a bond between two atoms, there is less room for them to move around and repulse others nearby. Therefore, the lone pair will push atoms away from them and displace where the bonded atoms can reside with the least amount of repulsive energy. This results in a different shape than if all the electrons in a molecule were engaged in tidy bonds.
This may be the wrong wording but I think because the lone pairs are more.. free? That's what makes them more negative, therefore having a strong repulsion which is why they have to be separated as far away from each other. Where they are then placed will affect the bonds near them which will cause a bend in the molecule because repulsion exists between those too.
Since lone pairs and bonds are both considered when determining the shape of a molecule, lone pairs affect the shape of the molecule because the repulsion of the lone pairs is stronger. And in order to get the atoms as far as possible for least repulsion in order to determine the shape of the molecules, the atoms bonded to the central atom would be further from the lone pairs as compared to if the lone pair was another atom bonded to the central atom, which affects the overall shape of the molecule.
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