(Polar molecules, Non-polar molecules, etc.)
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Lone pairs take up more space on the molecule than bonding pair electrons because they face a lot of repulsion from neighbouring lone pairs and bonding pairs so they usually cause the molecule to have a bent/angular shape.
Using the VSEPR theory we've been learning in class, we are able to predict the structure of atoms surrounding the central atom. In order to find the structure, we must first determine the structure by identifying regions of electron density. A region of electron density can either be bonding or non-bonding, and for your question regarding non-bonding regions, the number of lone pairs on the central atom are the number of regions of non-bonding electron densities. Due to their repulsive characteristics, lone pairs help repel the positive attraction of atoms surrounding the central atom, and therefore we see different shapes and structures form as a result of stronger repulsive forces from varying amounts of lone pairs.
Hi! So to answer your question about lone, unpaired electrons on radicals: I believe that Lavelle might have said this quickly or in passing, but it is my understanding that unpaired electrons on radicals are considered a region of electron density. Although, because there is only 1 electron and not 2 in a pair, the repulsions the unpaired electron creates is weaker and thus, the angles it creates with nearby bonded atoms are smaller.
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