(Polar molecules, Non-polar molecules, etc.)
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Molecular geometries can be specified in terms of bond lengths and bond angles. The bond length is defined to be the average distance between the nuclei of two atoms bonded together in any given molecule. A bond angle is the angle formed between three atoms across at least two bonds. The bond angles of each atom has to be equally spaced from one another. This is calculated experimentally, the closer they are the less or smaller the angle is which makes the degree smaller but you do not have to remember the exact number for all of structural planes.
I believe we need to know some general angles: tetrahedral - 109.5º, linear - 180º, trigonal planar - 120º (I'm not too sure if we need to know octahedral or trigonal bipyramidal). Outside of that, we probably only need to know some trends. For example, although trigonal pyramidal has a shape similar to a tetrahedral, there is a lone pair that pushes the atoms bonded to the center closer together, creating bond angles slightly less than 109.5º (the bond angles of a tetrahedral).
You do have to know the general numbers such as 109.5 degrees for tetrahedral and 120 degrees for trigonal planar to name a few. You will also have to understand how the lone pairs will affect these angles although the exact bond angle for every molecule does not have be memorized.
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