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the octet rule is in a covalent bonds atoms share electrons until a noble gas configuration is reached. This was seen in the notes when he used the example with two fluorine atoms, combined they follow the octet rule since they have a noble gas configuration with eight electrons each in the valence shell (sharing two electrons).
I prefer to understand it this way: when forming covalent bonds, atoms tend to share e- so that they have 8 e- (2 s-election and 6 p-electron) in their outmost shell. so for us, we just try to make all the atoms in a covalent bond formation as close to the 8-electron state as possible.
It's also good to note that the idea of filling octets is simply a guideline, not a rule. In the case of expanded valence shells like in the case of P, Cl, or S, these elements are able to have bonds that go beyond what an octet would allow.
The octet rule concerns atoms wanting to share their electrons in order to complete their valence shell and be the most stable they can. To do this, atom want to either complete their last orbital shell or get rids of some on the last and share/lend it to another atom. They would want to share and have 8 valence electrons among themselves. However, atoms such as P, S, and Cl can have more than 8 valence electrons as they had a d-orbital to put electrons there. After n=3, those atoms can have an expanded octet since there is an empty orbital (d) that is not used.
it's just a rule that says you need to have a filled shell valence electrons in order for the compound to be "happy" and "satisfied" with their situation. since the goal is 8 valence electrons for a lot of the most abundant elements, it's just called the octet rule but the main goal is to have a complete outer shell not necessarily 8 because once you get to period 3 theres a chance to have more bonds.
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