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Are we allowed to draw bonded elements with two dots or do we have to use the line system? For example, To form SO4^2-, can we put two dots in between S and each of the O’s or do we need to put the line?
I honestly prefer the one where you use the lines to represent the bonds. In a Lewis structure, it's important to distinguish between the bonded electrons and the lone pairs. However, it's more difficult to do so if you represent the bonds with dots instead of lines.
As said above either is fine, but lines are useful in counting the electrons and also being able to keep track of charges when calculating formal charges as well. This continues in to the fact that when we come to resonance structures it makes it easier to visualize the different electron placements than single dots, which can become difficult to keep track of if messy or misplaced. But it is a model that should work best for you and others to easily understand.
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