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An example of dispersion forces is the non polar carbon dioxide molecule. Dispersion forces are considered Van der Waals forces, which occur between molecules. Hydrogen bonding can be observed between water molecules or N,O,or F bonds with hydrogen. These are important to know because they help us better understand the interactions and their relative strengths.
Overall dispersion/van der waal forces occur among all molecules, but they're weak and only happen by chance. Hydrogen bonds are much stronger although more specific in nature. I don't think we'll need to memorize any particular example (although H2O is an easy one to remember for hydrogen bonds) but we should know how to recognize what kind of forces are at play when given a certain molecule. Also, in a workshop I saw a question that asks if a molecule can form hydrogen bonds with itself that was trickier than usual, so be careful!
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