Constitutional isomers are compounds that have the same atoms, but arranged in a different structure. This is completely different from resonance structures, because both isomers are real molecules and can have very different properties. So don't get the two mixed up. Remember, resonance structures have double-headed arrows between them. Isomers don't. Because I'm lazy, I'll just use the first example I find in my book...
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Remember how it's bonding that really makes molecules what they are? These compounds have different bonding structures, so I would expect them to have very different chemical and physical properties.
Addendum: People should know what common or important molecules look like. I just realized, as I was about to close my textbook, that "molecule B" is, in fact, acetone, a chemical you might be familiar with. Acetone is an important solvent. I used it in the laboratory all the time in my chemistry classes. It's also in paints and stuff. And it's used to make acrylic glass. As for the other molecule (A), its name is 2-propenol and I'm pretty sure it's just an enol form of acetone, so basically it is highly unstable and will typically turn into acetone by itself. But that's a topic for another day.
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