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What chemistry principles should one study in their spare time?
I understand that a broad and intricate knowledge of the basics are important, but I'm not at all sure what basics I should start with. My idea was to read through a general chemistry textbook, but it's turning out to be somewhat overwhelming. I'm looking to pursue a career in organic chemistry (organic chemistry textbooks are too specific and don't really allow for a broad understanding of the subject matter).

I'm already taking chemistry courses at a university; the aim of this question, to restate, is to help me figure out where I should be concentrating in my spare time.

Chemical formulas, naming, reactivity. At least that is what I would see as being important. Ohh and Structure.

I am an inorganic chemist. I have a colleague who is a biological chemist. I once asked him, "What, besides biological chemistry, do you think is most important for your students to understand?" His answer? Physical chemistry. Besides inorganic chemistry, that's my answer too.

Thermodynamics, kinetics, bonding. Not so much at the level of being able to derive thermodynamic relationships with partial derivatives, but having a sort of honors-level freshman chemistry understanding.

Know order-of-magnitude numbers! How strong are typical bonds? How much energy is kT (or RT on a per mole basis). What is the energy range of visible light? Infrared radiation? NMR frequencies? What are typical bond lengths? etc...

You'd be amazed at how important these kinds of things are to chemists of all kinds - organic, inorganic, or analytical.

Is it a new subject to you? Then definitively dimensional analysis. This is what my students struggle with the most. They keep on asking me for the formula for a specific type of problem, and I keep on telling them that they can figure it out using units. This is also the sort of thing that is difficult at first, then stupidly easy once you get it.
Then, learn the rules for significant figures - and do not ever think that it would be easier to do a series of cross multiplications. There's a reason why the CCSS recommend NOT teaching cross multiplication: it's a trick that prevents you from solving more complex problems.
The rest is "simple": start with the nucleus, then the electrons, study periodicity, reactivity, bonds, and then layer down additional levels of complexity. As you do, be sure to create plenty of graphic organizers to make sure that you always get the big picture.

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