I've begun to read some classic chemistry papers like Lewis' "The Atom and the Molecule" and was really happy to see how readable they are, even for me, someone with at best a lazy undergraduate's knowledge of physics, chemistry, and biology. But through Wikipedia and several chemistry education websites, I've learned there's roughly two centuries of work in chemistry where the periodic table was developed, several elements were first identified, atomic masses were calculated, the gas laws were formulated, etc., before the development of quantum theories in roughly the first quarter of the 20th century.
Can anyone recommend a book or article that surveys this period and describes the observations and experiments that led to these discoveries? I'm frustrated by the typical timeline presented in high school and undergraduate general chemistry classes that begin with very advanced theories of the atom and subatomic particles like ionization energy, quantum numbers, Planck's constant, apropos of nothing!
I doubt I'm the first to make the analogy, but it's like science is taught like religion. A bearded man said something a long time ago and it is true. Don't ask how we know the number of atoms in a gram of carbon-12, just memorize 6.02 x 10^23 and know that it is good.
Edit: I just rearranged the last sentence of the first paragraph to make it clearer.
In his biography Isaac Newton, James Gleick has a brief Chapter 9 on Newton's work in inorganic chemistry (alchemy). You might have some luck starting there. Gleick's footnotes are suggestive and nothing Newton turned his attention to can be safely ignored.
You might also find some place to begin here at a U. Indiana web site on the "Chymistry of Isaac Newton:
Shapin and Schaffer's Leviathan and the Air-Pump goes into a lot of detail into some of the early work of Robert Boyle. (More what we would today call his physical work than his chemical work, but the differences were blurry then.) It does an impressive job of both merging the technical details (trying to get inside what Boyle actually did, saw, and said) with the social context (how he tried to convince people that his assertions about how the world worked were accurate). It gives a real feel for the period.
The work of Lawrence Principe is very well-respected. William R. Newman's work on Newton's (al)chemical interests is also very well-respected. I am not very deeply read in the history of chemistry, much less early-modern chemistry, but these are the two names that always come up in this field. There are many others and their bibliographies can point you all manner of interesting directions.
As for how science is taught — the goal of history in a science class is not the goal of history in a history class. Usually history is taught in a science class only to make a mnemonic for learning present-day science, or to give the students historical ideals to aspire to. It is usually very poor history, because it strips away everything that we currently think is "wrong," and often completely re-interprets the work of those in the past to fit the needs of the present. Which is fine for science class, I guess. But it's not a real historical understanding. There is a very rich discipline of the study of the history of science, including the history of chemistry, and basically the starting assumption any serious scholar of it makes is that you have to understand what people were thinking in their own time, according to their own questions and priorities, and not worry so much about what line of thinking turned out to be right or not. If you are interesting in the philosophy of the history of science (e.g., how should it be regarded, taught, thought about?), Thomas Kuhn's The Structure of Scientific Revolutions (1962) is what I always start my students with, because he introduces these issues very clearly and in an interesting manner, and even all these decades later it is still a startling contrast to how science is usually talked about and taught. (One doesn't have to agree with Kuhn's argument for how science works to find his book stimulating; I am not a Kuhnian.)
A good general, entry-level, academic source which I was assigned as an undergraduate in a History of Science class is Trevor Levere's Transforming Matter: A History of Chemistry from Alchemy to the Buckyball. It's a relatively short text and would give more of an overview than the other titles that have been mentioned so far.
Levere is a historian of science and specifically of chemistry.