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In introductory chemistry books, courses, ...

Many "definitions" contain words like: typically, most, often, likely, generally.

I read since questions on this site mentioning different definitions of same concept in different books.

I just read about a concept where the explanation contained smth like "some other chemists believe it should be the other way".

Why are there many non-rigorous definitions in introductory chemistry?

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Because there often exceptions to rules, for which the explanation requires higher level chem to explain – rch Jul 5 '14 at 8:14
"requires higher level chem to explain" that is what I was afraid of, but good answ anyway – foobar Jul 5 '14 at 8:30
Chemistry has many exceptions, thus it becomes wrong to permanently define anything as right or wrong. Hence, the large uses of words such as the ones you have listed. – Gummy bears Jul 5 '14 at 8:43
Hi foobar! I think your question could be very interesting but as you posed it seems you are starting with wrong assumptions and misconceptions why do you say non-rigorous? Or what you mean for informal? Can you provide some practical examples? – G M Jul 5 '14 at 11:56
I deliberately avoided examples, because in my experience that makes people occupied wit the example and then I never get an answer. – foobar Jul 5 '14 at 12:12

The problem you are encountering has two origins:

  1. Historically, chemistry has accumulated many models for chemical behavior that work most of the time. Some of these models are based on completely invalid theory (VSEPR), but they provide a set of rules that work. Some are based on decent theory (the octet rule, hybridization), but generate inconsistencies because the underlying theory is incomplete. Most of these models work in most cases, so they remain because they are easy to use.

  2. Higher level theories/models exist that contain less inconsistencies and fewer exceptions, but the maths are hard. At the simplest, these models require multivariable calculus, linear algebra, and/or differential equations. At the more complex, we are talking about a computer spending 30 minutes (or more) iterating through the matrix approximations to many-electron wavefunctions (for which there are still no exact solutions) to find the best self-consistent minimum-energy solution. We're talking about problems in theoretical chemistry that used to consume one person's PhD thesis to just derive one proof and complete one calculation (or a small group of related calculations).

The field of chemistry has chosen to be more accessible to beginners by allowing the continuation of such imperfect models. There are a number of reasons for this. First, it allows students to progress through the more qualitative chemistry courses while they work up to the math requirements. Second, it allows students of other sciences (especially biology and medicine) to develop a conceptual understanding of chemistry (which they need far more than the calculus-based understanding).

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How is VSEPR completely invalid? – Dissenter Jul 5 '14 at 16:16
Just derive one proof? For example? – user26143 Jul 5 '14 at 19:01
@Dissenter - VSEPR is a wonderful model that works nearly every time. However, it is based on the notion that electron pairs occupy fixed localized positions in space (which is not in agreement with modern bonding theories). – Ben Norris Jul 5 '14 at 19:25
@user26143 -In the days when the most powerful computer was a calculator the size of a room, physicists and physical chemists did all of their math by hand. The Hartree-Fock method of approximating solutions to many-electron wave-functions is iterative. The outputs of the first attempt are used as the start point for the second. Consider that it might take 500 or 1000 iterations of complex differential equations masquearding as complex linear algebra. – Ben Norris Jul 5 '14 at 19:29
In that case you could perhaps see how solving the electronic structure of a single molecule without modern computational software might be a herculean effort. I do not remember those days (because I was born after they ended), but my older colleagues do. – Ben Norris Jul 5 '14 at 19:31

I like this merriam-webster definition of rigorous:

done carefully and with a lot of attention to detail

Chemistry is an experimental science there are a lot of patterns that work fine in most of the cases but not in all (e.g. the Octet rule) these are called rules of thumb. Chemistry is however a rigorous science, simply there are exceptions that don't follow clear patterns or easy simplifications so they are harder to predict or to comprehend for a student in an introductory text.

As in all the science (physics, mathematics etc. etc.) there are some topics that are still debated, this don't mean that introductory chemistry is non-rigorous. I suggest you to read some books about history of chemistry (e.g. Asmiov, A Short History of Chemistry), you will find that chemistry has been for most of his history (and it is in part now days) a trial and error research, followed by the attempt to find a theory, a pattern or a sense to the observations done, this doesn't mean that there isn't a rigorous approach but simply that reality don't fit the scheme that we propose so easily.

I think maybe most of the text books don't emphasize in this aspect of chemistry, but most of the reasoning is a posteriori.

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@foobar Can you find me a reference that states the rigorous has this meaning please, I'm not a native english speaker! :-) thanks! However in your example it depends which properties you used to classify the elements into the groups. Take this example from math: some mathematicians believe that 0 belong to natural numbers other say that it isn't (this is a true fact) following your reasoning math is a non-rigorous science.... – G M Jul 5 '14 at 12:35
@foobar mmm that's not so obvious in my opinion. I think you should rearrange at least your last phrase, say that introductory chemistry is a mess or informal is more an opinion than a truth. And It is a pity because the question if well posed could lead to interesting answer. – G M Jul 5 '14 at 12:53
My point was that I expected definitions, from which I can make a decision without further searching for clarification. i.e. words such as "typically" or "likely" do not belong into a definition. – foobar Jul 5 '14 at 13:04
@foobar - what you are looking for sounds like a way to simplify chemistry to a series of algorithms that work every time. The field as a whole is not quite there yet for a variety of reasons. – Ben Norris Jul 5 '14 at 14:47

I used to teach an introductory chemistry course and found that the understanding of most chapters would have been improved by having already knowing other chapters, but you have to start somewhere with something. Different texts have things ordered differently and different instructors present material in different orders even using the same text.

Introductory chemistry by nature covers a very wide variety of topics. As an example, I had to cover the basics of organic nomenclature as part of an introductory chemistry class and I had about 5 weeks to cover the organic section, maybe less if I needed more time to cover the material I taught earlier in the semester. Obviously, even the nomenclature part of organic chemistry will be more rigorous in a two semester Organic sequence.

Introductory chemistry is a challenging class to teach - if you don't plan well enough how much time to devote to a specific topic you are at risk of either running out of time to cover something or most of your class not understanding something important.

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