This is a guest post from one of our regular Thesis columnists Michelle Francl, who recently penned a Thesis article ($) about back-of-the-envelope calculations (illustrated with one of Michelle’s own calculations done, of course, on the back of an envelope!).
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Guessing wisely got me my Ph.D., I joke with my general chemistry students. They are horrified, confusing ‘guessing’ with ‘making up a number’. When I explain that guessing in this context is the art of making meaningful estimates of chemical quantities with incomplete information under less than ideal circumstances — for example, in the middle of your doctoral defense or on a general chemistry midterm — and that I expect them to master this arcane art, they are generally even more horrified.
Estimation of chemical quantities is, in my opinion, one of the most important skills a chemist can have. It is also one that my students are simultaneously skeptical of — why not just use a search engine to find the ‘real’ value or crunch numbers to 8 decimal places in your calculator — and intimidated by (I probably don’t help by telling this story about Fermi).
Standing at the board, muttering under my breath and scratching seemingly unconnected numbers and symbols here and there is unlikely to relieve the impression that estimation is black magic, but it makes the point that there is an underlying process, and provides a visual map that can be annotated. Where did I get that value for a bond length, why do I use 3 for pi?
I emphasize the need to gather a tool kit of anchor points (key chemical values) and maps (relationships between quantities) and provide examples. Here is the handout (pdf) I just posted for the fall semester physical chemistry class (covering quantum chemistry), with a map of the electromagnetic spectrum, annotated with anchor points I find helpful. More anchors and constants (hacked off to just one significant figure) are on the back.
This is obviously not the only map and set of anchor points that chemists need. Eugene Douglass and Chad Miller, doctoral students at Yale, have begun a collection of maps at Practically Science. And of course there are Benson and Buss’ rules for estimating thermochemical values. (Chemical trivia — Jerry Buss was the owner of the Los Angeles Lakers).
It would be a fascinating exercise to create an atlas of the chemical world, a collection of maps and anchor points for various subdisciplines. What maps would you include?