Hidden figures: 2.303, slide rules and classrooms mired in the last century

A five -place table of logarithms from my dad's CRC Handbook of 

Mathematics (why is that set of values circled?) and a circa 

1958 Hemmi 257 slide rule designed for chemical calculations.  

 Wonder why random values of 2.303 are "hidden" in formulae? To make them easier to use with a slide rule.¹ 

A slide rule?  The last slide rule slid out the door of Keuffel & Esser in 1975 (they sent their engraving equipment to the Smithsonian).  You can still find them, used and even new - still packaged up to sell to engineers and scientists.  The Oughtred Society has a online museum, as well.

We still have my mother-in-law's K&E, in it's leather case with her name impressed into it.  Family history says she bought it with the money she earned tutoring Jackie Robinson in chemistry at UCLA.

I have an essay out in this month's Nature Chemistry, "It figures", about how the computational tools we use shapes what we teach and not necessarily in good ways. Given that slide rules were obsolete by the time many of my student's parents were born, why does their use still linger in general chemistry book?  (The 2.303's in texts are lowly going away. I checked texts running back about a decade.)

More critically to my mind why, several decades after  digital computing tools became ubiquitous on college campuses do many physical chemistry texts eschew any discussion of numerical techniques for solving the rate equations for a chemical reaction?  I suspect the chasm between the computational tools used in the field and those used in the classroom is a result of apathy. We teach what we learned as we learned it.  As I note in the article, I don't think it is defensible on intellectual grounds.

Don't know how to use a slide rule?  It's fun, it's geeky. No need to buy one to play, check out this simulator and the instructions at Nature Chemistry!

You can read the article here:  http://rdcu.be/sY5Q

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1.  2.303 is the natural log of 10. To change the base of logs recognize that
x = b^log_bx
so
ln(x) = ln(10^log₁₀x)
ln(x) = log₁₀x ln(10)
ln(x) =(log₁₀x)(2.303)
ln(x) = 2.303(log₁₀x)

A day in pchem lecture: NMR, lululemon yoga pants and tattoos

By lululemon athletica
(Flickr: Yoga Journal Conference)
 [CC BY 2.0], via Wikimedia Commons

It's the end of term, two more 90 minute lectures left in my introductory quantum chemistry and spectroscopy course.  We've done the basics of wave functions and expectation values, we've looked at linear variation theory and written code to do Hückel MO calculations, we've covered rotational and vibrational and rotational-vibrational spectroscopy.  So what to do with these last few days?  The quantum mechanics of NMR.

I kicked off today's lecture by looking at magnetic field strengths, what's the earth's magnetic field (5 μT) or of a refrigerator magnet (5 mT), compared to the superconducting magnets used in NMR, which are on the order of 10T. (1T is one tesla.)  This led to a quick review of the risks in MRI, which aren't about the energy of the radiation used (which is billions of times lower than X-rays), but more about the interactions of the high magnetic fields, the radiofrequencies and metals.

A hand shot up and student who is an EMT describes a patient whose tattoo started burning during an MRI.  I pointed out this is a known phenomenon, and while most inks don't pose an issue, it should discourage you from DIY tattooing.  Then a student asked, "Is it true you can't wear lululemon pants when you have an MRI?"

I admitted this was out of my zone, but promised to follow up.

I can now report that yes, wearing lululemon pants — or any clothing with metallic microfibers, such as those great antimicrobial t-shirts — in an MRI can lead to serious burns, particularly in patients that have been sedated or are otherwise unconscious and unable to signal their discomfort.  Even non-ferromagnetic materials presents problems in the MRI as eddy currents can develop around them, creating little induction heaters.  Loops of all sorts, even skin to skin contact between a patient's own body parts can lead to heating and subsequent burns.  And tattoos with large loops in them?  They can heat as well.

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Other things I learned this afternoon.  You can levitate a frog with a 16T field (thank you Wikipedia), and neutron stars have magnetic fields on the megaTesla scale.

Changing exams

I just handed out a math assessment in my physical chemistry class, the same one I’ve used for the last several years. I generally don’t re-use exams (though I know colleagues who do), though I do re-use questions. By now I’ve been creating exams for more than a quarter of a century, and I wonder what the drift has been like over that time. How are the questions I ask now different (or not!) from what I asked 25 years ago? Or have the questions remained the same, and just the answers changed?

Fueling my introspection are the selections from the University of London’s 19th century bachelor’s degree exams. (H/T to a tweet from Nature Chemistry and the RSC). The chemistry question is one I could envision asking my students on an exam: “Explain the nature, from a chemical point of view, of the chief operations involved in the production of a photograph.”

The only catch, of course, is that the answer I’m expecting could be quite different than what the examiners in 1892 expected. In 1892, production of a photographic print necessarily involved silver, developers and fixing agents — and a darkroom. In 2011, production of a print could involve silicon and germanium, and a clean room. The theoretical underpinnings are less about pH and solution chemistry and more about semi-conductors and quantum mechanics.

What other reasonable exam questions might I ask, where the answers have changed so dramatically?

(And you have to love the example English question - just how important were werewolves in the 19th century?)

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Photo of 39/365 Kodak Vigilant Six-20 Antique Camera, by M.Christian on Flickr.

Releasing the Tension

My youngest son, Barnacle Boy, swims like a fish. When he was small, he could stay under water just a second longer than I though he should be able to -- I'd be ready to reach under and haul him to the surface, and then up he would pop. I began to wonder if he had gills.

Nowadays I'm certain he has no gills, though he can still hold his breath for a long time. He's not quite completely adapted to an aquatic life, though. He suffers from water in the ears. And he hates to hear himself sloshing...

The standard remedy for water stuck in the ears is "SwimEar" - an ad for which reads in part:

"Once water enters this tube...surface tension will cause this water to adhere firmly to the walls of the canal, thereby blocking it. Why is this water so difficult to remove? This is due to surface tension effect as well as the fact that it is extremely difficult to break the vacuum that is created behind the trapped water in the ear canal."

Despite the popping sensation you can get when your ears finally clear from water, there is no vacuum behind the water (really, I'm certain). As the ad implies, the trouble is that water is clingy, and therefore has a high surface tension. The high surface tension is what impedes the flow of water out of the ear canal -- think of getting the water out of a thin straw. The ear canal is behaving like a capillary. Reduce the surface tension and the fluid will release.

SwimEar is just a solution of isopropyl alcohol with a dash of glycerin added for comfort. (Ethanol, or ethyl alcohol, is what we drink - but to a chemist, an alcohol is a molecule that has a "tail" of (mostly) carbons and hydrogens topped off by a hydroxyl group: OH. Ethanol is CH₃CH₂OH, isopropyl alcohol is (CH₃)₂CHOH.) The isopropyl alcohol lowers the surface tension of the water (so will a bit of soapy water for that matter).

What do flamingos, Cheetos and Quantum Chemistry have in common?

The vibrant colors of flamingos and Cheetos Cheez Whiz™ are both the result of related carotenoid dyes. Carotenoids (named for the vegetable in which they were first found!) are based on a linear conjugated diene skeleton, and provide nature with many colorful accents. Canthaxanthin, for example, is fed to captive flamingos to produce their characteristic pink color (a similar pigment found in brine shrimp does the same favor for wild flamingos). Astaxanthin is responsible for the characterstic color of lobsters. Canaries, whose signature color is a greenish yellow, can be turned red if they are fed paprika during their molt. The new feathers will grow in orange-red.

If you're tired of only changing the color of your hair, you can try for a pumpkin look for fall. The compound that gives this class of vegetable pigments its name - β-carotene - when consumed in large quantities by humans, will turn them orange. [Really, but don't try this at home! It was observed clinically in Britain during WW II when food shortages led some people to include large amounts of carrots in their diets.]

If you thought the bright color of Cheez-Whiz and Cheetos was artificial -- it's not. Bixin or annatto, a natural pigment used for centuries, is the source of that unforgettable orange. Researchers have recently elucidated the biochemical pathway for the synthesis of bixin and are pursuing genetic engineering approaches to its bulk synthesis in tomatoes [Florence Bouvier in Science, 300:2089-2091, June 27, 2003].

What does this all have to do with quantum chemistry? A very simple quantum mechanical model, the particle in a one-dimensional box, can be used to predict the color of conjugated dyes.

UPDATE: Bixin isn't used to color Cheetos, but is used in Cheez Whiz.