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)

What is the half-life of a tweet?

My tweets apparently have a half-life of about two hours, but I have no idea if that's unique to me.  My spouse is new to Twitter and as I was showing him how he could see some data about his tweets, I noticed that the graph of the data looked familiar.  Probably because I taught chemical kinetics twice last year (in pchem and general chemistry).

Over lunch today, while waiting for my car to be serviced, I decided to explore the kinetics of my tweets.  I used data from the first 10 hours after I posted a tweet, and used tweets that had several hundred total impressions and few retweets.  Using five data sets from the past month, I fit the tweets to linear models for 0th, 1st and 2nd order kinetics.  R² values suggest that a 1st order model is most appropriate, with a rate constant of 0.35/hour, which translates to a half-life of 2.0 ± 0.4 hours.  I'm curious if that's relatively constant for me, or whether it's characteristic of other parameters, but time is up.

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Perhaps because I'm writing this outside in a park, I'm reminded of an infamous problem about the temperature dependence of the chirp rate of male snowy tree crickets in many general and physical chemistry texts.  A discussion of the phenomenon (first recorded in the late 19th century, and not true of cricket everywhere) can be found in Thomas Walker and Nancy Collins. “New World Thermometer Crickets: The Oecanthus Rileyi Species Group and a New Species from North America.” Journal of Orthoptera Research 19 (2010): 371–376. 

Weird Words of Science 12: A need for speed

The nectar busily gathered by the bees outside my window has a high sucrose content. The bees add the enzyme invertase to the nectar to catalyze the inversion of the sucrose to glucose and fructose that are the major sugars in honey. Humans can speed up the same reaction by heating the syrup or by adding a touch of acid.

Both enzyme and catalysis are lofty words lifted by scientists in the 19th century to serve more prosaic ends.

Enzyme's first meaning in the bread used for the Eucharist in the Greek Orthodox tradition. It means "leavened". It's not such a stretch to borrow the word to describe stuff that encouraged cellular reactions to proceed, what had been called the ferment.

Catalysis was originally used to describe the collapse of a nation, its origins can be traced to the mid 17th century. It comes from the Greek "to loosen". In the 19th century, Berzelius suborned the term to describe the process by which chemical reactions are facilitated. Catalysts participate in a reaction, but are in the end are restored to their original form, like molecular Phoenixes. Why did Berzelius settle on this term? Did he hope to imply that the constraints which bound the reaction to a slow pace are loosened by a catalyst?

Turning Sugar Inside Out

This week's worksheet in general chemistry asks my students to analyze the chemical kinetics (the speed) of this reaction:

C₁₂H₂₂O₁₁ (sucrose or table sugar) + H₂O (water) -> C₆H₁₂O₆ (glucose) + C₆H₁₂O₆ (fructose).

It's called the inversion of sucrose, and the resulting mix of glucose and fructose is tagged invert sugar. The name suggests that table sugar has been turned inside out or perhaps upside down, but in fact it's simply been split into two simpler sugars. The inversion is not of the sugar itself, but of the way it bends polarized light. If you pass a beam of polarized light through a solution of regular table sugar, the light will "rotate" or bend to the left. The mixture of glucose and fructose "inverts" the rotation, and bends the beam to the right.

Invert sugar is less like to crystalize than regular sugar, making it ideal for sweetening candy or jams. The reaction in the absence of a catalyst is slow at room temperature, but can be completed . The simplest way to catalyze the reaction is with an acid, often citric acid or ascorbic acid (Vitamin C), and many jam recipes call for one or the other.

So why do these compounds "bend" polarized light? Like many biological molecules, they are chiral or handed. The right handed or D form bends the polarized light toward the right, the left handed form (denoted L) left.

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Another name for the D form of glucose is dextrose, named for the direction in which it bends polarized light.

How did the leopard get it spots?

Biomorphogenesis, the process by which biological forms arise during development, is a fascinating area that crosses many fields, including computer science, mathematics, biology and chemistry. How do the stripes develop on a zebra? Alan Turing, one of the first computer scientists and the man who developed the computational engine that cracked the Enigma code in World War II, took on this problem in the early 1950s. In 1952 he published, "The Chemical Basis of Morphogenesis" [Phil. Trans. R. Soc. London B 1952, 237, 37-72]. He posits in this paper that oscillating chemical reactions, such as the Belousov-Zhabotinsky reaction, could lead to temporal-spatial differences in pigmentation. You can see why this might be the case in this animation of the reaction.

The BZ reaction is complex, the proposed mechanism consists of almost 20 steps - much more complex than those we are discussing in general chemistry this week! You can watch the BZ reaction in this video clip - the color changes look like magic.