edited bv:
RON
DELORENZO
Middle Georgia College Cochran, Georgia 31014
Ants and Chemical Kinetics R. Thomas Myers
Kent State University Kent, OH 44242 While a t the Mount Wilson Observatory the astronomer Harlow Shanlevl studied2 the effect of temoerature on the rate of locomotion of ants (Liometopum apiculatum). His results can he used to enliven the sessions on chemical kinetics. The data are amenable to standard treatment of kinetic data. He reported observations on average speed for 40 different groups of ants, with at least 15ants ineachgroup, for a total of 850 ants. The temperatures varied from 9 to 38 'C. These data are reproduced in the table and represented graphically in Figure 1. A
.
Rate 01 Travel of Ants, as Reported by Shapleyd Temp Oc 34 30 35 21
16
15.5 14.5 14.5 38.5 17
average speed
temp
cm/s
C '
4.35 3.05' 5.08 2.23 1.36 1.27 1.10 1.10 6.60 1.28
33.5 31 37 26
23.5 22 20 18 20 36
average speed cm/s 4.77 3.06' 5.67 2.56 2.29 2.17 1.86 1.70 2.04 5.62
temp C '
38 36 33 25.5 24.5 17 19 22 14
14.5
average speed temp 'C cm/s 6.06 5.52 4.32' 2.94 2.65 1.61 1.62 2.16
12.6 10.3 9.0 14.5 14.5 15.5
average speed cmls
1.01
18.6 18.5
1.05 1.18 1.16 1.48 1.44
1.16
12.5
0.77
18
temp.
0.77 0.64 0.44 1.11
OC
Figure 1. Speed-temperature relation for Llometopum apiculahnn. Solid points involve shading wilh cardboard. The curved line cwrespondr to the straight line in Figure 2.
~ a ~ h d apair t a ismeaverage for at least 15 ants. Lowest tempratures(founh coivmn and lasf two data points in third column) were obtained in December; m e r s at higher temperatures were in May and June. (The data marked withasterisks involved shading the ants with apiece 01 cardboard.)
Ants are small cold-blooded (poikilothermic) creatures, so their inner temoerature is verv close to the temnerature of the environment. The rate OF chemical reactions in their bodies is almost completely controlled by the temperature of the environment. (Shapley found no other influence of external variables. such as humiditv, wind weed, or illumination, The large; worker ants did-travel sfightly faster than the smaller ones, and ants traveled slightly faster toward the nests than away.) Three of the data points (asterisks in the table) were obtained by shading the ants with cardboard. Shapley was not sure that the ants were completely equilihrared tothe temperature, sothesepointsareumittcd in my treatment of the data. Figure 1 shows that the speed of the reaction increases with temperature. The temperature coefficient (the ratio of
Figure 2. Arrhenius plot, in s vs. 1/T, far ants. Slope is -6.98 X an energy of activation of 58.0 kJImol.
'Dr. Shapley (pronounced shap-lee) was an activist. He helped bring many refugees to the United States from Nazi Germany. He helped shape the nascent UNESCO (United Nations Educational and Cultural Organization). Because of his liberal views he was harassed by Sen. Joe McCarthy. 2Shapley. Harlow. Proc. Natl. Acad. Sci. 1920, 6, 205.
speeds at 10 O C intervals) is about 2; hence the data fit the very rough rule that the rate of many reactions approximately doubles or triples with a 10 "C rise in temperature. Another way to approach the data is to compute the energy of activation for the reaction. This is done by use of the
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Volume 67
Number 9
September 1990
lo3K, giving
781
Arrhenius equation, discussed in texts in physical chemistry. One common form is as follows. Ink = -EJRT
+ In A
In this equation, k is the rate constant (here equated to the speed, s), E, is the activation energy, R is the universal gas constant (8.314 J/mol/K), and T is the absolute temperature. A graph of In k vs. 1/T is a straight line, with slope of -E.IR. The quantity exp(-E,lRT) gives the fraction of molecules that have energies equal to or greater than the activation energy, and the quantity A is the frequency factor, which can he interpreted as being the number of collisions in which the reactants have the correct orientation to produce a reaction. Figure 2 is a graph of in s vs. 1 / T , where in indicates the natural logarithm. I t is indeed a good straight line, with a correlation coefficient of -0.9833, and slope of -6.98 X 10a K. This gives an activation energy of 58.0 kJ/mol, or 13.9
762
Journal of Chemical Education
kcal/mol, as expected for a temperature coefficient of this magnitude (near room temperature). The data can also he used to point out the deviations that are common in scientific observations and to serve as a basis for a discussion of precision and accuracy. The effect of size and direction of the ants can also he discussed. Finally, you might quote the poem" of Ogden Nash. The Ant The ant has made himself illustrious Throuah constant industry industrious. So what? Would you be calm and placid If you were full of formic acid?
Reproduced with permission of Curtis Brown. Ltd
