provocative research Everyone knows that on the island with Robinson Crusoe was his man Friday. Not generally known was the fact that Friday was a scientist who performed many elaborate experiments, especially with gases. Now these facts have come to light because the noted anthropologist Sir Humphrey Harvey has recently discovered the notebook in which Friday recorded his researches. Harvey had great difficulty in deciding whether Friday's experiments were worthwhile or not because of the units in which Friday recorded his data. For example, Friday measured pressure by collecting bird droppings on a barrel stave affixedto his apparatus. Consequently, all of his pressure readings are in birddroppings per barrel stave (Bd/Bs) units. By care fully reproducing some of Friday's experiments (with pigeons), Harvey determined that 15 torr = 1.70 Bd/Bs when the bird droppings were confined to an area on the end of the barrel stave measuring 13 X 16 mm. Similarly, Friday used old goat bladders to contain his gases and consequently all volume readings are in units of old goat bladders (Ogb). By averaging the values obtained from ten old goats, Harvey found that 1.00 Ogb = 265 Bombay Gin bottles. After an interval of two months, Harvey then determined that 1.00 Bgb (BombayGin Bottle) = 0.85 1. Friday was aware of Avogadro's law, though not by name. Harvey is convinced Friday rediscovered it, as well as Boyle's and Charles' laws. However, Friday measured numbers of gaseous particles by a unique, but reproducible, method. He would carefully introduce a leak into the old goat bladder, squeeze it forcefully and note the high-pitched screech as the gases were exhaled. This procedure invariably attracted chipmunks which abound on the island. Since the number of chipmunks which rushed to the opening of the cave (which was the location of Friday's laboratory) were directly proportional to the sound frequency and this was a function of the numbers of molecules, Friday's unit for number of molecules was measured in number of chipmunks (Chip). Harvey determined that 12 Chip = 1.00 mole. Friday measured temperature as follows: he would suspend an old goat bladder in the shade and measure its volume by an unclear method (that portion of t,he manuscript was eaten away, apparently by chipmunks). Then, suspending the old goat bladder in a vat of gently boiling papaya slurry, he found the volume was increased to 7/5 its original value. By dividing this difference in temperature into degrees papaya slurry ('Ps) Friday concocted a temperature scale. Harvey reproduced these experiments and found that a temperature range of 11% corresponds to a temperature range of 23'C, and the freezing point of water is -14"Ps on Friday's scale. Thus, absolute zero is
-145"Ps. Harvey ingeniously devised a new unit called absolute degrees papaya slurry ("Ps-Ahs) which starts a t absolutc zero = 0" and, naturally the freezing point of water = 131°Ps-Abs. Apparently, Friday's most detailed and discriminating experiments were concerned with a substance which he called "Banana gas". A facsimile of one of Friday's data sheets is given in the table. Some Doto from Friday's Notebook
Bird droppings/ Barrel stavc
Degrees papaya slurry
Chipmunks
Old gost bladdors
23 28 40 38 23 26
12.2 17.6 15.5 42.0 10.3 20.7
3 7 5 4 12 6
1 2 1 1 4 2
Further work on banana gas was performed by Friday in an attempt to determine some of its physical properties. In one of his experiments he found that a 2 Chip sample of banana gas contained in one old goat bladder and maintained a t a temperature of 13.5'Ps exerted a pressure of 16 Bd/Bs. Friday weighed the empty old goat bladder prior to the experiment and found that it weighed 97.35 Bd. It weighed 98.57 Bd when it contained the 2 Chip of banana gas. Sir Harvey has appealed to his chemist friends in the colonies to supply answers to the following questions (1) Is banana gas ideal? ( 2 ) What is its molecular weight? (3) What is its chemical formulrt?
He seems doggedly convinced that enough data was collected by Friday for such an analysis. He even presumes (in a leap of the imagination) that Friday had performed such an analysis. However, this is mere conjecture on his part as those pages in the notebook are missing. Friday Experiments Answered 1. Is banana gas ideal? An ideal gas, by definition, is one that follows the relation P V = knT, where P is pressore, V is volume, n is nnmber of moles, T is absolute temperature, and k is a constant of proportionality. A demonstration of the constancy of k under varying conditions is sufficient to prove ideality. In Friday's experiments we must convert degrees papaya slorry to absolute degrecq papaya shrrry, then calcdate and compare the ideal gas eonst,ant. T("P8) T('Ps-Abs) k = PV/nT (Bd-Oah/Bs- chi^-'Pa-Abs)
10.3 20.7
155.3 174.7
(23 x 4jji12 x 155.3) = ,0493 (26 X 2)/(6 X 174.7) = .-,0496 average = ,0406
Volume 46, Number 8, August 1969
/
497
The average value of k is 0.0496 (Bd-Ogb/Bs-Chip-oPs-Ahs). Since, in Friday's work, chipmunks and old goat? bladders are quanbiaed, we may not expect too great a precision in his determinations. The average deviation in k is 0.0006 (Bd-Ogh/BsChip-"Ps-Abs) and the relative average deviation is thus (.0006/ ,0496) X 100 = 1.270. However, two of the six values are outside the range established by the average deviation (0.05020.0490). Applicat,iou of significant figures limitations imposed by the pressure readings (apparently, in this series of experiments, bird droppings were also quantized) leads to an average value of k = 0.050 (Bd-Ogb/B~Chip-"Ps-Abs),which appears reasonably constant throughout the determinations. Tentatively, then, i t appears that banana gm is ideal, although fmther work is called for to firmly establish this point.' 2. What is the molecular weight of banana g a ~ ? Here, we must invoke the relation n = w/M where n = number of ehipmunks, w = bird droppingr; of gas, and M = molecnlar weight (chipmunkular weight?) of gas.
1.00 Bd
=
(2.08/1.70) X 20.4 g = 23.0 g
Then the molecular weight, A[, of banana gay is AT = 7.32 Bd/mole X 23.0 g/Bd = 183 g/mole
3. What is the chemical form~daof banana gay? I t wodd seem, in s. preliminary appraisal, dhat we are lacking in the data. necessary to make a determination of t,he chemical formula of banana gas. However, the untrained eye of the novice frequently passes over, withont a pause, what to the more seswned and astnte investigator ultimately t,orns ant to be the key ohservation in a major ncienlific st,udy. Such was t,he case in this ~.egard,a?, Sir Harvey, lacking formal training in the scientific discipline of chemistry, pawed over tda lightly what appeared to he a mere qnirk or paasion in mode of writing by Friday. Upon appeal t,o Sir Harvey, I have obt,ained a photographic copy of the title page of Friday's experiment,^ on banana gas. I reproduce it below:
Then M = win = (98.57 - 97.36)Bd/2 Chip = 1.22/2 Bd/Chip M = 0.61 Bd/Chip = 0.61 Bd/Chip X 12 Chip/mole = 7.32 Bd/mole The conversion factor for grams, g, to bird droppings is obtained as follows 15 torr = 1.7 Bd/Bs = 1.5 mm of Hg = L.5 em of Hg This is equivalent to a farce exerted by a 1.5 em colomn of mercury of cross-sectional area. 1.0 emP,or a farce of 1.5 em5 X 13.6 g/cm8 = 20.4 g thus The target area of the barrel stave involved is 1 . 3 c m X 1.6cm
=
2.0RcmP I t is obvio~athat Friday, wiaequsinled with o w modern sub script notation, was referring to gavams barium disodinm, BaNal (molecular weight = 183.32).
so that, 20.4 g/cmP = 1.70 Bdf2.08 cmz
Jack E. Bissey Rio Hondo Junior College Whittier, California 90601
Applieatiou for a. grant t,o p w m e this quetion fmther has been made t,o the Ford Foundation.
+
498
/
Journol of Chemical Education
