Illustrating Large and Small Numbers: A Problem for the Birds Chemists in their calculations use very large and very small numbers. While it is not trouble a t all to deal with such quantities, the visualization of them in terms of experience is something else again. The following problem may he of interest to young chemists-to-be. Between Shangri-La and Xanadu there is a mountain of granite. It is a perfect cube one mile on a side. Fate has decreed that a certain family of birds send one of their flock once every one hundred years to sharpen its beak by rubbing it on the mountain. In this process, one tenth of a milligram of the mountain is worn away each time. Haw many years will it take to wear sway the entire mountain? Compare this with Avogadro's Number. Compare the ratio of 1sec t o the total time with the solubility product constantsof HgS and Fe& 1ft3 of granite weighs 160lb 5.2803 X 160 X 454 X 1,000,000 = 1.091 X loz2yr Avogadrd's number = 6.023 X 1 P 3 Mean solar year = 3.156 x 107 mean solar sec (Lange's Handbook of Chemiltry) Hence. the number ofseconds in 1.091 X 1 P 2 y r = 3.44 X loz9 The other data are left for the students to find.
Louis Sattler
Brooklyn College of CUNY Brooklyn, New Yark
(For Solutionseepage 181)
Solution to Problem on Page 180 The solution to the problem of wearing away the granite mountain is: 0.0001 g of mountain is removed every 100 yr, hence 1.OOWl g of mountain is removed every 1,000,000yr We calculate the weight of the mountain in grams, and multiply the result by 1,000,000 to get the number of years needed for the complete job: This is a giant number in comparison with the K,, of HgS, 1.6 x 10-5' and Fe&, 1 X 10-88 because the ratio of 1 sec to 3.44 x 1029 mav be written as 0.291 x 10-Z9. The salubilitv. ~ t are taken from Therald Moeller ~" . r o d u e constants "Qualitative Analysis," McGraw-Hill Co., New Yark, 1st Ed., 1958, p. 518 ~~~
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1 Journal of Chemical Education
