This is a good way to find out about the size of Avogadro's Number but also to properly deal with scientific notation on a calculator.





You have 6.02 x 1023 dollars. If you spend this money at the rate of one billion (1 x 109) dollars per second, how long, in years, will it last? Place your estimate here:___________________________







Here is one solution!

Step 1

Determine how many seconds will be required to spend 6.02 x 1023 dollars at the rate of 1 x 109 dollars pers second. 6.02 X 1023 dollars = 6.02 x 1014 seconds required to spend all of the money.

1 X 109 dollars.second-1





Step 2

Determine the total number of seconds in one year. 60 seconds X 60 minutes X 24 hours X 365 days = 31,536,000 seconds in one year.

minute hour day year





Step 3

Divide the number of seconds required to spend $6.02 X 1023 by the number of seconds in a year. 6.02 X 1014 seconds = 1.91 X 107 years

31,536,000 seconds.year-1





It would take over 19 million years to spend Avogadro's number of dollars if the money were spent at the rate of one billion dollars per second.





If the money was to earn interest at the rate of one percent per year ($6.02 X 1021), it would be impossible to spend all of the money at the rate of one billion dollars per second (6).





Other examples of Avogadro's number :

32,600 chess boards would be required to accomodate Avogadro's number of hydrogen atoms, if, on each board, a person could place one atom on the first square, two on the second, four on the third, eight on the fourth, and so on (1).





If Avogadro's number of sheets of paper were divided into a million equal piles, each pile would be so tall that it would stretch from the Earth to the Sun and beyond. (2)





A CRAY S-1 super computer with a nominal speed rating of 1,000 mips (millions of instructions per second) would require 1.9 million years to process Avogadro's number of steps (3).





Avogadro's number of pennies placed side by side would stretch for more than a million light years (4).





Counting at a rate of one atom per second, for 48 hours per week, it would take the entire population of the world 10 million years in order to reach Avogadro's number (5).





In order to obtain Avogadro's number of grains of sand, it would be necessary to dig the entire surface of the Sahara desert (whose area of 8 X 106 km2 is slightly less than that of the United States) to a depth of 2 metres (6).





References:

(1) D. Todd, "Five Avogadro's Number Problems", Journal of Chemical Education, 62 , 76, 1985.

(2) D. Kolb, "The Mole", Journal of Chemical Education, 55 , 728-732, 1978.

(3) P.S. Poskozim, J.W.Wazorick, P. Tiempetpaisal and J.A. Poskozim, "Analogies for Avogadro's Number", Journal of Chemical Education, 63 , 125-126, 1986.

(4) F.A. Bettelheim and J. March, Introduction to General, Organic and Biochemistry, 2nd edition, New York, W.B. Saunders, 1988.

(5) W.L. Masterton, J. Slowinski and C.L. Stanitski, Chemical Principles, 6th edition, New York, W.B. Saunders, 1985