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AVOGADRO’S NUMBER
Look up into the sky on a clear night. You may be able to see about 3.000 stars with the
naked eye, but the number of stars swirling around you in the known universe is
approximately equal to Avogadro’s number 6.02 x 1023. Just think, the known universe
contains approximately a mole of stars. You don’t have to leave the Earth to encounter
such a large number. The water in the Pacific Ocean has a volume about 6.02 x 1023
milliliters and a mass about 6.02 X 1023 grams.
Avogadro’s number is almost incomprehensibly large. For example if one mole of
dollars was given away at the rate of a million dollars per second beginning when the
Earth was first formed some 4.5 billion years ago, would any remain today?
Surprisingly, about three fourths of the original mole of dollars would be left today; it
would take about fourteen billion, five hundred million more years to give away the
remaining money at one million dollars per second.
The impressively large size of Avogadro’s number can give us very important insights
into the very small size of individual molecules. In a single drop of water there are about
1.7 x 1021 water molecules. There are more teaspoons of water in the Atlantic ocean than
there are water molecules in a teaspoon of water.
Purpose: During the activity comparisons will be made to facilitate your comprehension
of both the magnitude of Avogadro’s number and the size of molecules, atoms and ions.
Data will be collected and used as conversion factors to solve problems using
dimensional analysis.
Procedure:
1. Determine the number of seconds one member of your lab group can count a 100 rice
grains using a stop watch.
2. Determine the length of 20 rice grains laid end to end in cm.
3. Determine the space filled volume of 100 rice grains using a 10 ml graduated cylinder.
4. Determine the mass of 100 rice grains.
Rhonda Alexander
Robert E. Lee High School Tyler, TX
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Conclusion:
1. How many years would it take you to count a mole of rice grains?
2. How many years would it take the population of the Earth to count Avogadro’s
number of rice grains?
3. How many rice grains laid end to end would it take to reach the sun?
4. If the nearest star is 4.3 light years away from the earth, how many rice grains laid end
to end would it take to reach the nearest galaxy?
5. Would a mole of rice grains laid end to end come closer to the sun or the nearest star?
6. How deep, in miles, would Texas be covered if a mole of rice grains were poured on
Texas?
7. The annual production of rice is 32,000,000,000,000 Kg. How many years would it
take to grow a mole of rice grains?
8. Assuming man has grown rice for 200,000 years, has there been a mole of rice grown?
USEFUL FACTS AND FIGURES AND IRRELEVANT TID BITS
One light year is 5,865,676,000,000 miles
2.54 cm is an inch
5280 feet are in a mile
A football field is 98.97 meters long
Texas has a surface area of 262,000 miles2
It is 93 million miles to the sun on a clear day at noon
Earth’s population is about 6 billion
MOLE FACT
If a mole of pennies were divided up and given to every person on the earth, each person
would receive person would receive 1.5 X 1016 pennies. Personal spending at a rate of
one million dollars a day would use up each person’s wealth in just over four thousand
years. Life would be comfortable; however, the surface of the earth would be covered in
copper coins to a depth of 420 meters.
Rhonda Alexander
Robert E. Lee High School Tyler, TX
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Teacher Notes Avogadro’s Number
The objective of the activity is to present the magnitude of Avogadro’s number and
molecules and atoms by providing comparisons. The students will determine the number
of seconds they can count 100 rice grains and the mass, length, and space filled volume
of a given number of rice grains. The measurements will be used to perform calculations
involving 6.02 X 1023 rice grains. Students are stunned by the small volume occupied by
100 grains of rice. Imagine their amazement when they calculate that Avogadro’s
number of rice grains will cover the state of Texas to a depth of 12 to 14 miles.
Materials:
• rice
• 50 ml beakers
• metric ruler
• balance
• stop watch
• 10 ml graduated cylinder
Helpful Hints:
• Students will have to use the information listed after the questions to solve some
of the problems.
• Most problems can be solved using factor label. Question number two is a
division problem and question five and eight do not require calculations.
• Students may need assistance with question number six. They need to find the
volume of Avogadro’s number of rice grains in miles3 using factor label method.
After the volume of a mole of rice grains in miles3 is determined they can find the
depth of the rice by dividing the volume by the surface area of Texas.
• After the students answer the questions, pour a mole of a substance into the palm
of your hand to illustrate the size of molecules and atoms compared to rice grains.
Sample Data and Solutions:
100 grains = 95 seconds
100 grains = 1.600 g
100 grains = 2.5 mL (including the space between the grains)
20 grains = 12.5 cm
(Answers will vary)
1. 6.02 x 1023 grains x 95s/100 grains x 1hr/3600s x 1day/24hr x 1yr/365.25 day =
1.8 x 1016yr
2. 1.8 x 1016/ 6 x 109 = 3 .0 x 106 yr
Rhonda Alexander
Robert E. Lee High School Tyler, TX
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3. 9.3 x 107 miles x 5280ft/1mile x 12in/1ft x 2.54 cm/1in x 20 grain/12.5cm =
2.4 x 1013 grains
4. 4.3 Lyr x 5.865676 x 1015miles/ 1 Lyr x 5280ft/1mile x 12in/1ft x 2.54 cm/1in x
20 grain/12.5cm = 6.5 x 1021grains
5. past both but closer to nearest star
6. 6.02 x 1023grains x 2.5 cm3/ 100 grains x 1in3/16.39 cm3 x 1ft3/1728cm3
x 1mile3/1.47197 x 1011 = 3610063.6 miles3
3610063.6 miles3/ 262,000miles2 = 13.7 miles
7. 6.02 x 1023grains x 1.6 g/100 grains x 1kg/1000g 1yr/3.2 x 1013 kg = 301,000yr
8. no
Rhonda Alexander
Robert E. Lee High School Tyler, TX