How Big is a Mole - Ms Beaucage
How Big is a Mole?
1) How far would a mole of paper clip reach?
Info:
1 mole: 6.02 X 1023 paperclips
Paper clip: 3 cm
Distance Earth-Sun: 1.496 X 108 km
Distance Sun-Centre of Milky Way: 2.77 X 104 ly (light year)
Diameter of Milky Way: 1 X 106 ly
Light year (ly): distance traveled by light in a year
Speed of light: 3 X 105 km/s
Universe: 1 X 1011 galaxies
1 paper clip = 3 cm X 1 km = 3 X 10-5 km
105 cm paperclip
1 mole of paper clips = 6.02 X 1023 paperclips
mole
6.02 X 1023 paperclips X 3 X 10-5 km = 2 X 1019 km
mole paperclip mole
d(Earth-Sun) = 1.496 X 108 km
( a mole of paper clips is longer than distance between Earth and Sun
distance of one light year (ly) in km:
3 X 105 km X 3600 s X 24 hr X 365 days = 9.46 X 1012 km
s hr day yr yr
d(Sun-edge of Milky Way) in km:
1 X 106 ly - 2.77 X 104 ly = 4.7 X 105 ly = 4.5 X 1018 km < 2 X 1019 km
2
(radius)
d(Sun-centre of Milky Way) in km:
2.77 X 104 ly X 9.46 X 1012 km = 2.67 X 1017 km < 2 X 1019 km
ly
( a mole of paper clips is longer than distance between Sun and the centre of the Milky Way
a mole of paper clips is longer than distance between Sun and the edge of the Milky Way
2) What is the volume of a mole of drops? Would it fill up the Pacific Ocean?
Info:
1 ml =1 cm3 = 20 drops
Pacific Ocean covers an area of 1.56 X 109 km2 with
an average depth of 5 km
Volume of a mole of drops:
6.02 X 1023 drops X 1 cm3 = 3.01 X 1022 cm3 X 1 km3
mol 20 drops 1015 cm3
= 3.0 X 107 km3
Since 1 cm3 X 1 km3 = 10-15 km3
1015 cm3
Volume of the Pacific Ocean: (area X depth)
1.56 X 109 km2 X 5 km = 7.8 X 109 km3
How much bigger is the Pacific Ocean?
7.8 X 109 km3 = 259 times bigger than a mole of drops
3.0 X 107 km3
3) Suppose you count 100 numbers per minute. At that rate, how long would it take you to count to 6.02 X 1023?
6.02 X 1023 numbers X 1 min X 1 hr X 1 day X 1 yr
100 numbers 60 min 24 hr 365 days
= 1.1 X 1016 years
Big Bang: 1 x 1010 years ago
( mole of numbers = 1.1 X 1016 years = 1 000 000 times bigger
Big Bang 1 x 1010 years
4) Suppose that an average page contains 1000 letters. How many pages would be in a book containing a mole of letters?
1 mole of letters: 6.02 X 1023 letters
6.02 X 1023 letters X page = 6.02 X 1020 pages
1 1 X 103 letters
Suppose that a book contains 600 pages: 1 X 1018 books
5) Suppose that you are Robin Mole the philanthropist. You have one mole of pennies to evenly give to every person on Earth. How rich would each person be? Give your answer in dollars.
World Population: 7 400 000 000 (year 2014)
1 penny = 0.01 dollar
6.02 X 1023 pennies X 1 dollar X 1 = $ 8.1 X 1011
100 pennies 7.4 X 109 persons person
$ 810 000 000 000
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