Module 5ii: What is a mole?

Look at the web site:

A Mole is a number!

It is Avagadro’s number!


What is Avagadro’s Number?

Why do the chemist worldwide have National Mole Day:

6:02 am to 6:02 pm on October 23rd each year?






Mathematical Connections to a mole:


On the above web site there are many analogies to illustrate a mole:

Analogies to illustrate the size

of Avogadro's number

  1. One mole of high school textbooks would cover the USA to a depth of about 320 km (200 miles)
  2. Water flows over Niagara Falls at about 650,000 kL (172,500,000 gallons) per minute. At this rate it would take 134,000 years for one mole of water drops (6.02 x 1023 drops) to flow over Niagara Falls.


  1. Avogadro's number (6.02 x 1023 ) is the approximate number of milliliters of water in the Pacific Ocean (7 x 108km3 or 7 x 1023 mL). (Analogy by M. Dale Alexander, Gordon J. Ewing, and Floyd T. Abbott, 1984.)
  2. If one mole of particles the size of sand grains were released by the eruption of Mount St. Helens, they would cover the entire state of Washington to the depth of a ten-story building. (Analogy attributed to Glenn Crosby.)
  3. Analogies by A. Truman Schwartz and Lucy T. Pryde:

f.       One mole of marshmallows would cover the USA to a depth of 105,000 km (6500 miles). NOTE: The volume of a marshmallow is estimated as 16 cm3 (1.0 in3 ). The area of the USA is 9.32 x 10 6 km2 or 3.6 x 10 6 mi 2.

g.      If an Avogadro number of pennies were distributed evenly among the 4.9 x 109 human inhabitants of earth, each man, woman, and child would have enough money to spend a million dollars every hour-day and night-and still have over half of it unspent at death.

h.      One guacamole is the amount of taco chip dip that can be made from an Avogadro number of avocados-plus appropriate quantities of tomatoes, onions, and chili. A train stretching to the North Star and back 2-1/2 times would be required to transport one guacamole. NOTE: This assumes that the volume of one standard avocado (pit removed) is 278 cm 3 and that other ingredients make up 25% of total volume. The average coal car has a capacity of 110 kL (4000 ft 3 ) and is 16 m (53 ft) long. The North Star is 680 light years distant.

i.        Suppose the Greek god Zeus, after observing the Big Bang 15 billion years ago, became bored and decided to count one mole of atoms. Zeus is omnipotent. He can count very fast (one million atoms per second) and, of course, never sleeps. He has currently completed over three-fourths of the task, and will be finished in just another four billion years.

j.        One mole of moles (animal-type), placed head to tail, would stretch 11 million light years and weigh 9/10 as much as the moon. NOTE: Each mole is assumed to be 17 cm long with a mass of 100 g. Speed of light = 3.0 x 10 8 m/s. Mass of moon = 6.7 x 1022 kg..

k.      One mole of marbles, each 2 cm in diameter, would form a mountain 116 times higher than Mount Everest. The base of the marble mountain would be slightly larger than the area of the USA. NOTE: Marbles are assumed to have hexagonal closest packing and the mountain has a cone of angle 30 degrees;. Area of USA = 9.32 x 106 km2.

More Analogies & Calculations for you to do:

Avogadro Number Analogies

Avogado's Number is so large many students have trouble comprehending its size. Consequently, a small sidelight of chemistry instruction has developed for writing analogies to help express how large this number actually is.

Before looking over the following examples, here's a nice YouTube video about the mole and Avogadro's Number.

1) Avogadro's Number compared to the Population of the Earth:

We will take the population of the earth to be six billion (6 x 109 people). We compare to Avogadro's Number like this:

6.022 x 1023 divided by 6 x 109 = approx. 1 x 1014

In other words, it would take about 100 trillion Earth populations to sum up to Avogadro's number.

If we were to take a value of 7 billion (approximate population in 2012), it would take about 86 trillion Earth populations to sum up to Avogadro's Number.

2) Avogadro's Number as a Balancing Act:

At the very moment of the Big Bang, you began putting H atoms on a balance and now, 19 billion years later, the balance has reached 1.008 grams. Since you know this to be Avogadro Number of atoms, you stop and decide to calculate how many atoms per second you had to have placed.

1.9 x 1010 yrs x 365.25 days/yr x 24 hrs/day x 3600 sec/hr = 6.0 x 1017 seconds to reach one mole

6.022 x 1023 atoms/mole divided by 6.0 x 1017 seconds/mole = approx. 1 x 106 atoms/second

So, after placing one million H atoms on a balance every second for 19 billion years, you get Avogadro Number of H atoms (approximately).

3) Avogadro's Number in Outer Space:

If all the matter in the universe were spread evenly throughout the entire universe, there would be approx. 1 x 10¯6 nucleons per cm3. We could do several things with that. For example:

a) What volume (in cm3) of space would hold Avogadro Number of nucleons?

6.022 x 1023 nucleons/mole divided by 1 x 10¯6 nucleons/cm3 = 6.022 x 1029 cm3/mole

b) How many Earths would equal this volume of space (take Earth's radius to be 6380 km)?

4) Avogadro Number of Coins:

Take a common coin of your country and stack up 30 of them. Measure the height in cm and divide by 30. You now have the average height of one coin in centimeters.

a) How high in cm is a stack of Avogadro Number of that coin?
b) How many light years is this? (Light travels 3.00 x 108 km per second)
c) How many "round-trips" is this to the moon? (Go there and back = one round-trip. The Earth-Moon distance (measured center-to-center is a bit more than 384,000 km.)

Another way to express this type of problem: If you placed one mole of pills (coins, etc.) with a diameter of 1.00 cm side by side, how many trips around the Sun's equator can you make?




1) Convert diameter of Sun from km to cm:

(1.392 x 106 km x (105 cm / 1 km) = 1.392 x 1011 cm

I looked up the diameter of the Sun online.

2) Calculate circumference of sun:

c = πd

c = (3.14159) (1.392 x 1011 cm)

c = 4.3731 x 1011 cm

3) Calculate trips around the Sun:

Since each pill = 1.00 cm, one mole of them covers 6.022 x 1023 cm

6.022 x 1023 cm / 4.3731 x 1011 cm

1.377 x 1012 times around the Sun.

5) Avogadro Number of Pieces of Paper:

If you had a mole of sheets of paper stacked on top of each other, how many round trips to the Moon could you make? (Hint: a stack of 100 sheets of ordinary printer paper is about 1.0 cm.)

You Solve:









6) The area of the state of California is 403932.8 km2. Suppose you had 6.022 x 1023 sheets of paper, each with dimensions 30 cm x 30 cm. (a) How many times could you cover California completely with paper? (b) Suppose each sheet of paper is 1 mm thick. How high would the paper be stacked?

You Solve:








7) If you drove 6.022 x1023 days at a speed of 100 km/h, how far would you travel?

You Solve:







8) If you spent 6.022 x 1023 dollars at an average rate of 1.00 dollar/s, how long in years would the money last? (Assume that every year has 365 days.)

You Solve:


Now it is your turn!

Find 10 more analogies to illustrate a mole using the web and write each in your lab note book or on this report form for a take home experiment for 10 points. Site each web site with the complete URL as I have done above. Using the Word Doc on Blackboard you may cut and paste your 10 analogies.


Can you also find illustrations of a mole?


Turn in the copy below when you take M-5ii exam.



Avogadro & The Mole


Title: What is a Mole?

All Roads in Chemistry Lead to a Mole!





Supplemental Online Lab    10 Points

Title: What is a Mole?

1.  A mole is a number!

2.  A count of objects (entities)!

3.  It is Avagadro’s Number.

What is Avagadro’s Number?

6.023 x 1023 entities  (Atoms, Ions, Molecules, electrons, protons)



To explain to a person the concept of Avagadro’s number into some kind of analogy measurement that the lay person can understand.

Analogy #1:



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Now for extra credit (up to 5 points):

You create an analogy that you can use to explain to someone.

You must show your work with dimensional analysis, like in the Roll-Mole analogy. (Please do not use the web)