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The great size of the mole can be taught in the following method.

Suppose you wins the powerball and the "pot" is 10,000,000 dollars. You, the winner, decide to verify your winnings by counting every bill. In the first instance the payoff is made in $10-bills. Lets begin the count.

You will count at a rate of 1 number every second. There will be no breaks for food or sleep. To determine how much time this till take, two values must be determined. The first value is the number of bills in the payoff. Since each bill is $10, one divides the total $10,000,000 by $10 and determines there are 1,000,000 bills in the pile. Next one needs to determine the time. We all know or should know that there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in one day. The count rate is 1 per second so to determine the count per day one multiplies these three values together 60x60x24 and the number of seconds, and also the number of bills one can count in 1 day, is 86,400. Next divide the number of bills, 1,000,000, by the number of second per day and the answer is that it will take 11 days 13 hours 46 minutes and 40 seconds of nonstop counting to complete this task.

Next assume the bills are $1-bills. This means there are 10 times as many bills and so it will take 10 times as long. Ten times as long is 115 days 17 hours 46 minutes and 40 seconds. This is how long, nonstop, one must count at a rate of 1 count per second to reach 10,000,000.

Lets assume you are paid in pennies. The total number of pennies
will be 100 x 10,000,000 which equals 1 billion or
1x10^{9} pennies. The time needed to count nonstop to 1
billion counting one number every second would be 1,000,000,000
divided by 86,400 secs/day. The amounts to 11574 days 1 hour 46
minutes and 40 seconds. We can convert the number of days to
years using 365 1/4 (average) per year which is 31 years 251 days
7 hours 46 minutes and 40 seconds.

A trillion is 1,000,000,000,000 and is equal to 1000 billions so the time needed to count to one trillion is 1000 times the time needed to count to 1 billion. It took 31 years 251 days 7 hours 46 minutes and 40 seconds to count nonstop to 1 billion so it will take approximately 31,000 (31x1000) years to count to 1 trillion if one counts 1 per second nonstop. Of course even counting to 110 million let alone 1 billion is near to impossible.

Avogadro's number is properly written as 6.022 x 10^{23}.
The number can be written as 0.6022 x 10^{24} which can be
written as 0.6022 x 10^{12} x 10^{12}. One
should recognize that 10^{12} is 1 trillion. Thus
Avogadro's number, given the term "mole" just as dozen is a term
meaning 12, contains 0.6022 trillion trillions. The time
necessary to count to a number of this size (known as its
magnitude) has not occurred in the entire lifespan of the
Universe as we estimate it. It would take 0.6022 x 1 trillion x
31,000 years or 1.886682 x 10^{16} years to reach a count
of this magnitude.

Chemists determined that molecules also have an average mass and
that by using the mass of one molecule multiplied times the
number of molecules desired, one could determine the mass needed
to obtain the equivalent number of parts. The molar mass, or
mass of a mole, is the sum of the mass of each molecule times the
number of molecules in a mole. The number of molecules (or
atoms) in a mole is constant for all substances and is 6.022 x
10^{23} which is known as Avogadro's Number.

So in chemistry, rather than trying to count the parts, we weigh the appropriate mass of the desired substance just like business weighs small parts to supply larger number of items.