Mole Count - down and out!

(C) - Copyright, 2000 F.W. Boyle, Jr., Ph.D.

The mole is a concept which can be quite confusing to many just introduced to the idea. Many texts and lecturers make the mistake of saying a mole equals such and such mass of a substance. The best way to make the concept of mole understood is to first discuss like terms such as dozen and gross which are terms representing specific counts and then state that such and such a mass of a particular substance contains an equivalent count of the counting unit mole.

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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 1x109 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 1023. The number can be written as 0.6022 x 1024 which can be written as 0.6022 x 1012 x 1012. One should recognize that 1012 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 1016 years to reach a count of this magnitude.

Weighing instead of counting

By now, the reader must be aware that counting large quantities of parts is time consuming. If we had to count all small things out, prices would skyrocket due to labor costs. Bulk small parts which are sold by quantities such as "BBs" are actually measured by weight. The average weight of a "BB" is determined by weighing a number of "BBs" and calculating the average. Then the desired number of "BBs" can be measured by weighing a mass or weight of "BBs" equal to the average weight times the desired number of "BBs".

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 1023 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.