The lightest atom is hydrogen; so we can assign it a relative weight of 1.  However, when you have hydrogen gas in a container, it forms small molecules of H₂.  This is also the case with a number of gaseous elements, such as oxygen and nitrogen.  Suppose we then took a box that was big enough so that when you filled it with hydrogen it would weigh 2 grams.  Well actually, I mean that when you fill it with hydrogen it weighs 2 grams more than when it was empty.  The same box, when filled with oxygen would weigh 32 grams more, nitrogen 28 grams.  This has been done, and the box is 22.4 liters big, and since a liter is about the same size as a quart and there are four quarts in a gallon, the box is a bit larger than 5 gallon jugs of milk.  Though any size box would have done; this 22.4 liter size is great because now you get the relative particle weight in grams.

The 22.4 liter box is filled with a mole’s worth of particles.  I have no idea why it is called a mole.

How many particles are in the box?  About 6 x 10²³.

That is a large number.

Years ago I went to a beach in early October.  No one was there and you could see the full length of the horizon in either direction.  That’s a lot of sand.  Is all that sand a larger number than Avogadro’s number?

Curiously enough we can answer this question; for I have counted this number…well not exactly, but more or less.  Here’s what we did.  We got some small packets of salt from the cafeteria.  Crystals of salt are about the same size as sand on the average, but they are more uniform.  Each student had a piece of colored paper and a small magnifying lens.  I measured out a small quantity of salt, say 1 cm³.  I then distributed the salt to the students in the class.  Each student counted the number of grains of salt on their piece of paper.  We added it up…it’s a pretty big number, say 900.  To make our calculations easier, we can call it 1,000.  Now all we have to do is get at the number of cm³ in a beach like the one at Assateague.

It was an unobstructed view; call it 3 miles in each direction.  6 miles is about 10 kilometers or 10,000 meters which is a million cm.  If we let the beach be as wide as a football field is long, we can say it is 100 meters wide, which is 10,000 cm.  Assateague is a barrier beach, so I suspect the sand is a pretty hefty pile.  I don’t know how deep the sand would be, but 200 meters seems generous to me; so we can call it 20,000 cm deep.  This gives us a volume for a hypothetical box, 1 x 10⁶ by 1 x 10⁴ by 2 x 10⁴, or 2 x 10¹⁴ cm³.  Since there are approximately 1 thousand grains of sand to each of these cm³, we get a grand total of 2 x 10¹⁷ grains.  This is a huge number…the total number of grains of sand at an open expanse of beach.  Yet, it is far smaller than Avogadro’s number, some 3 million times smaller.  That is if we counted out Avogadro’s number of grains of sand, we could make 3 million beaches like the one at Assateague!