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Macroscopic Objects

The number of objects in a mole is a fantastically large number: 6.02 × 10^{23} per mole or

602,000,000,000,000,000,000,000

It has to be this big because atoms and molecules, which the mole is used to count, are so incredibly small. A mole of water molecules has a mass of merely 18 g and a volume of 18 mL. If it helps, that is less than an ounce by weight and just a bit more than a tablespoon by volume. Obviously this is not an impressively large collection of material.

To get an idea of just how big this number is, work with your classmates to calculate reasonable answers to the following questions. Create a brief presentation to share with the whole class at the board. Split into small groups and work on just one question in each group. You may use computer and smart-phone resources to look up numbers that you don’t know. Googling the answer to the stated questions probably will not work!

- Would a mole of average-sized apples fill the entire volume of the Earth if the Earth were hollow? Calculate the volume of a mole of apples in cubic kilometers to make your comparison.
- How much would it cost to buy a mole of paperclips? How does this cost compare to the annual global economic output as measure by GDP (Gross Domestic Product)?
- Assuming paperclips are make of solid iron (Fe) how many metric tons of iron would be need to make a mole of paperclips? How many moles of iron would this be?
- Would a mole of paperclips laid end to end reach all the way to the the other side of the galaxy? Which is larger, the diameter of the galaxy (about 100,000 light-years) or the length of a line of a mole of paperclips?
- If there were a mole of pennies what mass of zinc would be needed to mint them? (Pennies have been 97.5% zinc since 1982). How much mass is that compared to the mass of the Earth? How tall would a stack of a mole of pennies be? Would the stack reach all the way to the Sun from the Earth? Would it reach from the Earth’s orbit to the orbit of Pluto?
- How heavy and how tall would a stack of a mole of sheets of paper be? Would it be taller than the world’s tallest skyscraper? Would it be larger than the diameter of the Earth? Would it be bigger than the diameter of the orbit of Jupiter?
- Say you had a mole of moles of water molecules. In other words, 6.02 × 10
^{23}moles of water. What would be the total mass and volume of this amount of water? Is it more or less than the amount of water in all the oceans of the Earth? Does Jupiter’s moon Europa have more or less water than a mole of moles of water?