The Mole

1. The Mole Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second?

2. Background: atomic masses • Look at the “atomic masses” on the periodic table. What do these represent? • The atomic mass of C is 12 (atomic # is 6) • We know there are 6 protons and 6 neutrons • Protons and neutrons have roughly the same mass. So, C weighs 12 u (atomic mass units). • What is the actual mass of a C atom in grams? • Answer: approx. 2 x 10-23 grams; 0.00000000000000000000002 g We have two problems here! • Atomic masses do not convert easily to grams • They can’t be weighed (they are too small)

3. What Is a Mole and Why Are Moles Used? • A mole is simply a unit of measurement. Units are invented when existing units are inadequate. Chemical reactions often take place at levels where using grams wouldn't make sense, yet using absolute numbers of atoms/molecules/ions would be confusing, too.

4. What Is a Mole and Why Are Moles Used? Cont’d • Like all units, a mole has to be based on something reproducible. • A mole is the quantity of anything that has the same number of particles found in 12.000 grams of carbon-12. That number of particles is Avogadro's Number, which is roughly 6.02x1023. • A mole of carbon atoms is 6.02x1023 carbon atoms. A mole of chemistry teachers is 6.02x1023 chemistry teachers.

5. Food for thought… • It's a lot easier to write the word 'mole' than to write '6.02x1023' anytime you want to refer to a large number of things! Basically, that's why this particular unit was invented!! • Okay... you may not find it too convenient when you are first learning how to use it, but once you become familiar with it, a mole will be as normal a unit as, say, a dozen or a byte.

6. The Mole Withtheseproblems,whyuseatomicmassatall? • Masses give information about # of subatomic particles • It is useful to know relative mass E.g. Q - What ratio is needed to make H2O? A - 2:1 by atoms, but 2:16 by mass • It is useful to associate atomic mass with a mass in grams. It has been found that 1gH,12gC,or 23gNahave6.02x1023atoms • 6.02 x 1023 is a “mole” or “Avogadro’s number” • “mol” is used in equations, “mole” is used in writing; one gram = 1 g, one mole = 1 mol.

7. Mollionaire Q: how long would it take to spend a mole of $1 coins if they were being spent at a rate of 1 billion per second? A: $ 6.02 x 1023 / $1 000 000 000 = 6.02 x 1014 payments = 6.02 x 1014 seconds 6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes 1.003 x 1013 minutes / 60 = 1.672 x 1011 hours 1.672 x 1011 hours / 24 = 6.968 x 109 days 6.968 x 109 days / 365.25 = 1.908 x 107 years A: It would take 19 million years