Going back to the equation we’ve listed here, note how it’s possible to compute the number of atoms in a sample given its mass. So let’s illustrate this important chemistry concept with a word problem:
On our wedding day 7.2 years ago, I gave my ex-wife a gold ring that weighed 3.66 grams. If the ring now weighs 3.49 grams, and she spent eight days on average every year of our marriage having tantric sex with her yoga instructor while I was working overtime, coaching our twin daughters’ soccer team, and generally bending over backwards to create a nurturing home for my family, how many atoms of gold were smeared across her yoga mat over the course of our marriage?
Let’s start with the atomic weight of gold. Who knows the value—anyone?
Yes, you there—uncomfortable looking young man in the Nickelback T-shirt.
Oh no, my dear boy, there’s no such thing as too much information in the world of chemistry. Every detail is crucial to solving the problems like these. What part of the problem do you feel is superfluous? The time frame? The mass of the ring? The fact that my ex-wife is a cheating she-devil who hollowed out our marriage like a pumpkin before carving the hideous, smirking face of her infidelities into it?
I thought so.
Well, since nobody is volunteering it, the atomic weight of gold is 196.96 grams. Next, we simply divide the difference in mass, .17 grams, by this value, and if we want that number as atoms, we just multiply the value by Avogadro’s number.
Avogadro’s number is a constant, meaning that you can always depend on it to be true. Kind of refreshing, isn’t it? Its value doesn’t change on you just because it feels like it. Or move in with its mother when the answer comes out unexpected or wrong. Or get defensive and claim it was “just at the gym” when confronted about why it came home two hours late and smelling like cheap merlot.
That said, let’s keep in mind the resulting number of atoms is limited by the least accurate measuring device we used, which in this case was the wire I hid in her gym bag. Since the recorder only measures to one hundredth of a second—how many digits will we have in our result?
Yes—young lady in front with the three WWJD bracelets and orange skin.
Well, no. Until abstract concepts like “forgiveness” can be rounded to two decimal places, it has no place in our equation here. Or science, for that matter.
So when we finally boil the math down, this comes out to 5.19 × 1020 atoms over 7.2 years, about 1.13 × 1019 of which were rubbed off on the taut, unreasonably perfect body of Donovan, her yoga instructor.
Which is an excellent transition into our next mole-based problem:
If I’ve consumed 12 liters of 1.5 molar single-malt scotch after the papers were finally filed, how many atoms of alcohol have I consumed over the course of this divorce?