Happy Birthday!

Yesterday, my Amedeo Blog turned 2!

Readerships went up over 100% in the second year.

Thank you.  Thank you.

My next mission is to start advertising this project appropriately to get more traffic here!

By The Numbers

                 If I wasn’t a scientist, I would be a baker.  I love making cookies, cupcakes, muffins, bread… I made soft pretzels from scratch once!  Today, I’ll be baking up some strawberry muffins and last night I finished a loaf of white bread while watching the Super Bowl.  Yes, I like to bake.

                According to Alton Brown, cooking and baking are just science, which is the absolute truth.  In many ways, the two disciplines parallel each other.  There’s a fair amount of ingenuity, flying by the seat of your pants, and creativity born of necessity.  Both subscribe to thinking through odd little problems every day, in addition to knowing where “the box” is we’re all supposed to think outside of and breaking it into pieces.  It’s fun!

                Everyone is familiar with the concept of a dozen.  “I want a dozen cookies!” means you’ll be getting twelve.  A baker’s dozen will throw you one extra.  The word is just a shorthand way of saying a number.  Much like score (20), gross (144), and pair (2), dozen means you have twelve of a certain something.  Let’s hope it is cookies and not, say, mice in your apartment.

                Scientists also have a word to mean a particular number of things: mole.  

                Let’s be real – it’s a weird word.  Moles are animals that live in the ground or are sometimes found on the prototypical green-faced witches (with a hair – always a hair!).  However, the word is actually Latin and means “heap” or “pile.”  This makes enormous sense when I tell you that a mole doesn’t stand for a big number – it stands for a HUGE number.  A mole doesn’t mean 1,000 things or even 1 million things.  No, no… it is far larger than that.  

A mole stands for: 602,000,000,000,000,000,000,000 things.

You can’t even quite wrap your mind around how big the number is.  If you had that many cookies, you’d drown in them.

Typically, the number is shorthanded to 6.02 x 10²³.  Meaning, you need to move the decimal 23 places to the right and then you’ll have the number written correctly with all the zeros and commas.  The nerdier of my bunch will refer to October 23^rd as “Mole Day,” but celebrating officially occurs between 6:02 am and 6:02 pm only.  No judgment.

I could go into how this number came to be set (it even involves my favorite Amedeo Avogadro!), but I’m going to leave that to science books.  Instead, I’m going to discuss why it’s so important to think in terms of moles when you’re a scientist.

Think about a situation where you have two proteins that you know bind to each other.  Let’s call them Molecule A and Molecule B.   Molecule A is much larger and heavier compared with Molecule B.  I’ve tried to visually show this in Figure 84.1.

For most experiments, you’d like to add the same number of Molecule A and Molecule B to a tube.  Molecules are too small to see so it’s not like we can count them out like muffins.  But, we can accurately measure mass in a laboratory.  Unlike a cookie that might have more or less batter in it, the mass of one Molecule A or one Molecule B does not change.  Ever. 

Let’s say one molecule of Molecule A weighs 1 g (molecules are obviously much much lighter than 1 g, but this is just an example) and one molecule of Molecule B weighs 0.1 g.  

What happens if we weight out 1 g of each (Figure 84.2)?  How many molecules of Molecule A and Molecule B will we have?  Well, one molecule of Molecule A weighs 1 g so we’ll only have one molecule.  One molecule of Molecule B weighs 0.1 g so we’ll have ten molecules.  Whoops.  That didn’t work out!  We probably should have gone for 10 g of Molecule A (10 molecules) and 1 g of Molecule B (10 molecules).

So what do scientists do?  Do they figure out the mass of one molecule, multiply by how many molecules they want and then weigh that out??

Sort of.  

Atoms and molecules are insanely small so their masses are insanely small.  My examples above are very unrealistic (but I wanted to demonstrate the concept without using super small numbers that would be confusing for you and me).  Weighing out three molecules of something isn’t exactly possible.  But!  Remember how big a mole is?  It’s really freaking big.  Instead of worrying about the mass of one molecule, we worry about the mass of a mole of molecules.  Remember, the mass of one molecule never changes so the mass of 10 molecules will never change and so the mass of 6.02 x 10²³ molecules will never change.

Let’s give some real life examples.

NaCl – table salt.  It’s just chilling in your kitchen right now.  The mass of one NaCl molecule is 9.7 x 10^-23 g (0.00000000000000000000097 g), but a mole of NaCl is 58.44 g.  Which is easier to weigh out?

Acetic acid,HCOOH – vinegar!  It’s catching up with your salt right now.  The mass of one acetic acid molecule is 7.6 x 10^-23 g (0.00000000000000000000076 g), but a mole is 46 g!

                You get the picture.  The mass of a mole of molecules (or atoms) is referred to as its molar mass.

                So, let’s look at our Molecule A and Molecule B example again, but with realistic numbers.

                Pretend the molar mass of Molecule A is 10 g and the molar mass of Molecule B is 2 g.  If you want to weigh out an equal number of molecules for A and B, then weigh out 10 g of Molecule A and 2 g of Molecule B.  How many molecules of each do you have?  6.02 x 10²³.  Instead of saying 6.02 x 10²³ molecules, however, we say “One mole of each.”   Ta-da!  So simple!  Check out Figure 84.3!

                Knowing the molar mass allows us to know exactly how much of a substance to weigh out and tells us exactly how many molecules/atoms/pigeons we are weighing out.  It’s a fabulous little number.

                One last, extra credit problem.  We’ll use the same numbers from Figure 84.3.

                I want an equal number of Molecule A and Molecule B.  I weigh out 25 g of Molecule A.  How many molecules of Molecule A do I have?  How much should I weigh out of Molecule B?  How many moles of each do I have?

                Answer in Figure 84.4!

REFERENCES

Zumdahl, Steven S. “Chemical Principles, 4^th Edition” (2002) Houghton Mifflin Company, Boston, MA.