Confessions of a Geeky Dad

I am stuck inside on a rainy Sunday on this Match Eve trying not to think too much about the 24 1/2 hours that remain until I find out if I matched into a residency program. Fortunately I have Chemistry to keep me company.

No not drugs. Chemistry- as in High School Chemistry.

Kaitlyn was having a little trouble with some chemistry homework and came to yours truly looking for help. Poor her. I have a reputation for handing out the "bonus plan" when I help with homework. Today's Bonus Lecture was about Avagadro's number but more on that later.
Invariably, I go off on some topical tangent until they get that glazed-over look in their eyes. utter, "Thanks, Dad", quickly gather their books, and dart out of the room like they stole something.
I admit it. I can be a bit of a geek and I still get excited about some concepts that I think are pretty cool and it truly is a thrill for me to see the look in their eyes when they finally understand something for the first time or look at something in a new way. Anyway...

Her class is working on determining empirical formulas given percent composition.

An example:
Calculate the empirical formula of a compound composed of 38.67 % Carbon, 16.22 % Hydrogen, and 45.11 %Nitogen  (For those that are interested a brief explanation follows the break.)


During my explanation I asked if she was familiar with Avagadro's Number and I was happy that she was. Of course I felt the need to fill in some of the blanks and connect a few dots. I found a paper I wrote on the subject from back in my undergraduate chemistry class and read some of it to her. The little kid in me loves the visualizations and examples used when trying to understand the enormity of scale that 6.02 X10²³ represents. Here are some of my favorites:

• A mole of beer cans would cover the surface of the earth to a depth of 200 miles!
• A mole of un-popped popcorn kernels would cover the suface to a depth of 9 miles!
• If you covered the entire state of Texas (roughly 260,000 sq mi.) with fine sand- there would be 1 mole of sand grains.
• Counting at 10 million per second...it would take 2 Billion years to count up to 1 mole

and my favorite:

• In a 8oz cup of water, there are more molecules of water present than there are cups of water in the entire Atlantic Ocean. (roughly 5000 times more)

Example problem:

Calculate the empirical formula of a compound composed of 38.67 % Carbon, 16.22 % Hydrogen, and 45.11 %Nitogen.

First, it is important to realize that the percentages given represent mass. That is, the compound consists of 38.67% Carbon by mass. 

Since different atoms have different masses (see periodic table) we first have to establish how many of each atom is represented by its particular percentage of mass.

Once we know how many of each atom (how many moles) are present, all that remains to do is observe the mole ratio in order to arrive at the empirical formula.

Since the percentages are literally parts of 100- we can use 100 of anything 100 tons, 100 pounds, or 100 kilograms. Since the molar masses are in the grams scale it makes sense to use 100 grams. So:

In our problem we see that of the total mass of the molecule, 38.67% is carbon- said another way for every 100g of molecule, there is 38.67 grams present. The same goes for Hydrogen and Nitrogen respectively.

Now we have to figure out how many atoms( in moles since there are so very very very many) are present in each percentage of mass. Let's take Carbon- we know that 38.67g are in each 100g of molecule. Looking up the molar mass (how much 1 mole of Carbon weighs) we see that 1 mole of Carbon = 12.01g. some quick arithmetic:

38.67g         1 mol
              X    -----------   =  3.220 moles
                    12.01 g

Doing the same for Hydrogen and Nitrogen we get 16.09 moles Hydrogen and 3.219 moles of Nitrogen.

Our formula right now would be C_3.22 H_16.09 N_3.219


using a greatest common factor of 3.2 we simplify to: CH₅N