Atomic weights

Oh, what about those trees and the atmosphere?

What's a mole?

Look at a table of the elements, and note the atomic weights of different elements. These have units of grams/"mole". E.g. hydrogen (~ 1 g/mole), carbon (atomic weight 12 g/mole) and oxygen (atomic weight 16 g/mole)...


Andi (Flickr)
$$1 \text{ mole} = 6.02 \times 10^{23} \text{ particles}$$ where the particles can be atoms, or can be molecules. 1 mole is approximately the number of atoms in one gram of hydrogen atoms. (It's precisely defined in terms of the Carbon-12 isotope...

The atomic mass of an element is the mass of one mole of atoms of that element.

And The molecular mass (sometimes called the "molecular weight") of a pure compound is the mass of one mole of molecules of that compound.

Here's an equation for making carbon monoxide: $$C+O\to CO$$

  • To make one molecule of carbon monoxide, we need one atom of carbon, and one of oxygen.
  • To make 10 molecules of carbon monoxide, we need 10 atoms of carbon, and 10 atoms of oxygen.
  • To make one mole of carbon monoxide molecules, we need one mole of carbon atoms, and one mole of oxygen atoms.
  • To make one mole of carbon monoxide molecules, we need one mole of carbon atoms (weighs ~12 g) and one mole of oxygen atoms (weighs ~16 g). We've made one mole of carbon monoxide, which weighs 12+16=28 grams.
  • To make 280 grams of carbon monoxide, we'd need 120 g of carbon and 160 g of oxygen.
  • The ratio of weights of oxygen and carbon in any quantity of carbon monoxide is 160:120 = 16:12 = 4:3.

So, if I decompose a certain amount of carbon-monoxide into its elements, and if I find I have 2 pounds of carbon, I know that I must have made 2 lbs*4/3=2.67 lbs of oxygen.

And in this case, I must have started with 2+2.67=4.67 pounds of carbon-monoxide.

A sample of hydrogen weighs 2 lbs. The same number of atoms of carbon would weigh how many lbs?

Tip:
Think of a chemical reaction as a relation between moles of substances.

We can think of reading this chemical equation... $$C+2H_2\to CH_4$$ as:
"1 mole of $C$ and 2 moles of $H_2$ combine to form 1 mole of $CH_4$. "

Then use the atomic weights--$C$: 12 g/mole and $H$: 1 g/mole-- to re-write this in terms of grams:
" 12 g of $C$ and 2$\times (2\times 1$ g) of $H$ combine to form...12+4*1=16 g of $CH_4$. "

Which is heavier? 1 mole of $CO_2$, or 1 mole of nitrogen gas ($N_2$)?

Practical application: Where do you run if a volcano explodes nearby, spewing $CO_2$, as they are wont to do? [See the sign greeting hikers on the Tongariro Crossing near "Mt. Doom" (Ngauruhoe) in New Zealand.]

Examples of what happens if you have equal weights of oxygen and hydrogen, say, one pound each. How much of what left over.

Applications

  1. What's the ratio of weights of a molecule of water ($H_2O$) and a molecule of nitrogen gas ($N_2$)?

  2. What is the ratio of weights of 1 mole of natural gas, $CH_4$ to 1 mole of $CO_2$?
  3. Balance the chemical reaction: $$\text{_1_}CH_4 +\text{___}O_2 \to \text{___}CO_2+\text{___}H_2O$$

    $$_1_CH_4 +_2_O_2 \to _1_CO_2+_2_H_2O$$

  4. Using the chemical reaction above, how many moles of carbon-dioxide are produced for each mole of $CH_4$?
  5. By figuring out the atomic weights of those moles... How many tons of carbon-dioxide are produced for every ton of natural gas burned?
  6. If oxygen and hydrogen combine into the compound H${}_2$O, then 1 pound of hydrogen would fully react with how many pounds of oxygen to form water?
    1. 1/2 pound
    2. 2 pounds
    3. 4 pounds
    4. 8 pounds
    5. 16 pounds

"Ideal gases"

In class, I made use of another useful observation:

At the same temperature and pressure, equal volumes of gas contain the same number of molecules, no matter what kind of gas.

For example, at one atm pressure, and at $0^o$C, one mole of just about any gas occupies 22.4 liters.

Image credits

D Searls