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Stoichiometry

Stoichiometry

Atomic Mass

Our Mass is Atomic

Remember chemical structures and formulas? Yeah, they're still important. We're going to use them to study the relationship between the mass of atoms and the mass of molecules. We're not talking about the "it's complicated" type of relationship. It's more like the relationship between members in a group of friends—and the friends are different types of elements. These relationships will help us study the composition of compounds and how that composition can change during a reaction. Stoichiometry will seem easy peasy lemon squeezy once we're finished.

The mass of an atom is determined by the number of protons, neutrons, and electrons it contains. But how do we determine the weight or mass of an atom? It's not as if we have a scale small enough to measure such a small weight. (Although we heard the Smurfs are hiding one.) That's not going to stop us, though. We can determine the mass of one atom relative to another atom.

The first step is to assign a mass value to a chosen element to act as a standard. The lucky element is carbon. One atomic mass unit (amu) is defined as a mass equal to one-twelfth the mass of a single carbon-12 atom. Who comes up with this stuff? The carbon-12 atom is the atom that has six protons and six neutrons. The atomic mass is defined as the mass of an atom expressed in atomic mass units.

How can this information help us determine the atomic masses of other elements? Experiments can be done to determine the relative mass of an element compared to carbon. For example, the hydrogen atom is 8.4% as massive as the carbon-12 atom. That means the atomic mass of a hydrogen atom is 8.4% of that of a carbon-12 atom (1.008 amu to be exact).

Still confused? Think of it this way. Let's say all of the scales in the world are busted. What a shame. To fix this predicament, we could create a new scale system that compares our weight relative to others. Let's say we all compare ourselves to The Hulk. We'll say The Hulk weighs exactly one Hulk unit (HU). If it's determined experimentally you weigh relatively 22% of what The Hulk weighs, you would weigh 0.22 HUs.

In other words, it not necessary to put a tiny atom on a scale to weigh it as long as we have a standard we can compare it to. Although we do not know how much the average iron atom's mass is, we do know that it is 56 times as massive as a hydrogen atom. That's where all the atomic masses on the periodic table come from. Bring that up at your next dinner party.



The periodic table: the atomic masses are located under the elemental symbols.

Perhaps you're a regular Sherlock Holmes and you notice the atomic mass given for carbon (C) on the periodic table above is 12.01 amu. Wait a minute, Shmoop, that's not 12.00 amu as we defined it earlier. What gives? Fear not, sleuth—there is a reasonable explanation. The difference is because most elements (including carbon) have more than one isotope. Isotopes are atoms of the same element that contain different number of neutrons in their nuclei. The periodic table shows the average mass of the mixture of isotopes for each element.



Relative abundances of carbon isotopes.

Carbon, for example, has two naturally occurring isotopes, carbon-12 and carbon-13.1 We say naturally occurring because other isotopes of carbon can be made in the lab. While we're at it, you may also see carbon-12 written as 12C or carbon-13 written as 13C. Don't fret. Both notations are correct. The number in superscript or after the dash indicates the mass number (A) of the atom which is the number of protons and neutrons. Not to be confused with the atomic number (Z), which is the number of protons.

http://media1.shmoop.com/images/chemistry/chembook_stoich_graphik_6.png
Protons, neutrons, and numbers, oh my.

We can calculate the average atomic mass of carbon by using the weight of each isotope and the percent natural abundance of each isotope. 

Check out this data for the carbon isotopes1:
  
Isotope Percent Abundance (%) Atomic Mass (amu)
carbon-12 98.90 12.00
carbon-13 1.10 13.00335
  
The average atomic mass can be calculated by multiplying the percent abundance by the atomic mass for each isotope then adding the values together. Check this out:

Average atomic mass of carbon = (percent abundance 12C)(atomic mass 12C) + (percent abundance 13C)(atomic mass 13C)

Average atomic mass of carbon = (0.9890)(12.000 amu) + (0.0110)(12.00335 amu)
= 12.01 amu

Remember to convert the percentages into fractions before doing the calculation or you'll end up with some outrageously incorrect atomic mass. For example, 97.63 percent becomes 97.63/100 or 0.9763.

There are a few ways we can check answers and avoid mistakes on questions that involve calculating average atomic masses. Because there are way more carbon-12 atoms than carbon-13 atoms in nature (98.90% versus 1.10%) we would expect the average atomic mass is closer to 12 amu than to 13 amu. Phew, so far so good. Also, you have a built in answer key in the form of the periodic table. Always double check your answers with those found below the elemental symbols.

Another common problem that might pop up on a quiz or exam is calculating the atomic mass of a particular isotope given its abundance, the mass, and the percent abundance of other isotopes. You also might be asked to calculate the average atomic mass. Using the same equation we used before, we'll solve for a different parameter. 

Check out some data for nitrogen (N)1:
  
Isotope Percent Abundance (%) Atomic Mass (amu)
nitrogen-14 99.632 14.0031
nitrogen-15 0.368 ?
Can you figure out the atomic mass of nitrogen-15? We'll wait.

Average atomic mass of nitrogen = (percent abundance 14N)(atomic mass 14N) + (percent abundance 15N)(atomic mass 15N)

Fill in what you know, and solve for the rest. Remember, you can get the average atomic mass of nitrogen from the periodic table. That value is given as 14.01 amu.

14.01 amu = (0.99632)(14.0031 amu) + (0.368)(atomic mass of 15N)

Do your thing and you get:

Atomic mass of 15N = 15.0001 amu

Brain Snack

The word "stoichiometry" is derived from two Greek words: stoicheion (meaning element) and metron (meaning measure).2

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