Prepare yourselves, mass is in session. Mass is a concept that is ubiquitous but is rarely really examined. What is mass really?
The first time someone asked me that question, I had no idea how to respond. I knew that mass was related to weight, but not how. It turns out that mass is just a measure of how much matter is in an object. In physics, mass is described as the amount of gravitational attraction the object has for neighboring bodies and an objects' resistance to acceleration. Since we're considering the chemistry component only, we're going to stick with the first description (though all are technically correct).
Just for fun (not important): what is the difference between mass and weight? The answer is simple: mass is the amount of matter in an object, weight is that amount of matter multipled by `g`, the acceleration due to gravity.
Since gravity can vary, weight can vary. This is why we weigh less on the moon: `g` on Earth is `9.8 "m"/("s"^2)` whereas on the moon it's `1.6 "m"/("s"^2)`. Weight varies, but mass never does. We say mass is an inherent property of an object. For example, a gallon of water may weigh `8 "lbs"` on Earth and `1.4 "lbs"` on the moon, but its mass is the same everywhere.
We went over atomic mass in the first series of posts. Recall that atomic mass is the total mass of all protons, neutrons, and electrons in any given atom.
| Particle | Charge | Mass (amu) | Mass (g) |
| Proton | +1 | 1 | `1.67*10^(-27)` |
| Neutron | 0 | 1 | `1.67*10^(-27)` |
| Electron | -1 | 0 | `9.11*10^(-31)` |
The mass of an atom of B, boron, would be calculated by adding up the masses of the number of protons, neutrons, and electrons in boron. Since boron's atomic number is 5, it has 5 protons, 5 neutrons, and 5 electrons.
`5m_p+5m_n+5m_e=5(1 "amu")+5(1 "amu")+5(0 "amu")=10 "amu"`
The atomic mass on the periodic table is `10.81 "amu"` though. How do we account for this difference? Well, it turns out that the number of neutrons vary for each element. Instead of all boron atoms having 5 neutrons, some may have 6, some 4, and some 7. Atoms of an element that vary in the number of neutrons are called isotopes. From experiments, we now know that only 20% of boron atoms contain 5 neutrons and the other 80% contain 6! Let's calculate the atomic masses of the new isotope with 6 neutrons.
`5m_p+6m_n+5m_e=5(1 "amu")+6(1 "amu")+5(0 "amu")=11 "amu"`
Let's also average out these isotopes while we're at it. 80% of the atoms have a mass of 11 amu and 20% have a mass of 10 amu.
`0.8(m_11)+0.2(m_10)=0.8(11 "amu")+0.2(10 "amu")=10.8 "amu"`.
That's the atomic mass shown on the periodic table! It turns out that the atomic mass on periodic tables is an average atomic mass of all isotopes for a given element.
A compound is something we'll explore a bit more in the next post, but for now just know that compounds are a combination of several different kinds of atoms. For example, `H_2O`, aka water, is a compound because it combines 2 atoms of H and 1 atom of O. The subscript 2 under the H indicates that there are 2 atoms of H. In order to calculate the mass of these compounds, we simply need to add the mass of all the constituent atoms together. `H_2O`, for example:
`MW_(H_2O)=2m_H+m_O=2(1.008 "g"/("mol"))+(15.99 "g"/("mol"))= 18.006 "g"/("mol")`
NOTE: MW stands for "Molecular Weight," which is just the total weight of the molecule.
Once you've found the molecular weight of a compound, you can treat it the same way as you did for individual atoms. Just like with atoms, the molecular weight of the compound is its conversion factor between grams and moles.
Imagine that you were going to buy a box of donuts and wanted to convey the amount of donuts that you wanted. Since most boxes of donuts contain 12 donuts, you would say something like "I'd like to buy a dozen donuts please." We often substitute certain numbers for terms like "dozen," a "score," etc. The mole is chemistry's equivalent of that. 1 mole is equivalent to `6.022*10^(23)`. This number is also called Avagadro's Number. Chances are if you went into the donut shop and tried to order a mole of donuts, the shop wouldn't be able to fulfill your order. After all, a mole is a huge number.
Can you imagine that many donuts though? Holy mole-y.
The concept of a mole is often a bit difficult to grasp. A mole is just a number, just like a dozen is just a number.
1 dozen C atoms = 12 C atoms
1 mole C atoms = `6.022*10^(23)` C atoms
The mole is useful because it allows us to describe a large number of something. In chemistry we often talk about incomprehensibly large amounts of atoms. Instead of saying "I have `8*10^40 "atoms"` , we can say "I have 20 moles of this atom."
Because of this, we often use the conversion factor `"g"/("mol")`. This conversion factor is equal to the atomic mass. In order words, 1 mole of oxygen weighs the atomic mass of oxygen. This is a pretty cool concept, so let me repeat it: The atomic weight of an element is equal to the amount of `"g"/("mol")` of that element. Let's do an example to illustrate this point.
#1. Convert 5 grams of carbon to moles.
We know from the periodic table that the atomic mass of carbon is `12.011 "amu"`. This means that the conversion factor between grams and moles for carbon is `12.011 "g"/("mol")`. Since we have 5 grams, we simply need to do a unit conversion:
`(5 "g" "carbon")((1 "mol")/(12.011 "g" "carbon"))=0.420 "mol" "carbon"`
Answer: `0.420 "mol" "carbon"`
Avagadro's Number allows us to convert between grams and moles. The mole is the SI unit for any amounts, so by converting from grams to moles, we know the exact number of atoms that we're dealing with. To conclude, here's a humorous picture.
1. What do you get if you cut an avacado into `6.022*10^23` pieces?
A guaca-mole!