Hi everyone! This is a short workshop on how to convert between grams, moles, and atoms. In our first year chemistry classes, we're going to be using all three of these variables to describe compounds and their quantities, and we are very often going to be converting between them. So it'll be quite handy for us to come into this class knowing the conversion factors between grams, moles, and atoms. In this workshop, we're going to convert between grams to moles, then from moles to atoms, and then finally grams to atoms.
So let's start off with converting grams to moles. The key to this is to use the molecular weight of a substance. That is really what allows us to go from grams to moles. The molecular weight of a compound is given in the units of grams per mole.
And so this gives us a very handy unit conversion factor to go between the mass of a substance in grams to the moles of a substance. And we can apply the same conversion factor setup that we used in the unit conversion workshop that we've looked at previously. So, for example, how many moles are in five grams of CO2?
Well, again, remember, anytime you're going from grams to moles, molecular weight is the key. So I have a little cutout of the periodic table boxes for both carbon and oxygen, so we can calculate the molecular weight of CO2. Remember, molecular weight can be calculated by looking at the atomic mass of each element and the number of atoms in each element.
Carbon, we only have one carbon in CO2, so its mass 12.01 grams per mole plus Now we have two oxygens, so it's going to be two times the mass of oxygen, 16.00 grams per mole, giving us a final weight, a final molecular weight of 44.01 grams per mole for CO2. Now we can use this again as our conversion factor to convert between grams to moles. recall from the unit conversion, we always set it up where we have our original measurement, our five grams. We multiply it and we set up our fraction. What we want in the end goes in the numerator.
What we want is moles. What we want to get rid of goes in the denominator. And what we want to get rid of is grams.
So our grams can cancel. Now our conversion factor that we use is our molecular weight. For every one mole, there are 44. 0.01 grams.
That is the weight of CO2. Putting this into our calculator, we get a moles of CO2 of 0.11 moles of CO2. And that's how we convert between grams to moles. Let's do another example. How many moles are in 6.3 grams of sucrose C12H22O11?
Again, first step is to calculate the molecular weight of sucrose, 12 carbon atoms, so 12 times its individual weight, 12.01 grams per mole, plus 22 hydrogens, so 22 times the atomic weight of hydrogen 1.008 grams per mole. And then finally, 11 oxygen. So 11 times 16.00 grams per mole, giving us an overall molecular weight of 342.3 grams per mole. Now that we have the molecular weight, we can set up our unit conversion, just like we've done previously. 6.3 grams.
We set up our fraction. What we want is moles. What we want to get rid of is grams.
Looking at our molecular weight of sucrose for one mole, 342.3 grams. Typing this into our calculator, we get 0.018 moles of sucrose. So hopefully you see from these two examples that converting from grams to is quite simple and it really solely relies on molecular weight.
If you have that, you can very easily convert between grams and moles. Once we have moles, the next conversion that we can do is converting from moles to atoms. And the key to this is Avogadro's number. Avogadro's number tells us that in one mole, there are 6.022 times 10 to the 23 atoms. So we can use this now as our conversion factor to go from moles to atoms.
And let's try out an example. How many atoms are there in three moles of sucrose C12H22O11? Well, again, we're going to set up our unit conversion factor.
fraction just like we've done in the past. We take our original measurement, three moles, we set up our fraction. What we want is atoms.
What we want to get rid of is moles. So this way our moles will cancel. Now for this, let's recall Avogadro's number. One mole equals 6.022 times 10 to the 23 atoms.
This is what we're going to use to input into our conversion fraction. There are 6.022 times 10 to the 23 atoms in one mole. Doing this math, 3 times 6.022 times 10 to the 23 gives us 1.807 times 10 to the 24 atoms. And that's it. Converting from moles to atoms really is dependent on Avogadro's number.
That is the key. The last exercise I want to go through is just tying this all together and going right back to the beginning with grams, but going from grams to atoms now. Now for this, the conceptual plan that we're going to use is we're going to go from grams to moles and remember in order to do this we're going to use the molecular weight and then from moles we can convert to atoms and for this we're going to use Avogadro's number. So that is our conceptual plan.
So let's start off first our step one will be to calculate the number of moles And step two will be to calculate the number of atoms. So we have five grams of methane, CH4. We need to calculate the molecular weight of methane, one carbon, so 12.01 grams per mole, plus four hydrogens, so four times 1.008 grams per mole.
And that gives us a molecular weight of 16.04 grams. per mole and this is for methane of course. Now let's convert from grams to mole.
We're going to set up our unit conversion. 5.0 grams. What we want is moles.
What we want to get rid of is grams. We use our molecular weight as our conversion factor. In one mole there is 16.04 grams.
This gives us an amount of moles of 0.31 moles C. H4. Now that we have moles, we can undergo step two.
We can set up another conversion factor, 0.31 moles. What we want is atoms. What we want to get rid of is moles. And for this, we use Avogadro's number.
Avogadro's number tells us 6.022 times 10 to the 23 atoms in one. mole. Putting that into our calculator and we get 1.87 times 10 to the 23 atoms. And that is our final answer.
So in this workshop, we've gone from grams to mole using the molecular weight, and then from moles to atoms using Avogadro's number.