In this video we are going to talk about how to go from mass to mole fractions, and then
from mole to mass fractions. So why would you want to do something like that, well often
you are given a stream and a molar flow rate, but you are given the compounds and elements
in mass fractions or mass percents, and you need change them in order to figure out exactly
how many moles you have of each element or compound. So as I said we are going to start.
We are going to go from mass to mole fractions, and you are usually given this in fractions
sometimes you are given it in mass percents. It's as you can see you do it the exactly same
way. So let's say we have a compound. That 36 percent by mass of carbon or 0.36,
16 percent hydrogen, 20 percent again by mass of oxygen, and 28 percent or 0.28 mass fraction
of nitrogen. So the first thing you do is assume a basis, now since these are mass
fractions you're going to want to assume your basis in mass. You can choose whatever
you want, but it often makes sense to choose a number like 100, because what that means
now is you have 36 grams of carbon, 16 grams of hydrogen, 20 grams of oxygen, and 28 grams
of nitrogen. The next thing you are going to want to do is change your mass to moles,
and in order to do that you use our old friend the molecular weight or the molar mass. So if
we have 36 gram of carbon, we divide it by its molar atomic mass, 12 grams per mole, and
that gives us 3 moles of carbon in our basis of 100 grams. We do the same for the rest
of our elements, and by the way here I am doing it with elements, but you can do it with
compounds as well. The processes is exactly the same. So this is 16 moles, we have 20
grams of oxygen, we divide it by 16 grams per mole and we get 1.25 moles, and finally our
28 grams of nitrogen is divided by 14 grams per mole which gives us 2 moles. So these
are the moles that are contained in a 100 grams of our compound. Step 3 is to add the moles
together, and if we do that we realize that we have 22.25 moles, and step 4 is to find
the mole fractions, and if you remember the definition of mole fraction. It is the mole,
for example, of carbon divided by total moles. So we are going to do that for each one. We
have 3 moles of carbon. If we divide that by 22.25 we have 0.135 and that's carbon.
For hydrogen we have 16 moles we divide that by 22.25 and we have 0.719 as a mole fraction.
Oxygen, 1.25 moles divided by 22.25 equals 0.056 moles, and finally with nitrogen we
have 2 moles we divide that by 22.25 moles and that equals 0.090. So these are our mole
fractions. One check you should always make is to add up all these mole fractions and
make sure it comes to one. Now we know how to go from mass fractions to mole fraction.
Let's do the same except go from mole to mass fraction, and we are going to start with the
same percentages except remember these are going to be mole fractions. So we have 36
percent carbon, 16 percent hydrogen, 20 percent oxygen, and 28 percent nitrogen. So those
are going to be our mole fractions. So now again we start with assuming a basis, however,
because these are mole fractions, again let's remember mole fractions. We should assume
a basis in moles. So we are going to assume a basis of 100 moles. The second step is to
change the moles to mass. Now here with 100 moles as our basis, that means we have 36
moles of carbon and we multiply it by our molar mass, which is 12 grams per mole, and
we get 432 grams. We do that with hydrogen, 16 moles times 1 gram per mole which gives us
16 grams. Oxygen, 20 moles times 16 grams per mole, which gives us 320 grams, and finally
nitrogen, which is 28 moles we multiply that by 14 grams per mole and we get 392 grams.
Step 3: add all the mass together and if you add all the mass and is in this 100 moles of our
compound we have 1160 grams, and our final step is to find the mass fraction, which for
example is the mass of carbon or hydrogen or oxygen or nitrogen over the total mass. So
let's see what that looks like. We will start with carbon there are 432 grams of carbon
and we divide that by 1160 grams, and our mass fraction is 0.372. Hydrogen, we have 16
grams we divide it by 1160 and our mass fraction is 0.014. Oxygen, 320 grams divided by 1160
is 0.276, and finally with nitrogen we have 392 grams divided by 1160, 0.338. These are
now our mass fractions and if we add them together we end up with 1, and again similarly
our mass and mole fractions are not necessarily the same, and that has to do with the differing
molar masses.