Mass and Mole Fractions (Conversions)

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.

17 thoughts on “Mass and Mole Fractions (Conversions)

  1. Thank you very much. It is always nice to find a straightforward and short explanation when I need to fresh knowledge.

  2. How to solve a gas sample contain argon and oxygen gases and has a total pressure of 2.35atm. IF the partial pressure of argon is 865 torr, what is the mole fraction for each of the gases in the mixture? Help

  3. need assistance with converting mass % composition to mole fraction and set up tables of composition, break temperature, arrest(halt) temperature for diphenylamine at 100% adding 10g naphthalene, 83.3% adding diphenylamine, 66,7% adding diphenylamine please assist.

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