I have the molecular formula for glucose.

And so let's just say that I had a sample

of pure glucose right over here,

this is my little pile of glucose.

I'm not even gonna tell you its mass,

but based on the molecular formula,

can you figure out the percentage of carbon

by mass of my sample?

Pause this video and think about it.

And as a hint, I've given you the average atomic masses

of carbon, hydrogen, and oxygen.

All right, now let's work through this together.

Now, the reason why the amount of glucose doesn't matter

is because the percent carbon by mass

should be the same regardless of the amount.

But to help us think this through,

we can imagine amount.

Let's just assume that this is a mole,

this is a mole of glucose.

So one way we could think about it is,

we say okay, for every mole of glucose,

we have six moles of carbon.

Because every glucose molecule has six carbon atoms.

So we could say, what is going to be the mass

of six moles of carbon divided by

the mass of one mole of glucose?

And once again, the reason why it's six moles of carbon

divided by one mole of glucose is because this,

if we assume this is a mole of glucose,

every molecule of glucose has six carbons.

So it's going to be six times as many carbon atoms

or six moles of carbon.

Now, what is this going to be?

Well, this is going to be equal to,

it's going to be in our numerator,

we're going to have six moles of carbon

times the molar mass of carbon.

Well, what's that going to be?

Well, we can get that

from the average atomic mass of carbon.

If the average atomic mass

is 12.01 universal atomic mass units,

the molar mass is going to be

12.01 grams per mole of carbon.

So times 12.01 grams per mole of carbon.

And notice the numerator will be just left with grams.

And then in the denominator,

what are we going to have?

Well, the mass of one mole of glucose,

for every glucose molecule,

we have six carbons, 12 hydrogens, and six oxygens.

So it's going to be the mass of six moles of carbon,

12 moles of hydrogen, and six moles of oxygen.

So it's going to be what we just had up here,

it's going to be six moles of carbon

times the molar mass of carbon,

12.01 grams per mole of carbon.

To that, we are going to add

the mass of 12 moles of hydrogen.

So 12 moles of hydrogen

times the molar mass of hydrogen,

which is going to be 1.008 grams per mole of hydrogen.

Plus six moles of oxygen,

times the molar mass of oxygen,

which is going to be 16.00 grams per mole of oxygen.

And the good thing is, down here, the units cancel out,

so we're left with just grams in the denominator.

And that makes sense.

We're gonna end up with grams in the numerator,

grams in the denominator, the units will cancel out,

and we'll get a pure percentage at the end.

So let's see, in the numerator,

six times 12.01

is 72.06.

And then in the denominator,

I'm just going to do the pure calculation first,

and then I'm gonna worry about significant figures.

So in the denominator,

we have 72.06 plus,

let's see, 12 times 1.008 is 12.096,

and then we have plus six times 16 is 96.00,

and this will be equal to 72,

if we're just thinking about the pure calculation,

before we think about significant figures,

72.06 divided by,

let's see, if I add 72 to 12, I get 84,

plus 96,

I get 180.156.

Did I do that right?

If I were just to add up everything,

not even think about significant figures.

So we can type this into a calculator

but we should remind ourselves

that our final answer should have

no more than four significant figures.

Because even down here,

if we were just doing this blue calculation here,

that should only have four significant figures,

it would have gotten us to the hundredths place,

and so when we add things together,

we should get no more than the hundredths place,

but even if we rounded over there

for significant figures purposes,

we would still have at least four,

we'd actually have five significant figures.

So this four significant figures

is our significant figures limiting factor.

So we just have to calculate this

and round to four significant figures.

72.06 divided by 180.156

is equal to,

and if we round to four significant figures,

this will be .4000.

So this will be, I'll say,

approximately equal to 0.4000.

Or we could say 40%

or 40.00% carbon by mass

when we round to four significant figures.

And we are done.