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## Chemistry library

# Worked example: Calculating molar mass and number of moles

The molar mass of a substance is the mass in grams of 1 mole of the substance. As shown in this video, we can obtain a substance's molar mass by summing the molar masses of its component atoms. We can then use the calculated molar mass to convert between mass and number of moles of the substance. Created by Sal Khan.

## Want to join the conversation?

- Is molar mass the same as molecular mass, or do they differ?

In some websites they say it's different and some say it's same.(24 votes)- They are not the same thing but many people use the terms incorrectly

Atomic mass and molecular mass should be in units of u (unified atomic mass unit)

Molar mass should be in g/mol (grams per mole)(54 votes)

- I don't understand how Sal finds the molar mass

is there an easier way or a formula to follow to calculate it?(9 votes)- The molar mass of any element is on the periodic table.

For a molecule or compound, simply add up all the molar masses of the elements, taking subscripts into account.

Eg for MgCl2 it would be equal to Mg + 2 x Cl = 24.305 + (2 x 35.45) = 95.21(18 votes)

- why we say NaCl or KCl always why we don't say ClNa or ClK instead.(6 votes)
- Traditionally, the most electronegative element is written last. However, there is no harm in writing ClNa, just as long as you know that chlorine is negatively charged and sodium is positively charged.(14 votes)

- How come at1:57the hydrogen is the only element not rounded off to the 2nd decimal point?(3 votes)
- It is probably because the atomic mass of hydrogen is so small that the extra precision makes a more significant difference when doing calculations with it.(20 votes)

- I don't understand finding the significant figures at the end of the example. What are significant figures, and what determines how many significant figures we round our final answer to? Maybe they've already gone over it and I just don't remember.(7 votes)
- The basic idea is that your answer to a calculation shouldn’t have more significant figures than the initial quantity given has. The initial quantity was 1.52 kg, that has 3 significant figures, so the answer should be given to 3 significant figures too.(7 votes)

- I don't really understand where the 1000 came from(3 votes)
- The question says it’s a 1.52 kg sample of glucose. In order to use the molar mass of glucose (~180 g/mol), the 1.52 kg needs to be converted into g first. That’s why it’s multiplied by 1000.(12 votes)

- How would you solve something like:

What is the mass of

3.5 mol of FeCl2

and

What is the mass of

5 x 10^-4 mol H2SO3(4 votes)- First, you can calculate the molar mass of FeCl2 by adding the molar masses of Fe (55.845 g/mol) and 2 atoms of Cl (2 times (35.446 g/mol). This gives a molar mass of 126.737 g/mol. Since each mole is 126.737 grams, you multiply 3.5 mols by 126.737 grams, giving you 443.58 grams.(8 votes)

- At3:20why did Sal write 180.16, as the answer was 180.156, why didn't he write 180.15?(4 votes)
- It's important to keep in mind significant figures are important for doing calculations in a science like chemistry. After a calculation would be able to use all the digits of the final number as our answer if we only wanted a mathematical answer. But in science we are more conservative with the digits we use because of the precision of our measuring instruments. And the rules we use to judge how many digits are permissible are significant figures, or sig figs.

You should look into sig figs in greater detail, but in this problem Sal is adding three numbers together. For addition the sig fig rule is that we can only have as many decimal digits as do in the calculation number with the lowest number of decimal digits.

So after multiplying Sal is performing this calculation: 72.06 + 84.156 + 96.00, which mathematically would yield 180.156. But because we only have two decimals digits for the 72.06 and 96.00 numbers, our answer is limited to two decimal digits. So we only want the 1 and 5 digits and want to discard the 6. Since the number we're discarding (6) is larger than 4 we round the digit it is next to up one number. So the 5 digit get upgraded to a 6 in the answer. So the final answer should be reported as 180.16 g/mol.

Hope that helps.(5 votes)

- why doesn't Sal just divide 1.52 kg by the atomic mass of an single glucose atom?(3 votes)
- If you follow the maths of the units, it doesn’t yield mols as the answer.

1.52 kg is the total mass of the sample. And since glucose is a molecule we would want the molecular mass, not the atomic mass. The molar mass of 180.16 g/mol is the same value as the molecular mass but with different units; 180.16 amu/molecule. So if we divide the total mass by the molecular mass we get:

1.52 kg/(180.16 amu/molecule), which yields an answer with a unit of (kg*molecule)/(amu), which isn’t mols like what was asked for. You’d have to do quite a lot of conversions to get that previous answer’s unit to mols. The method Sal used in the video would give the correct answer, but with considerably less work.

Hope that helps.(6 votes)

- at0:42,molar mass is equal to mass per mole? Like molar mass of
**H**in gram is 1 gm/1 mole ?(4 votes)- This is true! This is the case because 1 mole of a molecule is equal to 6.02214076×10^23 (avogadros constant) individual molecules. Avogadros constant is specifically chosen so 1u (or 1 dalton) is equal to 1 gram/mole. (see https://www.wikiwand.com/en/Avogadro_constant in the 3rd paragraph)(3 votes)

## Video transcript

- [Instructor] We are asked to calculate the number of moles in a 1.52
kilogram sample of glucose. So like always, pause this video and try to figure this out on your own and this periodic table of
elements will prove useful. All right, now if we're
trying to figure out the number of moles,
remember, mole is really, you can view it as a
quantity of something. If I said a dozen of something, you'd say oh, that's 12 of that thing. If I say a mole of something, I'm saying that's Avogadro's
number of that thing. And so we have a 1.52 kilograms sample of our molecule in question, of glucose so if we can figure out the mass per mole, or another way to think about it, the molar mass of glucose,
well then we just divide the mass of our sample
by the mass per mole and we'll know how many moles we have. So what is the molar mass of glucose? Well to figure that out, and that's why this periodic table of elements is useful, we just have to figure out the molar mass of the constituent elements. So if we first look at carbon, carbon, we see from this
periodic table of elements, has a molar mass of 12.01 grams per mole. We've talked about it in other videos, you could view this 12.01
as a relative atomic mass of a carbon atom, of as the average atomic
mass of a carbon atom, or what's useful, and this is where Avogadro's Number is valuable, if you have Avogadro's Number of carbons, it is going to have a mass of 12.01 grams. So carbon has a molar mass
of 12.01 grams per mole and now we can think about
hydrogen in the same way. Hydrogen has a molar mass
of 1.008 grams per mole, 008 grams per mole. And then last but not
least, we have oxygen here. Oxygen, we can see from our
periodic table of elements, it has a molar mass of
16.00 grams per mole. And so now we have all
the information we need from our periodic table of elements. So the molar mass of
glucose is going to be six times the molar mass of carbon plus 12 times the molar mass of hydrogen plus six times the molar mass of oxygen. So it's going to be six
times 12.01 grams per mole plus 12 times 1.008 grams per mole plus every molecule of
glucose has six oxygen plus six times 16.00 grams per mole. Six times 12.01 plus 12 times 1.008 plus six times 16 is equal to, and if we're thinking about significant figures here, the molar mass of hydrogen
goes to the thousandths place but we only go to the
hundredths for carbon and for oxygen, we're adding
all of these up together so it's going to be 180. I can only go to the hundredths place for significant figures, so 180.16. So that's equal to 180.16 grams per mole. And we could say grams of glucose, C6H12O6 per mole of glucose, C6H12O6 and then we can use this 1.52 kilograms to figure out how many moles we have. So if we start off with
1.52 kilograms of glucose, so that's C6H12O6, well first we can convert it to grams 'cause here, our molar mass
is given in terms of grams, so times, we're going to want kilograms in the denominator and
grams in the numerator, so how many grams are there per kilograms? Well, we have 1,000 grams for every one kilogram. So when you multiply these two out, this is going to give
you the number of grams we have of glucose which would be 1,520 and if you have your
mass in terms of grams, you can then divide by your molar mass or you can view it as multiplying
it by the moles per gram. So for every one mole of glucose, C6H12O6, we have 180.16 grams of glucose, C6H12O6, and this is going to get us, we get 1.52 times 1,000 is equal to, this is the number of
grams of glucose we have, and then we're going to divide by 180.16, divide by 180.16, gives us this number, and let's see, if we
see significant figures, we have three significant figures here, we have five here so we wanna round it to three significant figures, so it will be 8.44 moles of glucose. So our kilograms cancel with our kilograms and then our grams of glucose cancel with our grams of glucose and we are left with
8.44 moles of glucose, moles of C6H12O6. And we are done.