# Mathematical relationship between avogadro number and 1 mole

### Avogadro's law - Wikipedia

1 mole of atoms = × atoms = Gram atomic mass or Molar mass of Relationship between mole, number of particles and mass and. the volume occupied by 1 mole of a gas at STP of that substance Describe the relationship between Avogadro's number and one mole of any substance. What is the mathematical relationship between atomic mass units 1 mole of C atoms = x 10 to the 23rd (Avogadro's number) of atoms.

There are kind of more Byzantine definitions of a mole. This actually is not-- actually, let me copy and paste it from Wikipedia. This is Wikipedia's definition of a mole. And you hopefully at the end of this video you'll see that they're equivalent. But if you're just getting exposed to the concept, this to me, it's just not an easy concept. Basically, a "a mole is defined as the amount of substance of a system that contains as many elemental entities as there are atoms in 12 grams of carbon So if you just take the last part, atoms in 12 grams of carbon So that means that there are 1 mole of carbon let me write it like that-- carbon There are 1 mole of carbon 12 atoms in 12 grams of carbon.

And so that's why a mole is useful. So I could have just instead of writing 1 mole, I could have replaced this as there's 6. How do you figure that out? Or I guess, what else does this mean? I mean, we just added in carbon, they said it's the amount of substance of any molecule, if you convert between atomic mass units and grams.

This I find very confusing. How can we apply this in other places? So the first thing to realize is a mole is just a way of translating between grams and atomic mass units. One carbon 12 atom is what? What's its mass number? That's why it's called carbon 12 instead of carbon So its mass is 12 atomic mass units. So if you have something that has a mass of 12 atomic mass units and you have a mole of them, or you have 6.

So another way to think about it is 1 gram is equal to 1 mole of atomic mass units. I'll write amu's like that. Or you can write 1 gram is equal to 6. And the reason why this is useful-- and it's kind of addressed in this Wikipedia definition there-- is it helps us translate between the atomic world-- where we deal with atomic mass units and we deal with, oh, we've got an extra neutron now, let's add one to our atomic mass number-- and translating between that atomic world and our everyday world where we deal in grams.

And just so you know, a gram is still a pretty small amount of mass.

A kilogram is about 2 pounds. So this is not much.

### The mole and Avogadro's number (video) | Khan Academy

So there's a ton of atoms in a very small amount of-- in 1 gram of carbon, or at least in 12 grams of carbon, you have a ton of atoms. And just to hit the point home, I probably should have talked about this in the atom. This is a huge number.

**Avogadro's Number and Moles**

To maybe visualize it, if you think of-- I was told that in the diameter of a hair, if this is a hair and this is diameter of the hair, if you go this way there 1 million carbon atoms. Or if you were to take an apple and you were to try to figure out what fraction, if you were to make one of the atoms of an apple-- and obviously, an apple has a bunch of different types of atoms in it-- but if you were to take one of the atoms and make it the size of the apple, then the apple would be the size of the earth.

So an apple atom is to an apple as an apple is to the earth. So these are obviously-- it's hard for us to even process things of this size. When you just have one gram of-- well, let's say you have 1 gram of hydrogen.

## The mole and Avogadro's number

If you have 1 gram of hydrogen, that means you have 1 mole of hydrogen. How do I know that? Because hydrogen's atomic mass number is 1.

So in general, if you just take any element-- so what is the mass of, let me just pick, 1 mole of aluminum? So if I were to take 6. Well, each of them have an atomic mass number of So it's 13 amu's-- I don't have to put the s there-- times six point-- well, I won't write that way, actually. The problem for Dalton and other early chemists was to discover the quantitative relationship between the number of atoms in a chemical substance and its mass. In the laboratory, for example, the masses of compounds and elements used by chemists typically range from milligrams to grams, while in industry, chemicals are bought and sold in kilograms and tons.

To analyze the transformations that occur between individual atoms or molecules in a chemical reaction, it is therefore essential for chemists to know how many atoms or molecules are contained in a measurable quantity in the laboratory—a given mass of sample. For example, cans of soda come in a six-pack, eggs are sold by the dozen 12and pencils often come in a gross 12 dozen, or Sheets of printer paper are packaged in reams ofa seemingly large number.

Atoms are so small, however, that even atoms are too small to see or measure by most common techniques. Any readily measurable mass of an element or compound contains an extraordinarily large number of atoms, molecules, or ions, so an extremely large numerical unit is needed to count them.

The mole is used for this purpose. A mole is defined as the amount of a substance that contains the number of carbon atoms in exactly 12 g of isotopically pure carbon According to the most recent experimental measurements, this mass of carbon contains 6.

Just as 1 mole of atoms contains 6. It is not obvious why eggs come in dozens rather than 10s or 14s, or why a ream of paper contains sheets rather than or The definition of a mole—that is, the decision to base it on 12 g of carbon—is also arbitrary.

The important point is that 1 mole of carbon—or of anything else, whether atoms, compact discs, or houses—always has the same number of objects: One mole always has the same number of objects: Stacked vertically, a mole of pennies would be 4. If a mole of pennies were distributed equally among the entire population on Earth, each person would have more than one trillion dollars.

The mole is so large that it is useful only for measuring very small objects, such as atoms. The concept of the mole allows scientists to count a specific number of individual atoms and molecules by weighing measurable quantities of elements and compounds.

Because each element has a different atomic mass, however, a mole of each element has a different mass, even though it contains the same number of atoms 6. This is analogous to the fact that a dozen extra large eggs weighs more than a dozen small eggs, or that the total weight of 50 adult humans is greater than the total weight of 50 children. Because of the way the mole is defined, for every element the number of grams in a mole is the same as the number of atomic mass units in the atomic mass of the element.

Because the atomic mass of magnesium For example, 1 mol of water H2O has 2 mol of hydrogen atoms and 1 mol of oxygen atoms. Molar Mass The molar mass of a substance is defined as the mass in grams of 1 mole of that substance. One mole of isotopically pure carbon has a mass of 12 g. For an element, the molar mass is the mass of 1 mol of atoms of that element; for a covalent molecular compound, it is the mass of 1 mol of molecules of that compound; for an ionic compound, it is the mass of 1 mol of formula units.

That is, the molar mass of a substance is the mass in grams per mole of 6.