Atoms and molecules are infinitesimally small, and any bit of matter that's large enough to weigh contains such a large number that they would be impossible to count even if you could see them. So how do scientists know how many molecules are in a certain amount of a specific compound? The answer is that they rely in Avogadro's number, which is the number of atoms in a mole of the compound. As long as you know the chemical formula of the compound, you can look up the atomic weights of the atoms that comprise it, and you'll know the weight of one mole. Multiply that by the weight you have on hand, then multiply by Avogadro's number -- the number of particles in unit called a mole -- to find the number of molecules in your sample.

#### TL;DR (Too Long; Didn't Read)

If you know the weight of the compound in grams, you can find the number of molecules by looking up the weights of the component atoms, calculating how many moles you have and multiplying that number by Avogadro's number, which is 6.02 X 10^{23}.

## Avogadro's Number

Avogadro's number wasn't introduced by its namesake, Italian physicist Amadeo Avogadro (1776-1856). Instead, it was first proposed by French physicist Jean Baptiste Perrin in 1909. He coined the term when he determined the first approximation by observing random vibrations of microscopic particles suspended in liquids and gases. Subsequent researchers, including American physicist Robert Millikan, helped refine it, and today scientists define Avogadro's number as 6.02214154 x 10^{23} particles per mole. Whether the matter is in a solid, gaseous or liquid state, a mole always contains Avogadro's number of particles. That's the definition of a mole.

## Finding the Molecular Weight of a Compound

Every atom has a specific atomic mass that you can look up in the periodic table of the elements. You can find it as the number just under the element's name, and it's usually given in atomic mass units. That simply means that one mole of the element weighs the displayed number in grams. For example, the atomic mass of hydrogen is 1.008. This means that one mole of hydrogen weighs 1.008 grams.

To find the molecular weight of a molecule or compound, you have to know its chemical formula. From that, you can count the number of individual atoms. After looking up the atomic weight of each element, you can then add together all the weights to find the weight of one mole in grams.

## Examples

**1. What is the molecular weight of hydrogen gas?**

Hydrogen gas is a collection of H_{2} molecules, so you multiply the atomic mass by 2 to get the molecular mass. The answer is that a mole of hydrogen gas weighs **2.016 grams**.

**2. What is the molecular weight of calcium carbonate?**

The chemical formula of calcium carbonate is CaCO_{3}. The atomic weight of calcium is 40.078, that of carbon is 12.011 and that of oxygen is 15.999. The chemical formula includes three oxygen atoms, so multiply the weight of oxygen by 3 and add it to the other two. When you do this, you find the weight of one mole of calcium carbonate to be **100.086 grams**.

## Calculating the Number of Molecules

Once you know the molecular weight of a compound, you know how much Avogadro's number of that compound weighs in grams. To find the number of molecules in a sample, divide the weight of the sample by the weight of one mole to get the number of moles, then multiply by Avogadro's number.

**1. How many molecules are there in 50 grams of hydrogen gas (H _{2})?**

The molecular weight of 1 mole of H_{2} gas is 2.016 grams. Divide this into the number of grams you have and multiply by 6.02 x 10^{23} (Avogadro's number rounded to two decimal places). The result is (50 grams ÷ 2.016 grams) X 6.02 x 10^{23} = 149.31 X10^{23} = **1.49 X 10 ^{25} molecules.**

**2. How many calcium carbonate molecules are there in a sample that weighs 0.25 grams?**

One mole of calcium carbonate weighs 100.086 grams, so 0.25 moles weighs 0.25/100.86 = 0.0025 grams. Multiply by Avogadro's number to get 0.015 X 10^{23} = **1.5 x 10 ^{21} molecules in this sample.**

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