To **convert moles to molecules** you will need to use two equations and have at hand Avagadro’s number and the number of moles in your end substance. See below for examples and formulas.

**6.02 x 10 ^{23}**

**602,000,000,000,000,000,000,000**

In chemistry courses, you’ll frequently have to convert moles to molecules or molecules to moles using Avogadro’s number. To do this, you’ll want to be familiar with the definitions of both moles and molecules, the relationship between the two concepts, and the exact formula which uses Avogadro’s number.

## Defining Terms

Avogadro’s number represents a mole (often abbreviated mol), and it states that a mole of a substance has (6.022×1023) or 6.022×10^23 molecules per mole or atoms.

The 23 that is found behind the 10 in 6.022×10^{23} is in scientific notation, and it represents the fact that there are 23 zeros following the 10. Why 23 zeros? As you may have noticed, any chemical changes that occur in a reaction involve interactions between billions of atoms. It would be impractical to write out this number every time, so scientific notation is used as a convenient shorthand for the number of atoms in a mol.

“After my death, the molecules of my being will return to the earth and the sky. They came from the stars. I am of the stars.” — Charles Lindbergh

A mole can also be defined as the amount of substance a chemical has that is equivalent to the number of particles found in 12 grams of carbon-12. The purpose of Avogadro’s number is to define an easily identifiable proportion between mass at the atomic scale and the physical mass that is dealt with at the human scale.

**To sum up:**

Avogadro’s number is 6.022×10^{23}.

6.022×10^{23} represents the number of molecules in a mole of a substance, any substance.

## The History of Avogadro’s Number:

Though called Avogadro’s number, the person who originally estimated the number of particles in a certain substance was Josef Loschmidt, who put the value of particles in one cubic centimeter of gas at 2.6867773 x 1025 m^{-3}. The term Avogadro’s number was coined by a French physicist, Jean Baptiste Perrin. Perrin made an estimate of what he called Avogadro’s number. Avogadro had been the first physics professor in Italy and had created a hypothesis that suggested gases of equal volume at the same temperature and pressure should contain the same number of particles. Perrin used Loschmidt’s constant and Avogadro’s hypothesis to create the Avogadro number.

## Applying The Concept Of Moles

Remember that the relationship of moles to a number of atoms holds constant, regardless of how complicated a molecule is. As a simple example, a molecule of water (H2O) is made out of one hydrogen atom and two oxygen atoms. That means that in a mole of water, there would be one mole of oxygen and two moles of hydrogen.

## Calculating And Converting Moles and Atoms

The equation to convert moles to atoms is as follows:

B moles x 6.022×10^23 atoms/ 1 mole = C atoms

In other words, you take the number of moles of a substance (B) and then multiply it by Avogadro’s number (divided by one mole). An example calculation:

How many atoms are there in six moles of iron?:

6 moles x 6.022×10^23 atoms/ 1 mole = C atoms

This would give us 3.61 X 10^24 atoms.

It’s very easy to convert the number of atoms in a substance to some number of moles as well. All that needs to be done is the above calculation but in reverse. Instead of multiplying the number of moles by Avogadro’s number, you’d divide the number of atoms by Avagadro’s number.

C atoms X 1 mole/6.022×10^23 atoms = B moles

## Converting Moles To Molecules

To convert a number of moles to molecules, you first want to note how many moles are in the substance you have and the chemical makeup of the substance you’re analyzing. Going back to the H2O example, let’s say you have 4 moles of H2O. Take the number of moles (4) and then multiply it by Avogadro’s number:

4 mol x 6.022 x 10^23 = 24.0×10^23

You could simplify this number by moving the decimal point one space to the left, to get:

2.4 x 10^24

Note that if you did this you’d also need to increase the exponent because it now must reflect the fact that you’ve shifted the decimal point over.

## Molar Mass

Moles are also convenient ways of measuring the mass of an object. Though a chemist could easily measure quantities of matter through mass, chemistry often requires one to determine how many atoms of an element are present within one sample of a substance. Earlier, it was said that one mole is equivalent to the number of atoms found in twelve grams of carbon-12.

There’s another important property of Avogadro’s number to remember – one mole (of any substance) mass is always equal to the molecular weight of that substance. Molecular weight is defined in either atomic mass units (AMU) or using grams per mole (g/mol). G/mol is the notation that is most commonly used in laboratory settings.

“You look at the floor and see the floor. I look at the floor and see molecules.” — Dan Aykroyd

Since water’s molecular weight is 19.015 AMU (atomic mass units), one mole of water is equal to 18.015 grams of water.

To find molar mass, you take the given mass of a substance and divide it by the amount of that substance present in your sample, as defined in g/mols. If you know that the atomic mass of titanium is 47.88 g/mol, then it follows that for 47.88 grams of it there would be one mole’s work of atoms.

## Things To Remember About Moles:

- A mole is the quantity of a substance which possesses the same number of particles possessed by 12 grams of carbon-12.
- This quantity can also be expressed as Avogadro’s number: 6.022×10^23
- The mass in grams of a single mole of any compound will equal the molecular weight of the compound when expressed in AMUs.
- One mole of any substance will have 6.022×10^23 molecules of that substance.
- Molar mass or molar weight is the mass that one mole of a substance has, and they are defined in grams per mole.

## Quick Reference Guide For Calculating And Converting Moles:

**To convert particles (atoms or molecules) to moles:**

Take the number of particles and divide them by Avogadro’s number.

**To convert moles to particles (atoms or molecules):**

Take the number of moles and multiply them by Avogadro’s number.

**To convert grams to moles:**

Divide the initial mass of the substance by the compound’s molar mass (listed in the periodic table of the elements).

**To convert moles to mass:**

Multiply the starting number of moles with the compound’s molar mass.

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