Converting between Moles and Atoms
By understanding the relationship between moles and Avogadro's number, scientists can convert between number of moles and number of atoms.
Learning Objective

Convert between the number of moles and the number of atoms in a given substance using Avagadro's number
Key Points
 Avogadro's number is a very important relationship to remember: 1 mole =
$6.022\times10^{23}$ atoms, molecules, protons, etc.  To convert from moles to atoms, multiply the molar amount by Avogadro's number.
 To convert from atoms to moles, divide the atom amount by Avogadro's number (or multiply by its reciprocal).
Terms

mole
The amount of substance of a system that contains as many elementary entities as there are atoms in 12 g of carbon12.

Avogadro's number
The number of atoms present in 12 g of carbon12, which is
$6.022\times10^{23}$ and the number of elementary entities (atoms or molecules) comprising one mole of a given substance.
Full Text
Moles and Atoms
As introduced in the previous concept, the mole can be used to relate masses of substances to the quantity of atoms therein. This is an easy way of determining how much of one substance can react with a given amount of another substance.
From moles of a substance, one can also find the number of atoms in a sample and vice versa. The bridge between atoms and moles is Avogadro's number, 6.022×10^{23}.
Avogadro's number is typically dimensionless, but when it defines the mole, it can be expressed as 6.022×10^{23} elementary entities/mol. This form shows the role of Avogadro's number as a conversion factor between the number of entities and the number of moles. Therefore, given the relationship 1 mol = 6.022 x 10^{23} atoms, converting between moles and atoms of a substance becomes a simple dimensional analysis problem.
Converting Moles to Atoms
Given a known number of moles (x), one can find the number of atoms (y) in this molar quantity by multiplying it by Avogadro's number:
For example, if scientists want to know how may atoms are in six moles of sodium (x = 6), they could solve:
Note that the solution is independent of whether the element is sodium or otherwise.
Converting Atoms to Moles
Reversing the calculation above, it is possible to convert a number of atoms to a molar quantity by dividing it by Avogadro's number:
This can be written without a fraction in the denominator by multiplying the number of atoms by the reciprocal of Avogadro's number:
For example, if scientists know there are
Key Term Reference
 atom
 Appears in these related concepts: Description of the Hydrogen Atom, Early Ideas about Atoms, and Stable Isotopes
 conversion factor
 Appears in these related concepts: Solution Stoichiometry, Strategy for General Problem Solving, and MoletoMole Conversions
 dimensional analysis
 Appears in these related concepts: Converting between Mass and Number of Moles, MasstoMole Conversions, and Converting from One Unit to Another
 element
 Appears in these related concepts: The Periodic Table, Elements and Compounds, and The Periodic Table
 fraction
 Appears in these related concepts: SI Unit Prefixes, Separable Equations, and Fractions
 molecule
 Appears in these related concepts: Molecules, Levels of Organization of Living Things, and Chemical Reactions and Molecules
 proton
 Appears in these related concepts: Overview of Atomic Structure, Development of the Periodic Table, and Cationic ChainGrowth Polymerization
 solution
 Appears in these related concepts: Electrolyte and Nonelectrolyte Solutions, Turning Your Claim Into a Thesis Statement, and What is an Equation?
 substance
 Appears in these related concepts: Substances and Mixtures, Types of Synthetic Organic Polymers, and Complex Ion Equilibria and Solubility
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