Chemistry Molar Mass, Avagadro's number, and conversions

Avogadro's Number

Avogadro's number (𝑁𝐴) is the number of particles in 1 mole of a substance. 𝑁𝐴 = 6.022 × 10^23 particles/mol

Purpose of Avogadro's Number

Converts moles ↔ particles (atoms, molecules, ions, formula units)

Particles to Moles Formula

moles = particles / 6.022 × 10^23

Moles to Particles Formula

particles = moles × 6.022 × 10^23

Example of Mole Conversion

How many molecules are in 2.5 mol H₂O? 2.5 × 6.022 × 10^23 = 1.506 × 10^24 molecules

Molar Mass

The mass of 1 mole of a substance in grams (g/mol)

Purpose of Molar Mass

Converts grams ↔ moles

Grams to Moles Formula

moles = mass (g) / molar mass (g/mol)

Moles to Grams Formula

mass (g) = moles × molar mass (g/mol)

Example of Moles in Grams

How many moles in 36 g H₂O? 36 ÷ 18.016 = 2.00 mol H₂O

Example of Grams in Moles

How many grams in 0.50 mol CO₂? 0.50 × 44.01 = 22.0 g CO₂

Combining Avogadro's Number & Molar Mass Purpose

Convert grams → particles or particles → grams

Stepwise Method for Conversion

Grams → moles (use molar mass), Moles → particles (use Avogadro's number)

Example of Molecule Conversion from Grams

How many molecules in 18 g H₂O? Moles: 18 ÷ 18.016 ≈ 1, Molecules: 1 × 6.022 × 10^23 = 6.022 × 10^23 molecules

Example of Grams from Molecules

How many grams contain 3.01 × 10^23 CO₂ molecules? Moles: 3.01 × 10^23 / 6.022 × 10^23 = 0.500, Grams: 0.500 × 44.01 = 22.0 g CO₂

Subscripts in Chemical Formulas

Subscripts indicate the number of atoms of each element in one molecule or formula unit.

Purpose of Subscripts

Convert atoms ↔ molecules or moles of atoms ↔ moles of molecules

Atoms to Molecules Formula

Atoms → molecules: divide by subscript

Molecules to Atoms Formula

Molecules → atoms: multiply by subscript

Moles of Atom Formula

Moles of atom = moles of molecule × subscript

Example of H Atoms Calculation

How many H atoms in 2 mol H₂O? 2 × 2 = 4 mol H atoms

Example of O Atoms Calculation

How many O atoms in 3 mol CO₂? 3 × 2 = 6 mol O atoms

Converting Grams to Moles

If given grams, first convert to moles using molar mass: moles = grams / molar mass

Example Problem for Grams of Al₂O₃

How many grams of Al₂O₃ contain 4.33 × 10^−2 mol O atoms?

Mole ratio

Al₂O₃ has 3 O atoms per formula unit.

Moles of Al₂O₃

n(Al₂O₃) = 4.33 × 10⁻² = 1.443 × 10⁻² mol.

Mass of Al₂O₃

m = 1.443 × 10⁻² × 101.96 = 1.472 g Al₂O₃.

Grams to Moles Conversion Formula

n = m / M.

Moles to Grams Conversion Formula

m = n × M.

Moles to Particles Conversion Formula

particles = n × 6.022 × 10²³.

Particles to Moles Conversion Formula

n = particles / 6.022 × 10²³.

Moles of Atom to Molecules

Divide by subscript.

Molecules to Moles of Atom

Multiply by subscript.

Example Calculation

How many O atoms are in 12 g H₂O?

Grams to Moles for H₂O

n = 12 ÷ 18.016 = 0.6667 mol H₂O.

Moles of O Atoms from H₂O

n_O = 0.6667 × 1 = 0.6667 mol O atoms.

Moles to Number of O Atoms

0.6667 × 6.022 × 10²³ ≈ 4.01 × 10²³ O atoms.

Tips for Using the Conversion Map

Always start with the units you are given (grams, moles, or particles).

Follow the Arrows

Follow the arrows to get to your target units.

Use Molar Mass

Use molar mass for grams ↔ moles.

Use Avogadro's Number

Use Avogadro's number for moles ↔ particles.

Use Subscripts

Use subscripts for moles ↔ moles of atoms or elements in compounds.