Chapter 6: Chemical Composition – The Mole, Molar Mass, and Chemical Formulas

Chapter 6: Chemical Composition

Introduction to Chemical Composition

Chemical composition is fundamental to understanding how substances are quantified and related in chemistry. This chapter focuses on the concept of the mole, molar mass, and how chemical formulas are used to relate the masses and numbers of atoms, molecules, and compounds.

The Mole and Avogadro’s Number

Definition and Importance of the Mole

• The mole (mol) is the SI unit for amount of substance, allowing chemists to count atoms, ions, or molecules by weighing them.

• One mole contains $6.022 \times 10^{23}$ entities (Avogadro’s number).

• This number is so large because atoms and molecules are extremely small and numerous.

• The mole bridges the gap between the atomic scale and the macroscopic scale.

Avogadro’s Number

• Avogadro’s number ($6.022 \times 10^{23}$) is named after Amadeo Avogadro.

• It applies to any entity: atoms, molecules, ions, electrons, etc.

• For example, 1 mole of marbles would be $6.022 \times 10^{23}$ marbles.

Molar Mass and Atomic Mass

Atomic Mass Unit and Molar Mass

• The atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom.

• The molar mass of an element is the mass of 1 mole of its atoms, numerically equal to its atomic mass in grams per mole (g/mol).

• For example, the molar mass of copper is 63.55 g/mol.

Relationship Between Mass and Number of Particles

• We can convert between mass, moles, and number of particles using the following relationships:

$\text{Number of particles} = \text{moles} \times 6.022 \times 10^{23}$ $\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

Conversions Involving Moles, Mass, and Number of Particles

Converting Moles to Number of Atoms

To convert moles of a substance to the number of atoms, multiply by Avogadro’s number.

• Example: Convert 3.5 mol He to number of He atoms.

$3.5\ \text{mol He} \times \frac{6.022 \times 10^{23}\ \text{He atoms}}{1\ \text{mol He}} = 2.1 \times 10^{24}\ \text{He atoms}$

Converting Number of Atoms to Moles

• Divide the number of atoms by Avogadro’s number.

• Example: $1.1 \times 10^{22}$ Ag atoms to moles:

$1.1 \times 10^{22}\ \text{Ag atoms} \times \frac{1\ \text{mol Ag}}{6.022 \times 10^{23}\ \text{Ag atoms}} = 1.8 \times 10^{-2}\ \text{mol Ag}$

Converting Between Grams and Moles

• Use the molar mass as a conversion factor.

• Example: Calculate the number of moles in 0.58 g of carbon (C).

$0.58\ \text{g C} \times \frac{1\ \text{mol C}}{12.01\ \text{g C}} = 4.8 \times 10^{-2}\ \text{mol C}$

Converting Between Grams and Number of Atoms

• First, convert grams to moles, then moles to number of atoms.

• Example: How many aluminum atoms are in a 16.2 g aluminum can?

$16.2\ \text{g Al} \times \frac{1\ \text{mol Al}}{26.98\ \text{g Al}} \times \frac{6.022 \times 10^{23}\ \text{Al atoms}}{1\ \text{mol Al}} = 3.62 \times 10^{23}\ \text{Al atoms}$

Molar Mass of Compounds

Definition and Calculation

• The molar mass of a compound is the mass of 1 mole of its molecules or formula units.

• For ionic compounds, the smallest unit is called a formula unit.

• The molar mass is calculated by summing the atomic masses of all atoms in the chemical formula.

Example: Calculating Molar Mass of Water

• Water ($H_2O$):

• 2 H atoms: $2 \times 1.01 = 2.02$ g/mol

• 1 O atom: $1 \times 16.00 = 16.00$ g/mol

• Total: $18.02$ g/mol

Converting Between Grams and Moles of a Compound

• Example: Calculate the mass of 1.75 mol of water.

$1.75\ \text{mol H}_2\text{O} \times \frac{18.02\ \text{g H}_2\text{O}}{1\ \text{mol H}_2\text{O}} = 31.5\ \text{g H}_2\text{O}$

Converting Between Number of Molecules and Mass of a Compound

• Example: What is the mass of $4.78 \times 10^{24}$ molecules of $NO_2$?

$4.78 \times 10^{24}\ \text{molecules} \times \frac{1\ \text{mol}}{6.022 \times 10^{23}\ \text{molecules}} \times \frac{46.01\ \text{g}}{1\ \text{mol}} = 365\ \text{g NO}_2$

Chemical Formulas as Conversion Factors

Using Chemical Formulas to Relate Amounts

• Chemical formulas indicate the ratio of elements in a compound.

• These ratios can be used as conversion factors between moles of compound and moles of constituent elements.

• Example: $CO_2$ has 2 O atoms per 1 molecule of $CO_2$.

• So, $2\ \text{mol O}$ per $1\ \text{mol CO}_2$.

Converting Between Moles of a Compound and Moles of a Constituent Element

• Example: Find the number of moles of O in 1.7 mol $CaCO_3$.

$1.7\ \text{mol CaCO}_3 \times \frac{3\ \text{mol O}}{1\ \text{mol CaCO}_3} = 5.1\ \text{mol O}$

Converting Between Grams of a Compound and Grams of a Constituent Element

• Example: Find the mass of sodium in 15 g of NaCl.

$15\ \text{g NaCl} \times \frac{1\ \text{mol NaCl}}{58.44\ \text{g NaCl}} \times \frac{1\ \text{mol Na}}{1\ \text{mol NaCl}} \times \frac{22.99\ \text{g Na}}{1\ \text{mol Na}} = 5.9\ \text{g Na}$

Summary Table: Key Conversion Relationships

Given	Conversion Factor	Find
Grams	Molar Mass (g/mol)	Moles
Moles	Avogadro’s Number ($6.022 \times 10^{23}$)	Number of Particles
Moles of Compound	Chemical Formula Ratio	Moles of Element
Grams of Compound	Molar Mass & Formula Ratio	Grams of Element

Empirical and Molecular Formulas

• The empirical formula gives the simplest whole-number ratio of elements in a compound.

• The molecular formula gives the actual number of each type of atom in a molecule.

• Empirical formulas can be determined from the relative masses of elements in a compound.

• If the molar mass is known, the molecular formula can also be determined.

Learning Objectives for Chapter 6

• Convert between moles and number of atoms.

• Convert between grams and moles.

• Convert between grams and number of atoms or molecules.

• Convert between grams and moles of a compound.

• Convert between mass of a compound and number of molecules.

• Convert between moles of a compound and moles of a constituent element.

• Convert between grams of a compound and grams of a constituent element.