2.4 Chemical Formulas | Chemistry: Atoms First 2e

Learning Objectives

Symbolize molecular composition using molecular and empirical formulas
Represent bonding arrangements using structural formulas
Define the mole and Avogadro's number
Convert between mass, moles, and number of atoms or molecules

Core Concepts & Principles

Chemical formulas communicate the exact makeup of substances using elemental symbols and numerical subscripts.

Molecular Formulas: Show the exact number of each type of atom in a discrete molecule (e.g., glucose is C₆H₁₂O₆).
Empirical Formulas: Show the simplest whole-number ratio of atoms or ions in a compound (e.g., glucose's empirical formula is CH₂O).
Structural Formulas: Show both the types and numbers of atoms, as well as how they are connected via chemical bonds.

Formulas & Isomers

Molecular vs. Empirical: Molecular formulas are whole-number multiples of empirical formulas. If a molecular formula is C₂H₄O₂, dividing by the lowest common denominator (2) yields the empirical formula CH₂O.
Isomers: Compounds that share an identical molecular formula but possess different structures and chemical properties. Structural isomers differ in atom connectivity, while spatial isomers differ only in 3D orientation.

The Mole and Avogadro's Number

Counting atoms individually is impossible, so chemistry uses an amount unit called the mole.

Avogadro's Number ( $N_A$ ): Exactly $6.022 \times 10^{23}$ discrete entities (atoms, molecules, or ions) per mole ( $6.022 \times 10^{23} \text{ mol}^{-1}$ ).
Molar Mass: The mass of 1 mole of a substance, expressed in grams per mole ( $\text{g/mol}$ ). Numerically, an element's molar mass in $\text{g/mol}$ is equal to its atomic mass in atomic mass units ( $\text{amu}$ ).

The Central Bridge of Stoichiometry

The mole serves as the universal bridge between macroscopic laboratory measurements (mass in grams) and microscopic counts (number of atoms or molecules).

Problem-Solving Routines & Methods

Mass-to-Mole Conversion

\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}

Converts bulk mass into chemical amount.

Variables & Constants

m

=sample mass (g);

\text{MM}

=molar mass (g/mol)

Mole-to-Particle Conversion

\text{Number of Entities} = \text{Moles} \times N_A

Converts moles into actual atoms or molecules.

Variables & Constants

n

=amount in moles;

N_A

6.022 \times 10^{23}\text{ mol}^{-1}

Converting Mass to Number of Atoms or Molecules

1
Determine the molar mass (g/mol) of the element or compound by summing the atomic masses of all constituent atoms.
2
Convert the given mass (g) to moles by dividing by the molar mass: $ $ext{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$ $
3
Convert moles to particles (atoms or molecules) by multiplying by Avogadro's number: $ $ext{Particles} = \text{Moles} \times 6.022 \times 10^{23}$ $

Pro-Tip: Always track your units using the factor-label method. Grams must cancel out to leave moles, and moles must cancel out to leave atoms/molecules.

Practice & Concept Checks

Concept Check

What is the empirical formula of hydrazine, N₂H₄?

Concept Check

How many atoms of gold (Au) are in a 19.7 g sample? (Atomic mass of Au = 197.0 amu)

Key Terms & Vocabulary

molecular formulaFormulas

A representation of a molecule using chemical symbols and subscripts to indicate the exact number of each type of atom present.

Example: C₆H₁₂O₆ (glucose)

structural formulaFormulas

A drawing or formula that shows the types and numbers of atoms in a molecule, as well as how those atoms are bonded together.

Example: H-O-H for water

empirical formulaFormulas

A formula showing the simplest whole-number ratio of the elements in a compound.

Example: CH₂O for glucose

molecular massMass Metrics

The sum of the average atomic masses of all the atoms represented in a molecule's formula, expressed in amu.

Example: Water (H₂O) molecular mass = 18.02 amu

isomersMolecular Structure

Compounds that have identical molecular formulas but different structural arrangements or spatial orientations.

Example: Acetic acid and methyl formate

structural isomersMolecular Structure

Isomers in which the molecules differ in how their atoms are connected to one another.

spatial isomersMolecular Structure

Isomers in which the atoms are connected in the same order but have different relative orientations in 3D space.

moleQuantities

The amount unit representing 6.022 × 10²³ discrete entities (atoms or molecules).

Example: 1 mol of C = 6.022 × 10²³ carbon atoms

Avogadro's number (NA)Constants

The experimentally determined number of entities composing 1 mole of substance, equal to 6.022 × 10²³ mol⁻¹.

molar massMass Metrics

The mass in grams of 1 mole of a substance, numerically equivalent to its atomic or formula weight in amu.

Example: Carbon molar mass = 12.01 g/mol