Back/Chemistry: Atoms First 2e
Section 2.46 Key Terms

Chemical Formulas

Learning Objectives
  • Interpret molecular, empirical, and structural formulas and molecular models
  • Distinguish structural and spatial isomers
  • Use the mole, Avogadro constant, and molar mass to convert between mass and particle counts

Core Concepts & Principles

Formulas and Molecular Models

  • Molecular formula: The actual number of each type of atom in one molecule. A missing subscript means one atom; glucose is C₆H₁₂O₆.
  • Empirical formula: The simplest whole-number ratio of atoms or ions. Glucose reduces to CH₂O; titanium dioxide, TiO₂, contains twice as many oxygen atoms as titanium atoms. An empirical formula does not describe a separate molecule in an ionic crystal.
  • Structural formula: Shows atom types, numbers, and how bonds connect them. A bond is an attraction holding atoms or ions together.
  • Ball-and-stick model: Shows the arrangement of atoms and bonds in 3D, with atomic sizes not to scale. Space-filling model: Shows relative atomic sizes and the space occupied by atoms.

Subscripts and coefficients mean different things: H is one atom; 2H is two separate atoms; H₂ is one molecule containing two bonded atoms; 2H₂ is two molecules containing four atoms total. The common diatomic elements are H₂, N₂, O₂, F₂, Cl₂, Br₂, and I₂. Common sulfur is S₈.

A molecular formula is a whole-number multiple of an empirical formula. Molecular mass is the sum of the atomic masses of all atoms in a molecule, in amu. An empirical formula plus a measured molecular mass can identify that multiple: benzene's empirical formula is CH, with mass about 13 amu; a molecular mass near 78 amu gives a multiplier of 6 and formula C₆H₆.

Isomers

Isomers have the same molecular formula but different structures and properties. Structural isomers differ in atom connectivity (for example, acetic acid and methyl formate, both C₂H₄O₂). Spatial isomers have the same connectivity but different orientations in space; mirror-image carvone molecules can smell like spearmint or caraway.

The Mole and Molar Mass

A mole contains exactly 6.02214076×10236.02214076 \times 10^{23} specified entities—atoms, molecules, ions, or formula units. The Avogadro constant, NAN_A, is exactly 6.02214076×1023 mol−16.02214076 \times 10^{23}\text{ mol}^{-1}; 6.022×10236.022 \times 10^{23} is a rounded value used in calculations.

Molar mass is the mass of one mole, in g/mol. At the precision used here, its numerical value matches the atomic, molecular, or formula mass in amu, but the units and scales differ: one H₂O molecule has mass about 18.02 amu, while one mole has mass about 18.02 g. Sum each element's atomic mass multiplied by its formula subscript to find a compound's molar mass.

Mass → Moles → Particles

Molar mass connects grams to moles. Avogadro's constant connects moles to particle counts. Formula subscripts connect molecule counts to the number of atoms of each element.

Problem-Solving Routines & Methods

Finding Empirical and Molecular Formulas
  1. 1
    To reduce a molecular formula, divide every subscript by their greatest common divisor: C₂H₄O₂ becomes CH₂O.
  2. 2
    To find a molecular formula from an empirical formula, calculate the empirical formula mass.
  3. 3
    Divide the measured molecular mass by the empirical formula mass to find a whole-number multiplier, then multiply every subscript by it.
Pro-Tip: Changing a formula subscript changes the substance; a coefficient changes only the number of particles.
Mass and Moles
n=mM,m=nMn = \frac{m}{M}, \qquad m = nM
Variables & Constants
nn=moles;
mm=mass in grams;
MM=molar mass in g/mol
Moles and Particles
N=nNA,n=NNAN = nN_A, \qquad n = \frac{N}{N_A}
Variables & Constants
NN=number of specified particles;
nn=moles;
NAN_A=Avogadro constant
Counting Atoms in a Sample
  1. 1
    Divide sample mass by molar mass to obtain moles.
  2. 2
    Multiply moles by Avogadro's constant to obtain molecules or formula units.
  3. 3
    Multiply that count by the appropriate subscript to count atoms of one element, or by the sum of subscripts to count all atoms.
Pro-Tip: Reverse the same steps for particle-to-mass conversions; specify which particles you are counting.

Practice & Concept Checks

Concept Check
What is the empirical formula of hydrazine, N₂H₄?
Concept Check
How many water molecules and hydrogen atoms are in 1.80 g of H₂O? Use 18.0 g/mol.
Concept Check
Can a molecular formula alone tell you how atoms are connected or which spatial isomer is present?

Key Terms & Vocabulary

empirical formulaChemical Formulas
formula showing the composition of a compound given as the simplest whole-number ratio of atoms
isomersIsomers
compounds with the same chemical formula but different structures
molecular formulaChemical Formulas
formula indicating the composition of a molecule of a compound and giving the actual number of atoms of each element in a molecule of the compound.
spatial isomersIsomers
compounds in which the relative orientations of the atoms in space differ
structural formulaChemical Formulas
shows the atoms in a molecule and how they are connected
structural isomerIsomers
one of two substances that have the same molecular formula but different physical and chemical properties because their atoms are bonded differently
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