Difficulty: Introductory | Prerequisites: None (this is foundational material)
These two chapters form the toolkit you will use for every problem in general chemistry. Chapter 1 covers the metric system, dimensional analysis and density calculations. Chapter 2 introduces how chemists name and write formulas for ionic compounds, molecular compounds and acids. Master these and the rest of the course has a common language.
Chapter 1 is about converting between units using dimensional analysis (the "conversion factor" method) and applying density as a bridge between mass and volume. Chapter 2 is about writing correct chemical formulas from ion charges and naming compounds, whether they are ionic (metal + nonmetal), molecular (nonmetals only) or acids. Get comfortable with these mechanics and every later chapter builds on them smoothly.
Dimensional analysis (factor-label method)
A problem-solving technique in which you multiply a given quantity by one or more conversion factors so that unwanted units cancel and the desired units remain. Think of it as building a chain of fractions where every numerator and denominator pair equals 1.
Conversion factor
A ratio of two equivalent quantities expressed in different units, written as a fraction (e.g. 1 km / 1000 m). In simple terms, it is the bridge that lets you hop from one unit to another without changing the actual amount.
Density
Mass per unit volume of a substance, typically reported as g/mL or g/cm³. In simple terms, density tells you how heavy something is for its size, and it works as a conversion factor between mass and volume.
Ionic compound
A compound formed from a metal cation and a nonmetal anion (or polyatomic ion), held together by electrostatic attraction. Think of it as a positive piece and a negative piece snapping together so the overall charge is zero.
Molecular compound (covalent compound)
A compound formed exclusively from nonmetals that share electrons. In simple terms, no metals are involved, and you use Greek prefixes (mono-, di-, tri-, tetra-, etc.) when naming them.
Polyatomic ion
A charged group of covalently bonded atoms that acts as a single ion (e.g. SO₄²⁻, NO₃⁻, CO₃²⁻). Think of it as a cluster of atoms carrying one collective charge.
Binary acid
An acid consisting of hydrogen plus one other nonmetal element dissolved in water. The naming pattern is hydro__ic acid (e.g. HCl(aq) = hydrochloric acid).
Oxoacid (oxyacid)
An acid consisting of hydrogen plus a polyatomic ion that contains oxygen. The naming pattern maps from the polyatomic ion's suffix: "-ate" ion becomes "-ic acid"; "-ite" ion becomes "-ous acid" (e.g. SO₄²⁻ = sulfate, so H₂SO₄ = sulfuric acid; SO₃²⁻ = sulfite, so H₂SO₃ = sulfurous acid).
Every conversion problem follows the same pattern: start with what you are given, multiply by one or more fractions whose numerator and denominator are equal but in different units, and cancel until only the target unit survives.
Map your route before you calculate. Write the chain of units you need to pass through (e.g. km → m → µm) so you know exactly which conversion factors to set up.
Common prefixes you need cold:
kilo (k) = 10³
centi (c) = 10⁻²
milli (m) = 10⁻³
micro (µ) = 10⁻⁶
nano (n) = 10⁻⁹
Worked example: Convert 0.415 km to µm
Map: km → m → µm
0.415 km × (10³ m / 1 km) × (10⁶ µm / 1 m) = 4.15 × 10⁸ µm
Notice how km cancels in the first factor, m cancels in the second, and µm is the only unit left.
Density (d = m / V) lets you convert between mass and volume. Set it up as a fraction with the units you want on top.
Worked example: Mass of 5.50 L of mercury (density = 13.6 g/mL)
Map: L → mL → g → kg
5.50 L × (1000 mL / 1 L) × (13.6 g / 1 mL) × (1 kg / 1000 g) = 74.8 kg
When converting a unit raised to a power (like cm³ to mm³), the conversion factor must be raised to that same power.
Worked example: Convert 19.3 g/cm³ to g/mm³
Map: g/cm³ → g/m³ → g/mm³
19.3 g/cm³ × (100 cm / 1 m)³ × (1 m / 1000 mm)³
= 19.3 × (10⁶ / 10⁹) = 0.0193 g/mm³
The cube applies to the entire conversion factor, not just the number. (100)³ = 10⁶ and (1000)³ = 10⁹.
Ionic compounds are made of a metal cation and a nonmetal anion (or polyatomic ion). The formula must balance charges so the compound is electrically neutral.
Main-group metals have only one common charge, so the name is simply: cation name + anion name.
Na⁺ and NO₃⁻ → NaNO₃, sodium nitrate
Transition metals can have more than one charge, so a Roman numeral in parentheses follows the metal name.
Fe³⁺ and CO₃²⁻ → Fe₂(CO₃)₃, iron(III) carbonate
Fe²⁺ and NO₂⁻ → Fe(NO₂)₂, iron(II) nitrite
Cu⁺ and SO₄²⁻ → Cu₂SO₄, copper(I) sulfate
Cu²⁺ and PO₄³⁻ → Cu₃(PO₄)₂, copper(II) phosphate
Ni²⁺ and Cl⁻ → NiCl₂, nickel(II) chloride
Ni²⁺ and ClO₂⁻ → Ni(ClO₂)₂, nickel(II) chlorite
Mg²⁺ and HSO₄⁻ → Mg(HSO₄)₂, magnesium hydrogen sulfate
To find the subscripts, criss-cross the charge magnitudes. If both reduce to the same number, simplify.
Ionic: metal + nonmetal, or metal + polyatomic ion
Molecular: nonmetals only
Examples:
CuSO₄·6H₂O = ionic (copper(II) sulfate hexahydrate)
N₂O₄ = molecular (dinitrogen tetroxide)
LiCN = ionic (lithium cyanide)
HCl = molecular when pure, but also the formula of hydrochloric acid in water
SO₂ = molecular (sulfur dioxide)
Fe₂O₃ = ionic (iron(III) oxide)
Acids are compounds that produce H⁺ in water. Two families:
Binary acids (H + one nonmetal, in aqueous solution):
Pattern: hydro____ic acid
HCl(aq) = hydrochloric acid
HI(aq) = hydroiodic acid
H₃P(aq) = hydrophosphoric acid
Oxoacids (H + polyatomic ion containing oxygen):
If the polyatomic ion ends in "-ate," the acid ends in "-ic acid"
SO₄²⁻ = sulfate → H₂SO₄ = sulfuric acid
NO₃⁻ = nitrate → HNO₃ = nitric acid
ClO₄⁻ = perchlorate → HClO₄ = perchloric acid
If the polyatomic ion ends in "-ite," the acid ends in "-ous acid"
SO₃²⁻ = sulfite → H₂SO₃ = sulfurous acid
ClO⁻ = hypochlorite → HClO = hypochlorous acid
The "hypo-" and "per-" prefixes on the polyatomic ion carry through to the acid name.
d = \frac{m}{V}Density equals mass divided by volume. Rearranges to m = d × V or V = m / d.
Metric conversion staircase (each step is a factor of 10): kilo → base unit → centi → milli → micro → nano
Moving from a larger unit to a smaller one means multiplying by a power of 10. Moving the other way means dividing.
Acid naming map:
Ion suffix | Acid suffix | Example ion → Acid |
|---|---|---|
-ide (binary) | hydro___ic acid | Cl⁻ → HCl = hydrochloric acid |
-ate | ___ic acid | NO₃⁻ → HNO₃ = nitric acid |
-ite | ___ous acid | SO₃²⁻ → H₂SO₃ = sulfurous acid |
Students often forget to cube the conversion factor when converting units like cm³ to mm³. You must raise the entire factor (including the number) to the third power, not just the unit label.
Students frequently confuse the "-ite" / "-ate" endings on polyatomic ions. Remembering that "-ate" has one more oxygen than "-ite" (sulfate SO₄²⁻ vs sulfite SO₃²⁻) is essential for both naming compounds and naming acids.
When naming transition metal compounds, students sometimes leave out the Roman numeral. If the metal can have more than one charge, the Roman numeral is mandatory (e.g. FeCl₂ is iron(II) chloride, not just "iron chloride").
Students often set up conversion factors upside down. Always check: the unit you want to cancel should appear in the denominator of the conversion factor, and the unit you want to keep should appear in the numerator.
⚠️ Dimensional analysis is the single most-used technique on every exam in this course. If you can set up a conversion chain, you can solve most quantitative problems.
⚠️ Density problems often appear as multi-step conversions (L → mL → g → kg). Expect at least one on the final.
⚠️ Naming ionic compounds with transition metals (Roman numerals) and naming acids from polyatomic ions are very commonly tested. Know the "-ate → -ic" and "-ite → -ous" acid-naming rules cold.
⚠️ Compound unit conversions (g/cm³ → g/mm³ or similar) appear regularly. The exponent trap catches many students.
True or False: 1 km = 10⁶ mm. (True)
Fill in the blank: The density formula rearranged to solve for mass is m = ____. (d × V)
True or False: N₂O₄ is an ionic compound. (False, it is molecular, nonmetals only)
Fill in the blank: An acid whose polyatomic ion ends in "-ite" gets the acid suffix ____. ("-ous")
True or False: When converting cm³ to m³, you divide by 10⁶. (True, because (100)³ = 10⁶)
Q: Convert 2.50 km to µm.
A: 2.50 km × (10³ m / 1 km) × (10⁶ µm / 1 m) = 2.50 × 10⁹ µm
Q: The density of ethanol is 0.789 g/mL. What is the mass in grams of 250.0 mL of ethanol?
A: 250.0 mL × (0.789 g / 1 mL) = 197 g
Q: Write the formula and name the ionic compound formed from Ni²⁺ and ClO₂⁻.
A: Ni(ClO₂)₂, nickel(II) chlorite
Q: Name the acid H₂SO₃(aq).
A: Sulfurous acid. (SO₃²⁻ = sulfite, an "-ite" ion, so the acid ends in "-ous.")
Q: Write the formula for perchloric acid.
A: HClO₄. (Perchlorate = ClO₄⁻, an "-ate" ion, so the acid ends in "-ic.")
Q: Is LiCN ionic or molecular? Explain.
A: Ionic. Lithium is a metal and CN⁻ (cyanide) is a polyatomic ion.
Dimensional analysis from Chapter 1 is the backbone of stoichiometry in Chapters 3 and 4, where you will convert between grams, moles and molecules using molar mass and Avogadro's number as conversion factors. Density reappears in gas law problems (Chapter 10+). Naming compounds from Chapter 2 is required every time you write a balanced equation or identify products in a reaction.
Related Terms / Search Tags
unit conversion, dimensional analysis, factor-label method, metric prefixes, SI units, density, mass, volume, g/mL, g/cm³, ionic compound, covalent compound, molecular compound, polyatomic ion, transition metal, Roman numeral notation, binary acid, oxoacid, oxyacid, hydro-ic acid, -ate to -ic, -ite to -ous, chemical nomenclature, naming compounds, CHE 1100, NYU general chemistry, Che 1100 final review