Chapter 13 — Front Matter
Purpose and Overview
Every time iron rusts, wood burns, bread rises, or a battery powers a flashlight, a chemical reaction is happening. Atoms are rearranging. Substances are transforming. Old bonds are breaking and new bonds are forming.
For centuries, chemists could observe these transformations, but they had no compact way to write them down and share them precisely. A description like "burn carbon in air and you get a colorless gas that suffocates a flame" is accurate, but it is also cumbersome. It does not tell you how much carbon, how much air, how much gas, or what the atoms are actually doing.
Chemical equations solve this problem. A chemical equation is a symbolic statement that describes a chemical reaction: what substances enter the reaction, what substances exit the reaction, and how the atoms are arranged before and after. Learning to read, write, and balance chemical equations is one of the central skills of chemistry. Every stoichiometry calculation, every prediction about reactions, every industrial chemical process, and every biological pathway you encounter later in this course will depend on understanding equations. This chapter builds that foundation carefully, from meaning to symbol to balance.
Opening Question
When hydrogen gas and oxygen gas react, they produce water — a substance with completely different properties than either reactant. How would you write a description of this transformation that is precise enough for any chemist in the world to read? How could you communicate not just what substances are involved, but exactly how many atoms of each kind are rearranging? By the end of this chapter, you will be able to write, read, and balance the symbolic statement that captures all of this: 2H₂ + O₂ → 2H₂O.
9Sections
10Objectives
13Key Terms
6+Worked Examples
Learning Objectives
- 1Explain what a chemical equation represents and identify its major components.
- 2Distinguish reactants from products and describe the meaning of the reaction arrow.
- 3Read chemical formulas correctly, including element symbols, subscripts, and the seven diatomic elements.
- 4Distinguish between subscripts and coefficients and explain why subscripts cannot be changed when balancing.
- 5Count atoms in chemical expressions by multiplying coefficients by subscripts.
- 6State the law of conservation of mass and explain its particle-level basis.
- 7Balance chemical equations by adjusting coefficients using the inspection method.
- 8Interpret and write state symbols in chemical equations.
- 9Identify observable evidence that a chemical reaction has occurred.
- 10Interpret balanced equations as particle-level models of chemical change.
Sections 13.1 – 13.2
What Chemical Equations Represent
Purpose · Format · Reactants · Products · Atom Conservation
Section 13.1
What Chemical Equations Represent
When chemists write a chemical equation, they are doing three things at once. First, they are identifying the substances involved — the reactants that enter the reaction and the products that form. Second, they are communicating composition through chemical formulas, which show exactly which atoms are present and in what ratios. Third, they are making a quantitative statement about amounts through the coefficients that describe the ratios in which substances react and form.
A chemical equation is therefore a compact, information-rich description of a chemical change. Every symbol and number carries meaning.
Standard Format
Reactants are written on the left side, products on the right. An arrow — the reaction arrow — separates them, pointing left to right and meaning "react to form" or "yield." Multiple reactants or products are separated by plus signs on their respective sides.
| Component | Position | Meaning | Example |
|---|
| Reactants | Left of arrow | Substances present before the reaction | H₂ + O₂ |
| Reaction arrow (→) | Center | "React to form" or "yield" | → |
| Products | Right of arrow | Substances formed by the reaction | H₂O |
| Plus signs | Both sides | Separates multiple substances | CO₂ + H₂O |
| Coefficients | Before formulas | Relative number of units of each substance | 2H₂ |
| State symbols | After formulas | Physical state of each substance | H₂O(l) |
The Arrow Is Not an Equals Sign
The reaction arrow (→) means transformation, not equality. The left side does not "equal" the right side the way 2 + 2 = 4. The arrow says the substances on the left are chemically converted into the substances on the right. In some reversible reactions, a double arrow (⇌) is used — you will study those in Chapter 22.
Particle-Level Meaning
Chemical equations do not just describe what you can see. They are models of events at the level of individual atoms and molecules. When hydrogen and oxygen react, H–H bonds and the O=O double bond break, atoms rearrange, and new O–H bonds form to produce water molecules. Every formula in every equation is a window into that invisible world.
Section 13.2
Reactants and Products
Reactants are the starting materials of a chemical reaction — the substances present before the reaction occurs, always on the left side of the equation. A reaction may have one reactant or several. Products are the substances formed by the reaction, appearing on the right side. Reactants and products are chemically different substances with different formulas, different structures, and often completely different observable properties.
Example 13.2.1
Identifying reactants and products
- EquationCH₄ + O₂ → CO₂ + H₂O
- ReactantsMethane (CH₄) and oxygen (O₂) — the substances present before the reaction.
- ProductsCarbon dioxide (CO₂) and water (H₂O) — the substances formed as a result of the reaction.
- Key PointIron metal (Fe) is shiny and magnetic. Oxygen gas (O₂) is invisible. Their product, iron(III) oxide (Fe₂O₃), is reddish-brown and brittle — completely different properties than either reactant.
Atoms Follow the Arrow
Atoms are not created or destroyed in a chemical reaction. Every atom in the reactants must appear somewhere in the products. Atoms rearrange — bonds break on the left, new bonds form on the right — but the count of each type of atom never changes. This is why chemical equations must be balanced.
Sections 13.3 – 13.5
Formulas, Coefficients, and Conservation
Element Symbols · Diatomic Elements · Subscripts vs. Coefficients · Counting Atoms · Conservation of Mass
Section 13.3
Chemical Symbols and Formulas in Equations
Chemical equations use the universal symbolic language of chemistry: element symbols and chemical formulas. If you are uncertain about reading a chemical formula, review Chapters 9, 10, and 11. This section focuses on the ideas that matter most for writing and balancing equations.
The Seven Diatomic Elements
When an element symbol appears in an equation representing a pure element, it usually means that element in its most common structural form. However, seven elements do not exist as single atoms under normal conditions — they exist as diatomic molecules (two atoms bonded together). These seven must always be written with the subscript 2 when they appear as pure elements in any equation.
| Element | Symbol | Name | State at Room Temperature |
|---|
| Hydrogen | H₂ | Hydrogen gas | Gas |
| Nitrogen | N₂ | Nitrogen gas | Gas |
| Oxygen | O₂ | Oxygen gas | Gas |
| Fluorine | F₂ | Fluorine gas | Gas |
| Chlorine | Cl₂ | Chlorine gas | Gas |
| Bromine | Br₂ | Bromine | Liquid |
| Iodine | I₂ | Iodine | Solid |
Memory Device for Diatomic Elements
The seven diatomic elements can be remembered with the phrase "BrINClHOF" (bromine, iodine, nitrogen, chlorine, hydrogen, oxygen, fluorine) or arranged into the mnemonic "I Have No Fear Of Ice Cold Beer" — one diatomic element per word. Writing O instead of O₂ for pure oxygen gas in an equation is a significant error.
Coefficients Versus Subscripts — A Critical Distinction
One of the most common errors in equation work is confusing coefficients with subscripts. They are fundamentally different and must never be mixed up.
Subscripts vs. Coefficients
Subscript — Part of the chemical formula. Tells you the composition of one molecule or formula unit. Changing a subscript changes the identity of the substance. H₂O and H₂O₂ are entirely different compounds.
Coefficient — A number in front of the formula. Tells you how many units of that substance are present. Coefficients can be changed freely when balancing because they do not change the identity of any substance.
To represent two water molecules: write 2H₂O, not H₄O₂. Never change a subscript to balance an equation.
Never Change Subscripts to Balance
Subscripts are locked. They are part of the chemical formula for that specific substance, determined by its actual molecular or ionic structure. Only coefficients may be adjusted during balancing. Changing H₂O to H₂O₂ does not give you two water molecules — it gives you one molecule of hydrogen peroxide, a completely different compound.
Section 13.4
Subscripts and Coefficients
To find the total number of atoms of a given element in any expression, multiply the coefficient by the subscript for that element. This is the fundamental atom-counting skill that makes balancing equations possible.
Example 13.4.1
Counting atoms using coefficients and subscripts
- Problem 1How many oxygen atoms are in
4CO₂?
- Solve
Subscript for O in CO₂ = 2
Coefficient = 4
Total O atoms = 4 × 2 = 8
- Problem 2How many hydrogen atoms are in
3NH₃?
- Solve
Subscript for H in NH₃ = 3
Coefficient = 3
Total H atoms = 3 × 3 = 9
- Problem 3How many oxygen atoms are in
2Ca(NO₃)₂?
- Solve
Inside parentheses: NO₃ has 3 oxygens
Subscript outside parentheses = 2
Oxygens per formula unit = 2 × 3 = 6
Coefficient = 2
Total O atoms = 2 × 6 = 12
Answers: 8 O atoms | 9 H atoms | 12 O atoms
Section 13.5
Conservation of Atoms
The law of conservation of mass states that in any chemical reaction, the total mass of the reactants equals the total mass of the products. This law was established through the careful experimental work of Antoine Lavoisier in the late 1700s. Lavoisier performed reactions in sealed containers and demonstrated that no mass was gained or lost. Before his work, some chemists believed that burning released a mysterious substance called phlogiston. Lavoisier's measurements showed instead that burning was combination with oxygen — and that mass was always conserved.
At the particle level, conservation of mass makes perfect sense: atoms are not created or destroyed in chemical reactions. They are only rearranged. Because atoms have mass, and because the same atoms that enter a reaction also leave it (in new arrangements), the total mass cannot change.
This is why unbalanced equations are scientifically incorrect. An equation showing more atoms on the product side is claiming atoms were created from nothing. An equation showing fewer atoms is claiming atoms vanished. Neither is possible. Every correctly written equation must have equal numbers of each type of atom on both sides.
Example 13.5.1
Checking for atom balance
- EquationIs
H₂ + O₂ → H₂O balanced?
- Left side
H: 2 (from H₂)
O: 2 (from O₂)
- Right side
H: 2 (from H₂O)
O: 1 (from H₂O)
- VerdictHydrogen is balanced (2 = 2). Oxygen is NOT balanced (2 ≠ 1). This equation must be corrected.
Not balanced — oxygen atoms are not conserved. Correction follows in Section 13.6.
A Useful Mental Image
Imagine building with colored blocks: 4 red and 6 blue. No matter how you rearrange them into new structures, you must still have exactly 4 red and 6 blue at the end. Chemical reactions work exactly this way. Atoms rearrange into new substances, but the count of each type of atom never changes.
Section 13.6
Balancing Chemical Equations
The Only Rule · Inspection Method · Three Worked Examples · Tips for Difficult Equations
Section 13.6
Balancing Chemical Equations
Balancing a chemical equation means adjusting the coefficients in front of chemical formulas so that every type of atom has the same count on both sides. Balancing is not optional. An unbalanced equation is an incorrect equation. Every stoichiometry calculation in Chapters 15 and 16 will depend on correctly balanced equations — if the equation is wrong, every calculation built on it will be wrong.
The One and Only Rule
You may only change coefficients — never subscripts. Subscripts are part of the chemical formula and fixed by the identity of the substance. Coefficients indicate quantity and may be freely adjusted. An implied coefficient of 1 is never written.
The Inspection Method (Trial and Error)
At this level, the standard approach is inspection: adjust coefficients and recheck atom counts until all elements balance. With practice, this becomes systematic. Follow these steps:
- Write the unbalanced equation with correct formulas for all reactants and products.
- Count the atoms of each element on both sides.
- Start with the most complex formula, or with an element that appears in only one reactant and one product.
- Adjust a coefficient to balance that element. Recount all atoms.
- Continue adjusting one element at a time, rechecking each time.
- Balance hydrogen and oxygen last — they often appear in multiple substances.
- Check that all elements are balanced and all coefficients are in their lowest whole-number ratio.
Worked Example 13.6.1
Formation of water from hydrogen and oxygen
- Start
H₂ + O₂ → H₂O (unbalanced)
- Count
Left: 2 H, 2 O
Right: 2 H, 1 O ← oxygen not balanced
- Fix OPlace coefficient 2 in front of H₂O to get 2 oxygens on the right:
H₂ + O₂ → 2H₂O
New count: Left: 2 H, 2 O | Right: 4 H, 2 O ← oxygen balanced; hydrogen not
- Fix HPlace coefficient 2 in front of H₂ to get 4 hydrogens on the left:
2H₂ + O₂ → 2H₂O
- Check
Left: 4 H (2×2), 2 O
Right: 4 H (2×2), 2 O (2×1) ✓ balanced
Balanced equation: 2H₂ + O₂ → 2H₂O
Worked Example 13.6.2
Combustion of methane
- Start
CH₄ + O₂ → CO₂ + H₂O (unbalanced)
- Count
Left: 1 C, 4 H, 2 O
Right: 1 C, 2 H, 3 O
- Fix HCarbon is balanced. Place 2 in front of H₂O to match the 4 hydrogens on the left:
CH₄ + O₂ → CO₂ + 2H₂O
New count: Left: 1 C, 4 H, 2 O | Right: 1 C, 4 H, 4 O
- Fix ONow 2 oxygens on the left, 4 on the right. Place 2 in front of O₂:
CH₄ + 2O₂ → CO₂ + 2H₂O
- Check
Left: 1 C, 4 H, 4 O (2×2)
Right: 1 C, 4 H, 4 O (2+2) ✓ balanced
Balanced equation: CH₄ + 2O₂ → CO₂ + 2H₂O
Worked Example 13.6.3
Reaction of iron with oxygen — finding a common multiple
- Start
Fe + O₂ → Fe₂O₃ (unbalanced)
- Count
Left: 1 Fe, 2 O
Right: 2 Fe, 3 O
- Fix FePlace 2 in front of Fe:
2Fe + O₂ → Fe₂O₃
New count: Left: 2 Fe, 2 O | Right: 2 Fe, 3 O — Fe balanced; O not
- Fix ONeed equal oxygens: LCM of 2 and 3 is 6. Place 3 in front of O₂ (giving 6 O left) and 2 in front of Fe₂O₃ (giving 6 O right):
2Fe + 3O₂ → 2Fe₂O₃
Now right side has 2×2 = 4 Fe, but left side has only 2 Fe.
- Fix Fe againAdjust Fe coefficient to 4:
4Fe + 3O₂ → 2Fe₂O₃
- Check
Left: 4 Fe, 6 O (3×2)
Right: 4 Fe (2×2), 6 O (2×3) ✓ balanced
Balanced equation: 4Fe + 3O₂ → 2Fe₂O₃
Tips for Challenging Equations
Polyatomic ions: If a polyatomic group like SO₄²⁻ or NO₃⁻ appears unchanged on both sides, treat it as a single unit when counting. This simplifies the process considerably.
Fractions: If balancing produces a fractional coefficient (like ½), multiply all coefficients by the denominator to convert everything to whole numbers.
Start with the most complex formula or with an element that appears in only one reactant and one product.
Sections 13.7 – 13.8
States of Matter and Observable Evidence
State Symbols · Aqueous Solutions · Signs of Chemical Reactions
Section 13.7
States of Matter in Equations
A chemical equation can include symbols to show the physical state of each substance. These state symbols appear in parentheses immediately after the chemical formula. They are not decorative — they describe actual conditions and help predict what will happen during the reaction.
| Symbol | State | Meaning | Example |
|---|
(s) | Solid | The substance is in solid form | Fe(s) |
(l) | Liquid | The substance is in liquid form | H₂O(l) |
(g) | Gas | The substance is in gaseous form | O₂(g) |
(aq) | Aqueous | The substance is dissolved in water | NaCl(aq) |
Full Example with State Symbols
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)
This tells you: methane and oxygen are gases that react, producing carbon dioxide gas and liquid water. If the reaction occurs at very high temperature and water is produced as vapor, you would write H₂O(g) instead.
The (aq) symbol is especially important in chemistry. It means the substance is dissolved in water — individual ions or molecules spread throughout a solution. Table salt NaCl dissolves to give Na⁺(aq) and Cl⁻(aq) ions floating freely through water, surrounded by water molecules. This is chemically different from solid NaCl(s), where ions are locked in a rigid lattice. You will use (aq) extensively in Chapter 17 when writing ionic equations for reactions in aqueous solution.
Knowing that a product forms as a gas tells you it may escape as bubbles if the reaction occurs in a liquid — a visible sign of reaction. Knowing a product forms as a solid in aqueous solution tells you it will precipitate out. State symbols in an equation carry all of this predictive information.
Section 13.8
Evidence of Chemical Reactions
A chemical equation is written in the world of symbols, but it represents events that happen in the physical world. One of the important skills in chemistry is connecting what you observe to what the symbolic equation describes. When you observe a chemical change, you are seeing the result of atoms rearranging. The equation translates those observations into a precise particle-level description.
Common Signs of a Chemical Reaction
- PrecipitateWhen two aqueous solutions mix and a solid forms and settles (or clouds the solution), a precipitate has formed. The equation will show a product marked (s) in an otherwise aqueous system. Example: mixing silver nitrate and sodium chloride solutions produces white silver chloride solid.
- Gas FormationBubbles forming during a reaction (when heat is not involved) indicate gas production. The equation will show a product marked (g). Example: zinc reacting with hydrochloric acid releases hydrogen gas (H₂) as visible bubbles.
- Color ChangeMany reactions produce a color change as substances with different light-absorbing properties form. A dramatic, sudden color change is strong evidence of a chemical reaction. Example: adding iodine solution to a starchy food turns it dark blue-black.
- Temperature ChangeReactions that release energy warm their surroundings; reactions that absorb energy cool them. A noticeable temperature change that cannot be explained by simple mixing is evidence of a chemical reaction. You will study energy in reactions in Chapter 20.
- Light ProductionSome reactions release energy as visible light — burning substances glow, glow sticks produce light through chemical reactions, and fireflies produce bioluminescence through enzyme-catalyzed chemistry. Light production is dramatic evidence of a chemical event.
- New OdorChemical reactions often produce substances with new and distinctive odors. The formation of gases like hydrogen sulfide (rotten egg smell) or ammonia (sharp, irritating) signals that new substances have formed.
Not Every Change Is a Chemical Reaction
Dissolving sugar in water changes appearance but forms no new substance. Ice melting is a physical change — water's chemical identity is unchanged. Carbon dioxide fizzing from a soda is a physical change — gas was dissolved under pressure and is now escaping, not being produced by a reaction. Chemists look for multiple lines of evidence and check whether the original substance can be recovered by reversing the process. If it can (like re-freezing melted ice), the change is physical, not chemical.
Section 13.9
Reading Equations as Particle Models
Microscopic Meaning · Counting Molecules · Particle Diagrams · What Equations Do Not Show
Section 13.9
Reading Equations as Particle Models
Every chemical equation describes a story at the level of individual atoms and molecules. Learning to visualize that story — not just to count atoms abstractly — deepens your understanding of chemistry in ways that pay dividends throughout this course.
Example 13.9.1
The particle-level story of 2H₂ + O₂ → 2H₂O
- Symbolic2 molecules of H₂ and 1 molecule of O₂ react to produce 2 molecules of H₂O.
- Particle levelTwo H–H molecules and one O=O molecule collide and interact. The H–H bonds and the O=O double bond break. Each oxygen atom bonds to two hydrogen atoms, forming two H–O–H water molecules.
- Why these coefficients?The oxygen molecule supplies 2 oxygen atoms. Each water molecule needs 1 oxygen and 2 hydrogens. To use one O₂ and produce 2 water molecules, you need 4 hydrogen atoms total — exactly 2 H₂ molecules. The balancing reflects the actual geometry of the atoms involved.
The coefficients in a balanced equation describe the ratio of molecules (or formula units) that react and form. In 2H₂ + O₂ → 2H₂O, the ratio is 2 : 1 : 2. You could read this at any scale: 2 molecules of hydrogen react with 1 molecule of oxygen to produce 2 molecules of water. Or 2 dozen. Or 2 moles. These ratios — given by the coefficients — are the foundation of all stoichiometric calculations, which you will study in Chapter 16.
Particle Diagrams
A particle diagram is a simple sketch showing atoms and molecules on each side of an equation as spheres or symbols. For CH₄ + 2O₂ → CO₂ + 2H₂O, a particle diagram would show one carbon atom surrounded by four hydrogen atoms on the left (one CH₄ molecule), two pairs of oxygen atoms (two O₂ molecules), and on the right, one carbon bonded to two oxygens (CO₂) and two oxygen atoms each bonded to two hydrogens (2H₂O). Counting up: 1 C, 4 H, 4 O on each side. The diagram makes conservation of atoms visual and concrete.
What Equations Do Not Show
It is important to know the limits of what chemical equations communicate, so you do not read more into them than is there.
| What Equations Do NOT Show | Where to Find It |
|---|
| The mechanism — the exact sequence of bond-breaking and bond-forming steps | Advanced organic chemistry and biochemistry courses |
| The reaction rate — whether it takes milliseconds or centuries | Chapter 21: Reaction Rates |
| Energy released or absorbed | Chapter 20: Thermochemistry |
| Whether the reaction actually occurs under ordinary conditions | Requires experimental confirmation or thermodynamic analysis |
Despite These Limits
The balanced chemical equation remains one of the most powerful tools in chemistry. It tells you what substances are involved, what substances form, and the precise quantitative ratios in which they participate — ratios that make stoichiometry, production calculations, pharmaceutical dosing, and industrial chemistry possible.
Chapter 13 — Back Matter
Chapter Summary
- Sec 13.1A chemical equation identifies reactants (left), products (right), and uses a reaction arrow (→) to show transformation. Equations communicate substance identity, atomic composition, and quantitative ratios. They are models of particle-level events.
- Sec 13.2Reactants are starting materials; products are substances formed. Reactants and products are chemically different. Atoms follow the arrow — they rearrange but are never created or destroyed.
- Sec 13.3Element symbols and chemical formulas are the vocabulary of equations. The seven diatomic elements (H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂) must always be written with subscript 2. Coefficients indicate quantity; subscripts indicate composition — these are never interchangeable.
- Sec 13.4To count total atoms of any element, multiply the coefficient by the subscript. Parentheses in formulas require multiplying by the subscript outside them first. This atom-counting skill is the foundation of all equation balancing.
- Sec 13.5The law of conservation of mass: atoms are neither created nor destroyed in any reaction. Total mass of reactants equals total mass of products. An unbalanced equation is scientifically incorrect — it implies atoms appeared or vanished.
- Sec 13.6Balancing is done by adjusting coefficients only — never subscripts. The inspection method: count atoms, adjust one coefficient at a time, recheck, and continue until all elements balance with coefficients in lowest whole-number ratio.
- Sec 13.7State symbols (s), (l), (g), and (aq) indicate the physical state of each substance. They predict observable events such as precipitate formation (s) or gas evolution (g). The (aq) symbol means dissolved in water.
- Sec 13.8Observable signs of a chemical reaction include precipitate formation, gas production, color change, temperature change, light production, and new odors. Not every change is chemical — if the original substance can be recovered by reversing the process, the change is physical.
- Sec 13.9Balanced equations are particle models. Coefficients give the ratio of molecules that react and form — the same ratio at any scale. Equations do not show mechanism, rate, energy, or whether a reaction actually occurs. Stoichiometry in Chapters 15–16 builds entirely on balanced equation coefficients.
Key Terms Review
reactant
A substance that enters a chemical reaction; written on the left side of the equation, before the reaction arrow.
product
A substance formed by a chemical reaction; written on the right side of the equation, after the reaction arrow.
reaction arrow
The symbol (→) separating reactants from products; means "react to form" or "yield." It is a sign of transformation, not equality.
chemical equation
A symbolic description of a chemical reaction showing the formulas and relative amounts of reactants and products.
coefficient
A whole number placed in front of a chemical formula; indicates the relative number of units of that substance. The only number that may be changed when balancing an equation.
subscript
A number written below and to the right of an element symbol in a formula; indicates the number of atoms of that element in one formula unit. Cannot be changed without changing the substance's identity.
diatomic molecule
A molecule consisting of exactly two atoms of the same element. The seven diatomic elements (H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂) must be written with subscript 2 in equations.
conservation of mass
The principle that in any chemical reaction, total mass of reactants equals total mass of products. Atoms are neither created nor destroyed.
balancing
The process of adjusting coefficients in a chemical equation so that every type of atom has equal counts on both sides of the arrow.
state symbols
Parenthetical notations showing physical state: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).
precipitate
A solid product that forms from a reaction occurring in solution; indicated by the state symbol (s) when the surrounding substances are aqueous.
aqueous (aq)
A state symbol indicating that a substance is dissolved in water — individual ions or molecules spread throughout a water solution.
particle diagram
A visual model using circles or symbols to represent individual atoms or molecules in a chemical equation; used to visualize conservation of atoms concretely.
Balancing Practice
Balance each equation by adding coefficients. Do not change any subscripts. Check your work by counting atoms on both sides.
- H₂ + Cl₂ → HCl
- Na + O₂ → Na₂O
- Al + O₂ → Al₂O₃
- N₂ + H₂ → NH₃
- C + O₂ → CO₂
- Mg + HCl → MgCl₂ + H₂
- Ca + H₂O → Ca(OH)₂ + H₂
- Fe₂O₃ + CO → Fe + CO₂
- C₃H₈ + O₂ → CO₂ + H₂O
- Al + CuSO₄ → Al₂(SO₄)₃ + Cu
- KClO₃ → KCl + O₂
- Na₂O + H₂O → NaOH
- P + O₂ → P₄O₁₀
- C₂H₆ + O₂ → CO₂ + H₂O
- Fe + H₂O → Fe₃O₄ + H₂
For each balanced equation, answer the questions that follow.
Equation A
2Mg(s) + O₂(g) → 2MgO(s)
- What are the reactants? What is the product?
- How many atoms of magnesium are on the left side? On the right side?
- What does the state symbol (s) tell you about magnesium oxide?
- What observable change might you see if you burned magnesium in air?
- Is this equation balanced? Verify by counting all atoms.
Equation B
Zn(s) + 2HCl(aq) → ZnCl₂(aq) + H₂(g)
- How many different substances are involved in this reaction?
- Which substances are aqueous? Which is a gas?
- What observable evidence might suggest this reaction is occurring?
- How many hydrogen atoms are on the left side? On the right side?
- What does the coefficient 2 in front of HCl mean?
Equation C
AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
- What type of observable event does the (s) state symbol for AgCl predict?
- Is this equation balanced? Verify by counting atoms of each element.
- Describe in words what is happening to the silver ions in this reaction.
In each situation, a student observes a chemical change. Interpret the observations using what you know about chemical equations.
- A student adds vinegar (acetic acid) to baking soda (sodium bicarbonate). Bubbles form immediately, and the container becomes slightly cool. What does the bubble formation suggest about the products? What does the cooling suggest about energy?
- Iron wool is placed in a flame and glows with bright orange sparks. The product is a black powder. What type of observable evidence suggests a chemical reaction occurred? If the product is iron(III) oxide (Fe₂O₃), what were the reactants?
- Two colorless aqueous solutions are mixed. The mixture immediately turns bright yellow. No gas or solid is observed. What type of evidence suggests a chemical reaction? What might the yellow color tell you about the product?
- A student heats mercury(II) oxide (HgO), a red-orange solid. Small droplets of liquid metal form and a colorless gas is released. What two products are forming? What evidence suggests a chemical reaction has occurred?
Error Analysis
Each student has made an error. Identify and explain the error, then write the correct answer.
Problem 1
A student balances H₂ + O₂ → H₂O by writing H₂ + O₂ → H₂O₂
What error did the student make? Why is this wrong? What is the correctly balanced equation?
Problem 2
N₂ + H₂ → N₂H₂ (student claims this is balanced: 2 N and 2 H on each side)
What is wrong with this equation? Consider what the actual product of this reaction is and whether the equation represents a real substance correctly.
Problem 3
3Fe + 4H₂O → Fe₃O₄ + 4H₂ — student says the Fe₃O₄ coefficient should be changed to 3 to balance iron
Explain why this reasoning is incorrect and state whether the original equation is actually balanced. Count all atoms.
Problem 4
C₄H₁₀ + O₂ → 4CO₂ + 5H₂O — student then writes 13O₂ on the left because they count 13 oxygens total on the right
Explain the student's counting error (hint: how many oxygen atoms are in each H₂O?). Then write the correctly balanced equation.
Problem 5
Student says 2H₂O → 2H₂ + O₂ is NOT balanced because there are 2 molecules of H₂O but only 1 molecule of O₂
Is the student correct? Remember: balance is determined by counting atoms, not molecules. Check atom counts on both sides and explain.
- A chemical formula tells you the types and numbers of atoms in one unit of a substance. What does a coefficient in a chemical equation tell you that a formula alone does not?
- How many total atoms are represented by the expression 3Ca₃(PO₄)₂?
- What is the difference between a chemical change and a physical change? Give one example of each.
- The law of conservation of mass was confirmed experimentally long before atoms were directly observed. How could scientists confirm conservation of mass without seeing atoms?
- Explain why the equation N₂ + O₂ → NO is not correctly balanced and write the corrected equation.
- Silver tarnishes to form silver sulfide (Ag₂S) when silver reacts with hydrogen sulfide gas (H₂S) in the air, also producing water vapor. Write the balanced chemical equation for this reaction, including appropriate state symbols. (Silver: solid; H₂S: gas; Ag₂S: solid; H₂O: gas.)
- The balanced equation for fermentation of glucose is: C₆H₁₂O₆(aq) → 2C₂H₅OH(aq) + 2CO₂(g). (a) What are the reactant(s) and product(s)? (b) What gas is released? (c) Verify the equation is balanced by counting all atoms on both sides. (d) What observable evidence might you see?
- Chlorine gas reacts with sodium metal to produce sodium chloride. Write the unbalanced equation using correct formulas, then balance it.
- A student finds 6 oxygen atoms on the left side of an equation and 4 on the right. Can the student fix this by changing a subscript in a product formula? Explain.
- Hydrogen peroxide (H₂O₂) decomposes into water and oxygen gas. Write the balanced equation for this decomposition reaction.
Chapter 13 Checkpoint
Chapter 13 Checkpoint
Complete without assistance — assesses all key skills and concepts from Chapter 13
Section 1 — Vocabulary and Concepts
- Define reactant and product. In the equation CH₄ + 2O₂ → CO₂ + 2H₂O, identify both.
- Explain the difference between a coefficient and a subscript, and state which may be changed during balancing and why.
- State the law of conservation of mass and explain its particle-level basis.
- List the seven diatomic elements and explain why they must be written with subscript 2 in chemical equations.
Section 2 — Atom Counting
- How many oxygen atoms are in
5Fe₂O₃?
- How many hydrogen atoms are in
4NH₄NO₃?
- How many total atoms are in
2Al₂(SO₄)₃?
Section 3 — Balancing
- Balance:
H₂ + Br₂ → HBr
- Balance:
Al + Fe₂O₃ → Al₂O₃ + Fe
- Balance:
C₂H₄ + O₂ → CO₂ + H₂O
- Balance:
Cu + AgNO₃ → Cu(NO₃)₂ + Ag
Section 4 — State Symbols and Evidence
- Write state symbols for the following substances in the given conditions: solid calcium carbonate, liquid water, carbon dioxide gas, sodium chloride dissolved in water.
- A student mixes two clear aqueous solutions and immediately observes a white solid settling to the bottom. What type of product has formed? What state symbol appears in the equation for that product?
- Name four observable signs that a chemical reaction has occurred and give one example of each.
Section 5 — Reading Equations as Particle Models
- For the balanced equation 2H₂ + O₂ → 2H₂O, explain in your own words what is happening at the particle level. What bonds are breaking? What bonds are forming?
- Name two things that a balanced chemical equation does NOT tell you about a reaction, and identify where in this course you will find that information.
Section 6 — Error Analysis
- A student writes the following to balance an equation: the unbalanced form is H₂ + N₂ → NH₃, and the student "fixes" it by writing H₂ + N₂ → NH₆. Identify all errors and write the correctly balanced equation.
Looking Ahead
Chapter 14: Types of Chemical Reactions
Chapter 13 gave you the tools to write and balance chemical equations — the symbolic language of chemical change. Chapter 14 uses this foundation to explore the patterns that chemical reactions follow. Not all reactions are random or unpredictable. Chemists have found that most reactions belong to recognizable categories: synthesis, decomposition, single-replacement, double-replacement, combustion, and others. Knowing which category a reaction belongs to helps you predict what the products will be — even before you do the experiment. In Chapter 14, you will learn to recognize each major reaction type, predict products from reactant information, and balance equations in a variety of chemical contexts. Every balancing skill you built here will be applied to every new reaction type you encounter.
MGU Library Connection
- Chemical Nomenclature Reference — Chapter 11: Chemical Names and Formulas
- Ionic and Covalent Bonding Review — Chapters 9 and 10
- Stoichiometry — Chapter 16 (builds directly on balanced equations from this chapter)
- Reactions in Aqueous Solution — Chapter 17 (extends state symbols to ionic and net ionic equations)
- Appendix D: Polyatomic Ions (useful reference when balancing equations with polyatomic groups)
- Appendix E: Solubility Rules (used to predict precipitate formation in Chapter 17)