Reactions and Equations

Chemistry Fundamentals

Course 1 · Chapter 6 · Chemical Reactions and Equations: Writing Down a Change

Chapter 1 separated physical change from chemical change: in a chemical change new substances form. Chapters 4 and 5 then gave you the formulae of ionic compounds and of molecules. Now the two come together. A chemical equation is the shorthand chemists use to record a chemical change, using those formulae. Wikipedia's Chemical reaction article defines a reaction as "a process that leads to the chemical transformation of one set of chemical substances to another". This chapter covers how to read and write equations, why they must balance, how to balance one step by step, and the main types of reaction. It also covers what an equation leaves out, which is a lot.

Reactants and Products

The Chemical reaction article calls the starting substances "reactants or reagents", and says the reaction yields "one or more products, which usually have properties different from the reactants". That last phrase is Chapter 1's test for chemical change in other words: the product is a new substance with new properties. The Chemical equation article says "The reactant entities are given on the left-hand side, and the product entities are on the right-hand side", and the Chemical reaction article says the arrow "points in the direction in which the reaction proceeds".

Word equation

The substances written in words: hydrogen + oxygen → water. Easy to read, but it says nothing about how many of each (the format is my own teaching device (check)).

Symbol equation

The same change in formulae with coefficients. The Chemical equation article says a coefficient "specifies how many entities (e.g. molecules) of that substance are involved".

State symbols

Small labels after each formula. The Chemical equation article lists "(s) for a solid, (l) for a liquid, (g) for a gas, and (aq) for an aqueous solution".

"Aqueous" means dissolved in water (my own gloss (check)). Take the notation from Chapter 5: O₂ is a molecule of two oxygen atoms, so the subscript sits inside a formula and cannot be changed. The big number in front, the coefficient, is the part you are allowed to adjust.

Why an Equation Must Balance

The Chemical equation article states the requirement directly: "each side of the chemical equation must represent the same number of atoms of any particular element". The reason is the law of conservation of mass. Wikipedia's Conservation of mass article says "the mass of the system must remain constant over time", for systems closed to all matter transfers, and that mass conservation in chemical reactions was "finally confirmed by Antoine Lavoisier in the late 18th century". The page's history section says he "expressed his conclusion in 1773 and popularized the principle of conservation of mass", and that his experiments disproved the phlogiston theory, which held that mass could be gained or lost in combustion. The Chemical reaction article adds a connected credit: "Antoine Lavoisier developed the theory of combustion as a chemical reaction with oxygen."

The picture behind it, using Chapter 2, is that a reaction rearranges atoms and does not create or destroy them. In the lines of the Chemical equation article, the total electric charge also has to match on both sides, which matters once ions are involved (Chapter 4).

The caveats on the page The Conservation of mass article says the law "holds only in the classical limit", and that mass is not conserved in open systems, though energy transfers are usually too small to measure unless radioactivity or nuclear reactions are involved. It also says Lomonosov's priority is "sometimes challenged", and that the article itself needs more citations. For everyday chemistry, a closed container, balancing is correct. A burning candle seems to lose mass only because the gases escape (my own explanation (check)).

Balancing Step by Step: Hydrogen and Oxygen

The Chemical equation article says simple equations can be balanced "by inspection, that is, by trial and error". It had no hydrogen-and-oxygen example, so the working below is my own, with every count produced by a Python script. Start from the formulae, which must be right first: hydrogen gas is H₂ and oxygen gas is O₂ (the Diatomic molecule article from Chapter 5), and water is H₂O.

Step	Equation	H (left / right)	O (left / right)
1. Write the unbalanced equation	H₂ + O₂ → H₂O	2 / 2	2 / 1
2. Fix oxygen: 2 water	H₂ + O₂ → 2H₂O	2 / 4	2 / 2
3. Fix hydrogen: 2 hydrogen	2H₂ + O₂ → 2H₂O	4 / 4	2 / 2

Step 1 fails on oxygen: two atoms in, one out. You cannot repair this by writing H₂O₂ or O, because that changes the substance (Chapter 5's molecular formula) and so changes the chemistry; only coefficients may change. Doubling the water fixes oxygen but upsets hydrogen, so a second adjustment follows. This back-and-forth is normal. The Python check of the finished equation gave H = 4 and O = 2 on each side.

2H2(g) + O2(g)  →  2H2O(l)

left :  H = 2 x 2 = 4     O = 1 x 2 = 2
right:  H = 2 x 2 = 4     O = 2 x 1 = 2     balanced

State symbols were added here from the notation above; that hydrogen and oxygen are gases and water a liquid at ordinary conditions is my own general knowledge (check).

A second example: burning methane

The Chemical equation article and the Combustion article both give methane burning as CH₄ + 2 O₂ → CO₂ + 2 H₂O, and the Combustion article says "When a hydrocarbon burns in oxygen, the reaction will primarily yield carbon dioxide and water." Rebuilding it from the unbalanced start, my Python count gave:

Element	CH₄ + O₂ → CO₂ + H₂O	CH₄ + 2O₂ → CO₂ + 2H₂O
C	1 / 1	1 / 1
H	4 / 2	4 / 4
O	2 / 3	4 / 4

A balancing routine that usually works Balance the elements that appear in the fewest substances first, and leave an element that appears alone (such as O₂) until last, because changing its coefficient disturbs nothing else. Then recount every element. This routine is my own advice, not from a page (check).

The Main Types of Reaction

The Chemical reaction article names several types. The quotations are from that page; the example equations are noted where they come from.

Type	What the page says	Example
Synthesis	"two or more simple substances combine to form a more complex substance"	2H₂ + O₂ → 2H₂O (my classification (check))
Decomposition	"a more complex substance breaks down into its more simple parts"	2H₂O → 2H₂ + O₂ (balance checked in Python; the type is my classification (check))
Single displacement	"a single uncombined element replaces another in a compound"	2HCl + 2Na → 2NaCl + H₂ (the equation is from the Chemical equation article; classing it here is mine (check))
Double displacement	"the anions and cations of two compounds switch places and form two entirely different compounds"	AgNO₃ + NaCl → AgCl + NaNO₃ (my example (check))
Combustion	"an element or compound reacts with an oxidant, usually oxygen, often producing energy in the form of heat or light"	CH₄ + 2 O₂ → CO₂ + 2 H₂O (Combustion article)

All five examples balanced when I ran the atom counts in Python. A reaction can fit more than one label: burning hydrogen is both a synthesis and a combustion if you use the page's definition of combustion (my reading (check)). The labels are a way to recognise patterns and not exclusive boxes. Note too the Combustion article's definition: "a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant"; the terms exothermic and redox are not covered until later.

What a Balanced Equation Does Not Tell You

A balanced equation is a record of the atom count and of the proportions in which substances react. It leaves out a great deal.

Whether the reaction happens. The Chemical reaction article says "Reactions can proceed by themselves if they are exergonic, that is if they release free energy." Writing an equation does not make a reaction occur; the Chemical equation article says that for ionic equations, "If every ion is a 'spectator ion' then there was no reaction."
How fast. The Chemical reaction article says "The speed at which reactions take place is studied by reaction kinetics." The equation has no time in it. Chapter 9 returns to speed.
Conditions and catalysts. The Chemical equation article notes these are shown only if added above or below the arrow.
Direction. The Chemical reaction article says most reactions are reversible, "they can and do run in both directions", and that a double arrow marks equilibrium reactions.
Masses. A coefficient counts molecules, not grams. Turning counts into amounts you can weigh is the job of Chapter 7.

Common mistakes Changing a subscript to make the numbers fit (this turns water into something else); forgetting that a coefficient multiplies every atom in the formula it stands before, so 2H₂O has 4 hydrogen and 2 oxygen; and balancing the atoms but forgetting to recount after the last change. A short atom-count table, as above, catches all three. This list is my own experience-based advice (check).

What I did and did not read The Chemical reaction page is 252,170 characters long and I read the first 100,000, which stops in the organic chemistry section; the later sections were not read. The Chemical equation and Conservation of mass pages were reported to me as complete. The Combustion page is 117,368 characters and I read the first 100,000. All quotations came through the fetch tool's summary of each page, so check them against the pages before relying on them. Atom counts were run in Python. Statements marked "(check)" are my own knowledge or reasoning.

Where to Read More

Encyclopaedias. The Wikipedia articles Chemical reaction, Chemical equation, Conservation of mass and Combustion are the sources used here.
A school textbook. Look for graded balancing practice and the idea of ionic equations.
Practical. Write an equation for something you have seen happen at home, then do the atom-count table. If the counts do not match, the equation is wrong, not the world.

Exercises

Exercise 1

Balance and prove it. Balance N₂ + H₂ → NH₃ (nitrogen and hydrogen forming ammonia), showing each step. Then make an atom-count table with the left and right totals for each element before and after balancing, and say what you would be doing wrong if you changed NH₃ to NH₂.

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Exercise 2

Classify the reaction. For each balanced equation, name the type from this chapter (synthesis, decomposition, single displacement, double displacement or combustion) and give the one phrase from the type's description that justifies it: (a) 2H₂O₂ → 2H₂O + O₂; (b) CH₄ + 2O₂ → CO₂ + 2H₂O; (c) 2HCl + 2Na → 2NaCl + H₂; (d) AgNO₃ + NaCl → AgCl + NaNO₃. Say whether any fits more than one label.

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Exercise 3

From description to equation. Magnesium, a solid metal, burns in oxygen gas to form the white solid magnesium oxide. Write a word equation, then a symbol equation with state symbols, using the Chapter 4 idea of ion charges to get the formula of magnesium oxide. Balance it, show an atom-count table, and name one thing the equation does not tell you about the burning.

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Quick Reference

Reactants → products: starting substances on the left, new substances on the right
Word equation / symbol equation: words first, then formulae with coefficients
State symbols: (s) solid, (l) liquid, (g) gas, (aq) aqueous solution
Balance: same number of atoms of each element on both sides; change coefficients only, never subscripts
Why: conservation of mass, confirmed by Lavoisier in the late 18th century, per the Conservation of mass article
Types: synthesis, decomposition, single displacement, double displacement, combustion
Not shown by an equation: whether it happens, how fast, conditions, and masses
Always: recount every element after the last change

Coming next Chapter 7 turns the counts in an equation into quantities you can weigh and measure: the mole, the Avogadro constant, molar mass and simple stoichiometry.