Formulae and Equations

A chemical formula shows which elements a substance contains and in what ratio. A balanced equation has the same number of each type of atom on both sides, because atoms are rearranged, never created or destroyed. State symbols (s), (l), (g), (aq) show the physical state. Ionic equations show only the ions that actually react.

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Section 1 of 14

Learning objectives

Write formulae from names and ion charges.
Balance symbol equations and add state symbols.
Write ionic equations by removing spectator ions.

Pause and think

When you burn a candle, it gets smaller. Has mass been destroyed?

Section 2 of 14

Core idea

Start hereNothing lost, nothing gained

Burn 10 g of magnesium ribbon in a sealed flask and weigh it after: still the same total mass. Atoms rearrange in a reaction, but they never appear or vanish. Balanced equations are just a way of keeping that count honest.

The big idea

A formula fixes the ratio of atoms in a substance. A balanced equation keeps the number of each type of atom the same on both sides, by changing only the numbers in front of the formulae.

1. Writing formulae

Worked exampleIron(III) sulfate

Write the formula of iron(III) sulfate.

Goal: A neutral formula.
Strategy: Use the ion charges: $\mathrm{Fe^{3+}}$ , $\mathrm{SO_4^{2-}}$ .

$\mathrm{LCM}(3,2)=6$
Total positive charge must equal total negative charge.
$\mathrm{Fe_2(SO_4)_3}$
Two iron ions ( $+6$ ), three sulfate ions ( $-6$ ); brackets keep the sulfate ion together.

Answer

\mathrm{Fe_2(SO_4)_3}

✓ Check

2(+3)+3(-2)=0

✓.

2. Balancing

Worked exampleBurning propane

$\mathrm{C_3H_8+O_2\rightarrow CO_2+H_2O}$

Goal: Balance.
Strategy: Carbon first, then hydrogen, oxygen last (it appears alone).

$\mathrm{C_3H_8+O_2\rightarrow 3CO_2+H_2O}$
3 C on the left.
$\mathrm{C_3H_8+O_2\rightarrow 3CO_2+4H_2O}$
8 H on the left.
$\mathrm{C_3H_8+5O_2\rightarrow 3CO_2+4H_2O}$
O on the right: $6+4=10$ , so 5 $\mathrm{O_2}$ .

Answer

\mathrm{C_3H_8+5O_2\rightarrow3CO_2+4H_2O}

✓ CheckC 3, H 8, O 10 on each side ✓.

3. Ionic equations

Writing an ionic equation

Drawing diagram…

Only dissolved ionic substances are split into ions.

Common misconceptionSubscripts are sacred Changing

\mathrm{H_2O}

\mathrm{H_2O_2}

balances oxygen but makes hydrogen peroxide. Only coefficients may change.

Pause and think

Why is the ionic equation the same for every strong acid and alkali?

Summary

Charges balance in formulae.
Balance with coefficients.
State symbols (s)(l)(g)(aq).
Ionic equations omit spectators.

Coefficient: Number in front of a formula in an equation.
Spectator ion: An ion present but unchanged in the reaction.
State symbol: Shows whether a substance is solid, liquid, gas or aqueous.

HistoryBerzelius. In 1813 Jöns Jacob Berzelius invented the letter symbols we still use (O, H, Fe from ferrum) to replace alchemists' drawings.

Fun factConservation, the hard way. Lavoisier proved mass is conserved by heating tin in sealed glass vessels and weighing them before and after: the total never changed.

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