IMAT Chemistry · Stoichiometry and Reactions

Conservation of Mass, Balancing and Ionic Equations

Atoms are neither made nor destroyed in a reaction, so a correct equation has the same atoms, and the same total charge, on both sides.

All Stoichiometry and Reactions notes

Why this matters

Balancing appears in 2013, 2015 and 2020: a missing coefficient, the ratio of products when an organic compound burns, and picking the one correct equation. Ionic equations for a precipitate were asked in 2016 and 2022.

Concept 1 of 3: Conservation of mass and balancing an equation

A reaction only rearranges atoms into new partners. Every atom on the left must turn up on the right, so the total mass cannot change. Balancing is the bookkeeping that makes this true: you change how many of each substance take part, never what the substances are.

Definition

Law of conservation of mass: in a closed system the total mass of the products equals the total mass of the reactants.
A balanced equation has the same number of each kind of atom on both sides.
Change only the coefficients (the numbers in front). Changing a subscript changes the substance.
Start with an element that appears in only one substance on each side; leave elements that appear as the free element ( $\mathrm{O_2}$ , $\mathrm{H_2}$ , a metal) until last.
Use the smallest whole numbers. For a missing coefficient written as a letter, count one element at a time and solve for it.

Conservation of mass

\sum m_{\text{reactants}} = \sum m_{\text{products}}

$m$ mass of each substance taking part, in g

Worked example

Balance the equation for aluminium burning in oxygen:

\mathrm{Al} + \mathrm{O_2} \rightarrow \mathrm{Al_2O_3}

. Then check that mass is conserved. (Al = 27, O = 16)

Practice this conceptself-check · 4 quick reps

Never balance by changing a subscript

Turning

\mathrm{H_2O}

into

\mathrm{H_2O_2}

to fix the oxygen count makes hydrogen peroxide, a different substance. Options that balance the atoms with an impossible formula (MgOH,

\mathrm{Mg_2O}

) are wrong even when the atoms add up.

Concept 2 of 3: Balancing the combustion of organic compounds

When a compound of carbon and hydrogen burns completely, every carbon atom ends up in a

\mathrm{CO_2}

molecule and every pair of hydrogen atoms in a water molecule. So the products follow straight from the formula, and oxygen is balanced last. If the fuel already contains oxygen, less oxygen gas is needed.

Definition

For complete combustion of $\mathrm{C_xH_yO_z}$ in excess oxygen:

The only products are carbon dioxide and water.
Moles of $\mathrm{CO_2}$ = $x$ ; moles of $\mathrm{H_2O}$ = $y/2$ (per mole of fuel).
Moles of $\mathrm{O_2}$ needed = $x + y/4 - z/2$ .
If the result is a fraction, double every coefficient.
In too little oxygen, combustion is incomplete: carbon monoxide or soot (carbon) forms as well.

Complete combustion

\mathrm{C_xH_yO_z} + \left(x + \tfrac{y}{4} - \tfrac{z}{2}\right)\mathrm{O_2} \rightarrow x\,\mathrm{CO_2} + \tfrac{y}{2}\,\mathrm{H_2O}

$x, y, z$ numbers of C, H and O atoms in one molecule of the fuel

Worked example

Write the balanced equation for the complete combustion of butane,

\mathrm{C_4H_{10}}

Practice this conceptself-check · 3 quick reps

Count the oxygen already inside the fuel

Alcohols, sugars and other oxygen-containing fuels bring some oxygen atoms with them, so they need less

\mathrm{O_2}

than the hydrocarbon with the same carbon and hydrogen. Forgetting this gives a coefficient that is too large.

Concept 3 of 3: Ionic equations and spectator ions

In solution, soluble ionic compounds are split into separate ions. When two such solutions are mixed, most ions simply float around unchanged. The ionic equation keeps only the particles that actually change, which shows what the reaction really is.

Definition

Write soluble ionic compounds, strong acids and strong bases as separate ions.
Keep solids (precipitates), liquids, gases, water and weak acids as formulas.
Ions that appear unchanged on both sides are spectator ions; cross them out to get the net (simplest) ionic equation.
A correct ionic equation balances atoms and charge. The ion charges set the formula of the precipitate: $\mathrm{Pb^{2+}}$ needs two $\mathrm{I^-}$ , giving $\mathrm{PbI_2}$ .
State symbols: (s) solid, (l) liquid, (g) gas, (aq) dissolved in water.

Worked example

Silver nitrate solution is mixed with sodium chloride solution and a white precipitate of silver chloride forms. Write the net ionic equation and name the spectator ions.

Practice this conceptself-check · 4 quick reps

Simplest ionic equation means no spectators

An equation that lists every ion on both sides is balanced, but it is not the simplest ionic equation. Remove every ion that appears unchanged on both sides; what is left must still balance in atoms and in charge.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Conservation of mass and balancing an equation
Conservation of mass
$\sum m_{\text{reactants}} = \sum m_{\text{products}}$
Balancing the combustion of organic compounds
Complete combustion
$\mathrm{C_xH_yO_z} + \left(x + \tfrac{y}{4} - \tfrac{z}{2}\right)\mathrm{O_2} \rightarrow x\,\mathrm{CO_2} + \tfrac{y}{2}\,\mathrm{H_2O}$

Watch out for (3)

Never balance by changing a subscript
→ Conservation of mass and balancing an equation
Count the oxygen already inside the fuel
→ Balancing the combustion of organic compounds
Simplest ionic equation means no spectators
→ Ionic equations and spectator ions

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