Conservation of Mass and Balanced Equations

In any chemical reaction, atoms are only rearranged. Bonds between atoms break and new bonds form, but not a single atom is created or destroyed. Because every atom that starts the reaction is still present at the end, the total mass cannot change.

Law of conservation of mass: the total mass of the products of a reaction is equal to the total mass of the reactants. No atoms are lost or made.

This is why chemists write balanced symbol equations. A balanced equation is the atom-by-atom accounting record that proves nothing has gone missing.

Take the neutralisation of sodium hydroxide by hydrochloric acid:

$\text{NaOH}+\text{HCl}\to \text{NaCl}+{\text{H}}_2\text{O}$

Count the atoms on each side: 1 Na, 1 O, 2 H and 1 Cl appear on the left, and exactly the same 1 Na, 1 O, 2 H and 1 Cl appear on the right. The equation is balanced, so mass is conserved.

Balancing an equation means getting the same number of each atom on both sides. You do this by placing multipliers (large numbers) in front of formulae. You must never change a subscript (a small number inside a formula), because that would change the substance itself.

A multiplier in front of a formula multiplies every atom in that formula. A subscript applies only to the atom it follows. Changing a subscript changes what the substance is.

Compare these carefully:

Written	Meaning	Atoms of each element
$2{\text{H}}_2\text{O}$	two water molecules	4 H, 2 O
${\text{H}}_2{\text{O}}_2$	one hydrogen peroxide molecule	2 H, 2 O

$2{\text{H}}_2\text{O}$ is still water; ${\text{H}}_2{\text{O}}_2$ is a completely different chemical. That is why you only ever adjust the multipliers when balancing.

Worked example — balance the combustion of methane:

${\text{CH}}_4+{\text{O}}_2\to {\text{CO}}_2+{\text{H}}_2\text{O}$

Carbon is already balanced (1 each side). The left has 4 H but the right has only 2, so put a 2 in front of water: ${\text{CH}}_4+{\text{O}}_2\to {\text{CO}}_2+2{\text{H}}_2\text{O}$. Now count oxygen on the right: 2 (in CO₂) + 2 (in 2H₂O) = 4, so put a 2 in front of O₂.

${\text{CH}}_4+2{\text{O}}_2\to {\text{CO}}_2+2{\text{H}}_2\text{O}$

Final check: 1 C, 4 H, 4 O on each side. Balanced.

A reliable routine stops you guessing. Count each element, balance the most complicated formula first, save single elements such as O₂ or H₂ until last, then recount everything.

Worked example — balance the reaction of aluminium with oxygen to make aluminium oxide:

$\text{Al}+{\text{O}}_2\to {\text{Al}}_2{\text{O}}_3$

Oxygen appears as O₂ (a pair) on the left and O₃ (in threes) on the right. The lowest number that both 2 and 3 divide into is 6, so aim for 6 oxygen atoms on each side.

• Right side: put 2 in front of Al₂O₃ to give 6 O and 4 Al.
• Left side: put 3 in front of O₂ to give 6 O, then 4 in front of Al to match the 4 Al.

$4\text{Al}+3{\text{O}}_2\to 2{\text{Al}}_2{\text{O}}_3$

Check: left has 4 Al and 6 O; right has 4 Al and 6 O. Balanced.

When a single element such as O₂, H₂ or Cl₂ is the last thing left, balance it last. It has no other atoms attached, so changing its multiplier does not upset anything else.

If a reaction is done in an open container, the mass on the balance can appear to change even though mass is truly conserved. The apparent change is always explained by a gas that the balance cannot weigh entering or leaving.

When a metal is heated in air, it gains oxygen from the atmosphere. The oxide formed is heavier than the metal you started with because the mass of the reacting oxygen has been added.

Worked example — magnesium burning in air:

$2\text{Mg}+{\text{O}}_2\to 2\text{MgO}$

If 2.4 g of magnesium reacts completely, the product weighs more than 2.4 g. Using the balanced equation, 2.4 g of Mg combines with 1.6 g of oxygen from the air, so the white magnesium oxide left in the crucible weighs 4.0 g.

$2.4\text{g (Mg)}+1.6{\text{g (O}}_2\text{)}=4.0\text{g (MgO)}$

The balance seems to show mass being created, but the extra 1.6 g came from oxygen in the air. In a sealed container the total mass would not change at all.

The opposite happens when a reaction gives off a gas that escapes from an open container. The mass on the balance falls, because the escaping gas is no longer being weighed.

The classic case is the thermal decomposition of a metal carbonate, where heating breaks it down and releases carbon dioxide.

Worked example — heating calcium carbonate:

${\text{CaCO}}_3\to \text{CaO}+{\text{CO}}_2$

If 10.0 g of calcium carbonate decomposes fully, 4.4 g of carbon dioxide escapes into the air and 5.6 g of calcium oxide is left behind.

$10.0{\text{g (CaCO}}_3\text{)}=5.6\text{g (CaO)}+4.4{\text{g (CO}}_2\text{)}$

The solid mass in the tube drops from 10.0 g to 5.6 g. Mass is still conserved: the "missing" 4.4 g left the container as gas. Explain these observations using the balanced equation and the idea that gas particles have spread out into the surroundings.

Every measurement carries some uncertainty, so a single reading is never the whole story. When you repeat a measurement, the readings scatter a little around the true value, and you can use that scatter to estimate how confident you can be.

Estimate the uncertainty of a set of repeats from the range: the difference between the highest and lowest value. The result is usually quoted as the mean ± half the range.

Worked example — a student measures the temperature rise of a reaction four times and records 6.8, 7.2, 7.0 and 7.4 °C.

• Mean = (6.8 + 7.2 + 7.0 + 7.4) ÷ 4 = 28.4 ÷ 4 = 7.1 °C
• Range = highest − lowest = 7.4 − 6.8 = 0.6 °C
• Uncertainty = ± half the range = ± 0.3 °C

The result is reported as 7.1 ± 0.3 °C. A smaller range means more precise, more repeatable measurements. Spotting and ignoring an obvious anomalous result before averaging keeps the mean and range meaningful.

1. Changing a subscript to balance an equation

Only the large multipliers in front of formulae may be changed. Rewriting H₂O as H₂O₂ turns water into hydrogen peroxide and scores nothing. Balance by adjusting multipliers only.

2. Saying mass is created or destroyed

Mass is always conserved. When the balance reading changes in an open container, it is because a gas has entered or escaped, not because atoms have appeared or vanished. Always link the change to the gas in the balanced equation.

3. Forgetting a multiplier applies to the whole formula

In 2H₂O, the 2 multiplies everything, giving 4 hydrogen atoms and 2 oxygen atoms, not just 2 hydrogen atoms. Count every atom the multiplier acts on.

4. Explaining a mass decrease without naming the gas

"The mass went down" is not an explanation. State that a gas, such as CO₂ from a decomposing carbonate, escaped from the open container, which is why the mass of solid fell while total mass was conserved.

5. Confusing range and uncertainty

The uncertainty is half the range, not the whole range. For readings from 6.8 to 7.4 the range is 0.6, so the uncertainty quoted with the mean is ± 0.3.