Conservation of mass and balanced chemical equations: Students should understand the use of the multipliers in equations in normal script before a formula and in subscript within a formula.

The idea

Chemical equations use two kinds of multiplier, and confusing them changes the substance. A subscript sits inside a formula and multiplies only the atom or group immediately before it: in H₂O the 2 means two hydrogen atoms bonded to one oxygen, giving one water molecule. A normal-script number before a formula multiplies the whole formula: 2H₂O means two separate water molecules, so four hydrogen atoms and two oxygen atoms in total. When balancing, adjust the large number in front, never a subscript, because changing a subscript alters the identity of the substance.

For example: 2H₂ + O₂ → 2H₂O is balanced, whereas writing H₂O₂ would describe hydrogen peroxide, a different compound.

What earns the marks

• A subscript within a formula multiplies only the atom or group immediately before it, as in H₂O or Ca(OH)₂.
• A normal-script number before a formula multiplies every atom in that formula, as in 2H₂O giving four H atoms and two O atoms.
• Changing a subscript changes the chemical identity of the substance, so subscripts are fixed by the formula of each reactant and product.
• Balancing is achieved by placing or adjusting normal-script multipliers in front of formulae until the number of each type of atom is equal on both sides.
• Counting atoms in a displayed equation requires multiplying the front number by each subscript in the formula that follows it.
• The same conventions apply to formulae containing brackets, where a subscript after a bracket multiplies everything inside the bracket.

Common mistakes and how to put them right

• Treating a subscript as if it multiplied the whole formula, for example reading H₂O as two hydrogen molecules.

  Put it right by noting the subscript belongs only to the atom or group immediately before it.

• Balancing by altering subscripts, such as changing H₂O to H₂O₂.

  Put it right by keeping every formula unchanged and adjusting only the normal-script multipliers.

• Forgetting to multiply every atom when a front number is present, for example counting 2H₂O as only two hydrogen atoms.

  Put it right by multiplying the front number by each subscript in turn.

Exam tips

• When asked to balance an equation, count each element on both sides after every change and record the totals so errors are easy to spot.
• If an equation will not balance with whole-number multipliers, double all multipliers rather than introducing fractions or altering formulae.
• In written answers, distinguish clearly between a subscript and a front number, for example by describing 2H₂O as two molecules of water.