ChemistryICSE Class 9 · The Language of Chemistry

Valency, Radicals and Writing Formulae by the Criss-Cross Method (ICSE Class 9)

Updated 17 October 2026 · Fact-checked

Valency is the combining capacity of an element or radical. To write a formula, put the basic radical first, write each valency above its symbol, exchange them as subscripts, simplify and put a group radical in brackets if its subscript is more than 1. Variable valency is shown by -ous (lower) and -ic (higher). A free radical has an unpaired electron and is very reactive.

Swap the valencies so each becomes the other's subscript, and put the group radical SO₄ in brackets because its subscript is more than 1.

Illustration drawn for QuestionBuddy.

Understand Valency, Radicals and Writing Chemical Formulae by Criss-Cross

Valency. The combining capacity of an element. It can be found from the number of hydrogen atoms an atom combines with (HCl: Cl is 1; H₂O: O is 2; NH₃: N is 3; CH₄: C is 4) or from the electrons it loses, gains or shares. Metals lose electrons, non-metals gain or share them.

Radicals. A radical is an atom or group of atoms with a charge that behaves as one unit. Basic radicals are positive (Na⁺, K⁺, NH₄⁺, Mg²⁺, Ca²⁺, Zn²⁺, Al³⁺ ...); acid radicals are negative (Cl⁻, OH⁻, NO₃⁻, HCO₃⁻, SO₄²⁻, CO₃²⁻, PO₄³⁻ ...). The charge is the valency.

Variable valency. Some metals have two valencies. The lower one takes the ending -ous and the higher one -ic: ferrous Fe²⁺ and ferric Fe³⁺; cuprous Cu⁺ and cupric Cu²⁺. In modern names the valency is written in brackets: iron(II) and iron(III).

Criss-cross method.
1. Write the basic radical first, then the acid radical.
2. Write the valency above each symbol or radical.
3. Exchange the valencies and write them as subscripts.
4. Divide by the common factor, do not write 1, and place a group radical in brackets if its subscript is more than 1.

Compound	Working	Formula
Aluminium sulphate	Al 3, SO₄ 2 → Al₂(SO₄)₃	Al₂(SO₄)₃
Magnesium nitrate	Mg 2, NO₃ 1 → Mg(NO₃)₂	Mg(NO₃)₂
Calcium phosphate	Ca 2, PO₄ 3 → Ca₃(PO₄)₂	Ca₃(PO₄)₂
Ammonium carbonate	NH₄ 1, CO₃ 2 → (NH₄)₂CO₃	(NH₄)₂CO₃

Finding a valency from a formula. Reverse the process: for Al₂O₃ the subscript of Al (2) becomes the valency of O, and the subscript of O (3) becomes the valency of Al. For $M_{x} Y_{y}$ with Y of known valency, valency of $M = \frac{y \times valency of Y}{x}$ .

Free radicals. Distinguish from ions: a free radical is an atom or group with an unpaired electron, for example the hydroxyl radical ·OH (9 electrons), the chlorine atom Cl· (17 electrons) and nitric oxide NO. The hydroxide ion OH⁻ (10 electrons) and chloride ion Cl⁻ (18 electrons) have all electrons paired and are stable.

*Formation:* ultraviolet light splitting molecules high in the atmosphere, hot flames, vehicle engines.
*Effects:* very reactive; harm living cells (ageing, some cancers); chlorine radicals from CFCs damage the ozone layer; radicals from exhaust help form photochemical smog.
*Reduction:* cleaner fuels and catalytic converters, phasing out CFCs, avoiding tobacco smoke, antioxidants (vitamins C and E) in food.

Valency, Radicals and Writing Chemical Formulae by Criss-Cross: formulas and key facts

Criss-cross rule: $A^{x} B^{y} \to A_{y} B_{x} (then simplify)$; Group radicals in brackets.
Valency from formula: $valency of M = \frac{y \times valency of Y}{x}$; For M_xY_y.
Variable valency names: $ferrous F e^{2 +}; ferric F e^{3 +}; cuprous C u^{+}; cupric C u^{2 +}$; -ous lower; -ic higher.
Free radical: $free radical: unpaired electron; \cdot O H (9 e^{-}), O H^{-} (10 e^{-})$; Radical versus ion.

How to solve Valency, Radicals and Writing Chemical Formulae by Criss-Cross questions

Always check that total positive valency equals total negative valency.

1Write the symbols or radicals with their valencies.
2Exchange the valencies as subscripts.
3Simplify to the lowest ratio; omit the subscript 1.
4Bracket any group radical taken more than once.
5Check: (subscript × valency) of the cation equals that of the anion.

Valency, Radicals and Writing Chemical Formulae by Criss-Cross in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Reading a fertiliser bag

Suppose a bag is labelled "ammonium phosphate" and you need its formula.

Write the formula and check the charges.

Try it first, then show the solutionSolution

NH₄ is 1 and PO₄ is 3, so exchange: (NH₄)₃PO₄.
Check: positive $3 \times 1 = 3$ ; negative $1 \times 3 = 3$ . Balanced.

Answer: (NH₄)₃PO₄.

Memory hook: Exchange, simplify, check the charges.

Tricks to remember Valency, Radicals and Writing Chemical Formulae by Criss-Cross

Short memory aids. Say each one aloud once, then use it on a question the same day.

Criss-cross
The valency of one becomes the subscript of the other.
Use it when: Writing formulae.
-ous is lower, -ic is higher
Ferrous 2, ferric 3. Cuprous 1, cupric 2.
Use it when: Variable valency.
Radical versus ion
Radical: odd electron, reactive. Ion: paired electrons, stable.
Use it when: Free radical questions.

Valency, Radicals and Writing Chemical Formulae by Criss-Cross: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Valency of phosphate · 1 mark · MCQBoard level

The valency of the phosphate radical (PO₄) is:
(a) 1
(b) 2
(c) 3
(d) 4

Try it first, then show the solutionSolution

The phosphate radical is PO₄³⁻, so its valency is 3.

Answer: (c) 3

Example 2: Writing four formulae · 2 marks · Short answerBoard level

Write the formulae of (a) magnesium nitrate, (b) aluminium sulphate, (c) ammonium carbonate, (d) calcium phosphate.

Try it first, then show the solutionSolution

(a) Mg²⁺, NO₃⁻: Mg(NO₃)₂. (½)
(b) Al³⁺, SO₄²⁻: Al₂(SO₄)₃. (½)
(c) NH₄⁺, CO₃²⁻: (NH₄)₂CO₃. (½)
(d) Ca²⁺, PO₄³⁻: Ca₃(PO₄)₂. (½)

Answer: Mg(NO₃)₂; Al₂(SO₄)₃; (NH₄)₂CO₃; Ca₃(PO₄)₂

Example 3: Finding the valency of a metal · 3 marks · Short answerHarder board level

The sulphate of a metal M has the formula M₂(SO₄)₃. (a) Find the valency of M. Write the formulae of (b) its nitrate, (c) its phosphate, (d) its hydroxide.

Try it first, then show the solutionSolution

(a) Valency of M = subscript of SO₄ = 3 (check: $2 \times 3 = 3 \times 2$ ). (1)
(b) M(NO₃)₃. (½)
(c) MPO₄ (3 and 3 simplify to 1 and 1). (1)
(d) M(OH)₃. (½)

Answer: (a) 3 (b) M(NO₃)₃ (c) MPO₄ (d) M(OH)₃

Example 4: Variable valency · 3 marks · Short answerHarder board level

Name and give the valency of the metal in (a) Fe(NO₃)₃, (b) Cu₂O, (c) FeCl₂.

Try it first, then show the solutionSolution

(a) Ferric nitrate, iron(III); valency 3. (1)
(b) Cuprous oxide, copper(I); valency 1 (Cu₂ with O of valency 2). (1)
(c) Ferrous chloride, iron(II); valency 2. (1)

Answer: (a) ferric, 3 (b) cuprous, 1 (c) ferrous, 2

Example 5: Radical or ion? · 4 marks · Case-basedHOTS / competency

The hydroxyl radical (·OH) and the hydroxide ion (OH⁻) both contain O and H.
(a) Find the number of electrons in each (O = 8 electrons, H = 1 electron, and OH⁻ has one extra).
(b) Which is a free radical and why is it reactive?
(c) State one source of chlorine radicals in the atmosphere and one harm.
(d) State one way of reducing free radicals in the atmosphere.

Try it first, then show the solutionSolution

(a) ·OH: $8 + 1 = 9$ electrons; OH⁻: $9 + 1 = 10$ electrons. (1)
(b) ·OH has an unpaired electron (odd number of electrons), so it readily attacks other molecules; OH⁻ has all electrons paired. (1)
(c) Ultraviolet light splitting CFCs releases chlorine radicals, which damage the ozone layer. (1)
(d) Phase out CFCs, fit catalytic converters, use cleaner fuels. (1)

Answer: (a) 9 and 10 (b) ·OH; unpaired electron (c) CFCs; ozone damage (d) cleaner fuels, CFC phase-out

Where students lose marks in Valency, Radicals and Writing Chemical Formulae by Criss-Cross

The slips examiners see most often, and what to write instead.

Mistake: Formula not simplified after criss-cross
The ratio must be in its lowest terms: 2:2 becomes 1:1.
Wrong working
Magnesium oxide as Mg₂O₂.
Right working
MgO.
Do this: Divide by the common factor.
Usually costs: 1 mark.
Mistake: Brackets omitted around a group radical
Otherwise the subscript applies to one atom only.
Wrong working
Ca(OH)2 written CaOH₂.
Right working
Ca(OH)₂.
Do this: Bracket when the subscript is more than 1.
Usually costs: 1 mark.
Mistake: -ous and -ic reversed
-ous is the lower valency.
Wrong working
Ferric chloride FeCl₂.
Right working
Ferrous chloride FeCl₂; ferric chloride FeCl₃.
Do this: Lower = ous.
Usually costs: 1 mark.

Exam tips

State the valencies above the symbols in the working.
Always check that the positive and negative valencies are equal.
Write NH₄ first (basic radical) in ammonium compounds.
For free radicals mention the unpaired electron and one harmful effect.

Practice questions on Valency, Radicals and Writing Chemical Formulae by Criss-Cross

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The valency of the carbonate radical is:
(a) 1
(b) 2
(c) 3
(d) 4
Hint
CO₃²⁻.
Answer
(b) 2
Q2 · 1 mark · Very short answerBoard level
Write the formula of sodium bicarbonate.
Hint
Bicarbonate is HCO₃⁻.
Answer
NaHCO₃.
Q3 · 2 marks · Short answerHarder board level
Write the formulae of (a) zinc hydroxide, (b) aluminium nitrate, (c) ammonium sulphate, (d) lead(II) nitrate.
Hint
Use criss-cross.
Answer
(a) Zn(OH)₂ (b) Al(NO₃)₃ (c) (NH₄)₂SO₄ (d) Pb(NO₃)₂.
Q4 · 3 marks · Short answerHarder board level
Find the valency of the element or radical named in brackets in (a) Al₂O₃ (Al), (b) Ca₃N₂ (N), (c) Fe₂(SO₄)₃ (Fe), (d) Mg(HCO₃)₂ (the HCO₃ radical), (e) Cu₃(PO₄)₂ (Cu).
Hint
Reverse the criss-cross.
Answer
(a) Al 3 (b) N 3 (c) Fe 3 (d) HCO₃ 1 (e) Cu 2.
Q5 · 2 marks · Assertion-reasonHarder board level
Assertion (A): Iron forms two chlorides, FeCl₂ and FeCl₃.
Reason (R): Iron shows variable valency.
(a) Both true, R explains A.
(b) Both true, R does not explain A.
(c) A true, R false.
(d) A false, R true.
Hint
Valencies 2 and 3.
Answer
(a)
Q6 · 3 marks · Short answerHOTS / competency
A student writes these formulae: (i) Na₂Cl, (ii) Al(SO₄)₃, (iii) NH₄SO₄, (iv) Mg₂O₂. Find the mistake in each and correct it.
Hint
Check that the charges balance.
Answer
(i) NaCl (Na 1, Cl 1). (ii) Al₂(SO₄)₃ (Al 3, SO₄ 2). (iii) (NH₄)₂SO₄ (NH₄ 1, SO₄ 2). (iv) MgO (the ratio 2:2 simplifies to 1:1).

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What is a radical?Show answer
An atom or group of atoms with a charge that behaves as a single unit.
2.Valency of sulphate and phosphate?Show answer
2 and 3.
3.Ferrous or ferric: valency 3?Show answer
Ferric.
4.What is a free radical?Show answer
An atom or group with an unpaired electron, very reactive.
5.Formula of calcium hydroxide?Show answer
Ca(OH)₂.

Valency, Radicals and Writing Chemical Formulae by Criss-Cross: frequently asked questions

How are chemical formulae written by the criss-cross method?

Write the basic radical first, put each valency above its symbol, exchange them as subscripts, simplify and bracket group radicals taken more than once.

What is variable valency?

Some elements, like iron and copper, show more than one valency; the lower takes -ous and the higher takes -ic in the name.

What is a free radical?

An atom or group of atoms with an unpaired electron, such as ·OH or Cl·; it is very reactive and can damage cells and the ozone layer.