Writing chemical formulae

A chemical formula is a compressed sentence: it tells you exactly which elements are combined and in what whole-number ratio, without a single word. $CaSO_4$ says "one calcium, one sulphate radical" as plainly as a sentence would. Writing formulae correctly is a foundational skill in ICSE Class 9 Chemistry, and almost every mistake traces back to one missed idea — valency, the combining capacity of an atom or radical. This article builds the criss-cross method from that one idea, works through aluminium oxide and calcium sulphate in full, then pushes to a trickier case with two multi-atom radicals, ammonium sulphate, where brackets and simplification both matter at once. No mole concept, no equations to balance yet — purely how to write and read a formula from valencies.

The core insight

The criss-cross method writes a formula by swapping each species' valency into the other's subscript, then simplifying to the lowest whole-number ratio and bracketing any radical whose subscript exceeds one.

The core idea

Valency is the combining capacity of an element — the number of hydrogen atoms (or their equivalent) that one atom of the element can combine with, or displace, in forming a compound. Elements are monovalent (valency 1: H, Na, Cl), divalent (valency 2: O, Ca, Mg), trivalent (valency 3: Al, N in some compounds), or tetravalent (valency 4: C, Si). Some elements, particularly transition metals, show more than one valency depending on the compound (iron, for instance, forms both $Fe^{2+}$ and $Fe^{3+}$ compounds), which is why a question will always state which valency to use rather than expecting it to be guessed. A quick way to fix valency in memory is to link it to the periodic table's groups for the main-group elements you meet at this level: Group 1 elements (Na, K) are monovalent, Group 2 elements (Ca, Mg) are divalent, Group 13's aluminium is trivalent, and Group 14's carbon and silicon are tetravalent. Non-metals on the right side of the table combine to complete a stable outer shell, so oxygen (needing 2 more electrons) is divalent and chlorine (needing 1 more) is monovalent — the same combining-capacity idea from the other direction. A radical is a group of atoms that behaves as a single unit with its own fixed valency (charge), carrying its identity through reactions — the sulphate radical $SO_4^{2-}$ has valency 2, the ammonium radical $NH_4^+$ has valency 1, and the hydroxide, nitrate and carbonate radicals ( $OH^-$ , $NO_3^-$ , $CO_3^{2-}$ ) follow the same idea. The criss-cross rule itself is one line: the valency of species A becomes the subscript of species B, and the valency of B becomes the subscript of A.

\text{A}^{a}\ \text{B}^{b} \;\Longrightarrow\; A_bB_a

where: $a$ is the valency of species A, $b$ is the valency of species B, and the resulting subscripts are simplified to the smallest whole-number ratio if they share a common factor. A radical needing a subscript greater than 1 must be enclosed in brackets before the subscript is written, so the subscript is understood to apply to the whole radical, not just its last atom. Naming works in reverse: read off the elements/radicals present and combine their names by standard rules — a metal plus a non-metal ending in "-ide" for simple binary compounds (chlorides, oxides), and "-ate" or "-ite" for oxygen-containing radicals (sulphate, sulphite). So $CaSO_4$ is read back as "calcium sulphate" and $MgCl_2$ as "magnesium chloride," without needing to redo the criss-cross arithmetic in reverse — naming only requires recognising the parts already present in the formula.

Figure

Criss cross diagram showing valency of Al swapping to become the subscript of O and valency of O swapping to become the subscript of Al

Derivation AWhy the criss-cross ratio balances total valency

The goal is to show, without relying on memorised recipes, that the criss-cross formula $A_bB_a$ built from valencies $a$ and $b$ always balances the total combining capacity on both sides, which is precisely why the method is guaranteed to give a chemically valid ratio and not an arbitrary one.

Step 1. Start from the definition. Species A has valency $a$ , meaning one atom of A carries $a$ units of combining capacity that must be satisfied. Species B has valency $b$ , similarly carrying $b$ units per atom.

Step 2. In the compound $A_bB_a$ , the total valency contributed by the A atoms is $b \times a$ (there are $b$ atoms of A, each worth $a$ ), and the total valency contributed by the B atoms is $a \times b$ (there are $a$ atoms of B, each worth $b$ ).

Step 3. Compare the two totals: $b \times a$ from A and $a \times b$ from B are the same number, since multiplication does not care about order. The two sides balance exactly, which is the chemical requirement for a stable neutral compound — every unit of combining capacity on one side is matched on the other.

Step 4. This is exactly why criss-crossing works as a shortcut: swapping the valencies into subscripts is just a fast way of forcing $b \times a = a \times b$ to hold automatically, for any pair of valencies. Simplifying the subscripts by their common factor afterwards does not disturb this balance, since dividing both sides by the same number keeps them equal.

Worked example

Write the formula of ammonium sulphate, given valency of the ammonium radical ( $NH_4$ ) = 1 and valency of the sulphate radical ( $SO_4$ ) = 2.

Step 1. Write the two radicals with their valencies as superscripts: $(NH_4)^{1} \quad (SO_4)^{2}$ . Both are multi-atom radicals, so both are candidates for brackets once a subscript greater than 1 appears.

Step 2. Criss-cross the valencies: the valency of $SO_4$ (2) becomes the subscript of $NH_4$ , and the valency of $NH_4$ (1) becomes the subscript of $SO_4$ : $(NH_4)_2(SO_4)_1$ .

Step 3. Check for a common factor between subscripts 2 and 1 — none exists (HCF = 1), so the ratio is already simplest. But a subscript of 1 is never written, so the sulphate bracket and its 1 are dropped, while the ammonium bracket is kept because its subscript is 2.

Step 4. Final formula: $(NH_4)_2SO_4$ (ammonium sulphate). Verify by valency balance: $2 \times 1$ (from $NH_4$ ) $= 2$ , and $1 \times 2$ (from $SO_4$ ) $= 2$ — equal, confirming the formula. The formula of ammonium sulphate is $(NH_4)_2SO_4$ .

Common traps

Forgetting to simplify criss-crossed subscripts. Writing $Ca_2(SO_4)_2$ instead of simplifying to $CaSO_4$ — always check for a common factor first.
Omitting brackets around a radical needing a subscript greater than 1. $Mg(OH)_2$ , not $MgOH_2$ ; without brackets the subscript would appear to apply only to the last atom of the radical.
Mixing up which valency goes where. The valency of the first species becomes the subscript of the second, and vice versa — not a species' own valency as its own subscript.
Writing a subscript of 1 explicitly. By convention it is never shown: $NaCl$ , not $Na_1Cl_1$ ; and a bracket around a radical is dropped once its subscript reduces to 1.
Using the wrong valency for a variable-valency metal. Iron, copper and a few other metals form more than one series of compounds; always use the valency the question states rather than assuming a single fixed value.

Ask the tutor: Stuck on a formula with two radicals, like ammonium sulphate, or unsure when to bracket — ask your AI tutor to criss-cross it with you step by step.

Why does aluminium oxide become Al2O3 and not Al3O2?

Criss-crossing swaps each species' own valency into the other species' subscript, not into its own. Aluminium's valency is 3, so 3 becomes oxygen's subscript; oxygen's valency is 2, so 2 becomes aluminium's subscript — giving $Al_2O_3$ . Writing $Al_3O_2$ would mean putting each element's own valency on itself, which is the opposite of the rule and does not balance total combining capacity.

How do I know when to keep the brackets around a radical and when to drop them?

Brackets stay only when the radical's subscript is 2 or more, because then the subscript must clearly apply to the whole group, not just its last atom — as in $Mg(OH)_2$ or $(NH_4)_2SO_4$ . If simplifying the ratio ever brings a radical's subscript down to 1, as with calcium sulphate reducing to $CaSO_4$ , the bracket is dropped along with the unwritten "1", since a lone radical needs no bracket to be unambiguous.

Is there a shortcut for compounds with two different radicals, like ammonium sulphate?

The method is identical to element-element or element-radical cases — you are just criss-crossing two radicals instead of two elements. Write both with valencies as superscripts, cross them into subscripts, simplify if there is a common factor, then bracket whichever radical still has a subscript above 1. The only extra care needed is remembering that each multi-atom radical is bracketed independently, based on its own final subscript, not the other radical's.

Writing chemical formulae

The core idea

Worked example

Common traps

Before this

Where this leads