Formulae of compounds

Chemists never write "one atom of aluminium joined to one and a half atoms of oxygen" — formulae only ever use whole-number subscripts, and there is a reliable shortcut for finding them. Once you know the symbols of elements, the next skill in the ICSE Class 8 chapter "Language of Chemistry" is combining those symbols — and the symbols of radicals like sulphate or hydroxide — into the correct formula of a compound, using each part's valency. The tool for this is the criss-cross method: write the valencies as small numbers above each symbol, swap them across as subscripts, then simplify to the lowest whole-number ratio. It sounds mechanical, and once practised it is — but understanding why the swap works, and where students most often trip (forgetting brackets, forgetting to simplify), turns a memorised trick into a skill you can apply to any pair of elements or radicals, which is exactly what the next topic — writing and balancing chemical equations — depends on.

The core insight

The formula of a compound is found by criss-crossing the valencies of its two parts as subscripts and then simplifying to the lowest whole-number ratio, with radicals bracketed whenever their subscript exceeds one.

The core idea

Valency is the combining capacity of an element or radical — the number of hydrogen atoms (or their equivalent) that one atom of the element, or one unit of the radical, can combine with. It is a small whole number, and every compound's formula is built from the valencies of the two parts being joined.

Radicals are groups of atoms that behave as a single charged unit with a fixed valency, exactly like an element does. Common radicals: sulphate $\text{SO}_4$ (valency 2), nitrate $\text{NO}_3$ (valency 1), carbonate $\text{CO}_3$ (valency 2), hydroxide $\text{OH}$ (valency 1), ammonium $\text{NH}_4$ (valency 1). Common element valencies: $H = 1$ , $O = 2$ , $Na = 1$ , $K = 1$ , $Ca = 2$ , $Mg = 2$ , $Al = 3$ , $Cl = 1$ ; some elements like $S$ and $N$ show more than one valency depending on the compound. The criss-cross rule, written compactly for two parts $A$ (valency $a$ ) and $B$ (valency $b$ ), is:

A^{\,a}\,B^{\,b} \;\longrightarrow\; A_bB_a \text{ (then simplify).}

where: $a$ is the valency of the first element or radical $A$ , $b$ is the valency of the second element or radical $B$ , and the subscripts after the arrow are the other part's valency — the valencies have swapped places. If the resulting subscripts share a common factor, both are divided by it to reach the lowest whole-number ratio; a subscript of exactly 1 is never written out. Whenever a radical ends up needing a subscript greater than 1, it must be enclosed in brackets before that subscript is written, e.g. $\text{Ca(OH)}_2$ , never $\text{CaOH}_2$ — without the brackets the formula would misleadingly suggest two separate O and H atoms rather than two whole hydroxide units.

Figure

Criss cross diagram showing aluminium with valency three and oxygen with valency two swapping to become subscripts, giving Al2O3

Derivation ADeriving a formula with the criss-cross method

The goal, in general, is to turn a stated pair of valencies for any element or radical pair into the one correct, fully simplified formula for the compound they form — a procedure that must work identically whether the parts are two elements, an element and a radical, or two radicals, and must always land on whole-number subscripts with radicals correctly bracketed. Take calcium (valency 2) and the carbonate radical, $\text{CO}_3$ (valency 2), as the working example: calcium carbonate.

Step 1. Write the two parts side by side with their valencies marked as small numbers above each: $\overset{2}{\text{Ca}}\ \overset{2}{(\text{CO}_3)}$ . Marking the valency this way, rather than trying to hold both numbers in your head, is what prevents the swap in the next step from going wrong.

Step 2. Criss-cross the valencies: the valency of calcium (2) becomes the subscript written after the carbonate radical, and the valency of carbonate (2) becomes the subscript written after calcium. This gives $\text{Ca}_2(\text{CO}_3)_2$ , with the radical already bracketed because its subscript is greater than 1.

Step 3. Check for a common factor between the two subscripts. Here both are 2, sharing a common factor of 2, so divide each by 2: $\text{Ca}_1(\text{CO}_3)_1$ .

Step 4. Drop every subscript equal to 1 (they are never written), and drop the now-unneeded brackets since the radical's subscript is 1. This gives the final formula $\text{CaCO}_3$ — one calcium atom combined with one carbonate radical. Check the logic in reverse: in $\text{CaCO}_3$ , calcium contributes a total valency of $2 \times 1 = 2$ , and the carbonate radical contributes $2 \times 1 = 2$ — the two combining capacities balance exactly, which is the whole point of the criss-cross rule: it guarantees the finished formula is electrically and chemically balanced without you having to check it separately.

Worked example

Problem: Write the formula of calcium hydroxide, given calcium has valency 2 and the hydroxide radical ( $\text{OH}$ ) has valency 1. Then use the same valencies to find the formula of calcium chloride (chlorine, valency 1), to see how the method handles a case where no simplification is needed and a case where brackets are not needed at all.

Step 1. Mark the valencies: $\overset{2}{\text{Ca}}\ \overset{1}{(\text{OH})}$ . Calcium's valency is 2, the hydroxide radical's valency is 1.

Step 2. Criss-cross: calcium's valency (2) becomes hydroxide's subscript, and hydroxide's valency (1) becomes calcium's subscript (not written, since it is 1). This gives $\text{Ca}(\text{OH})_2$ .

Step 3. Check for brackets and simplification. The hydroxide radical now carries a subscript of 2, so it must stay in brackets: $\text{Ca(OH)}_2$ , not $\text{CaOH}_2$ . The subscripts 1 and 2 share no common factor, so no further simplification is possible.

Step 4. Repeat for calcium chloride using $\overset{2}{\text{Ca}}\ \overset{1}{\text{Cl}}$ : criss-crossing gives $\text{Ca}_1\text{Cl}_2$ , which becomes $\text{CaCl}_2$ once the subscript of 1 on calcium is dropped. Chlorine is a plain element, not a radical, so no brackets are ever needed around it, however large its subscript.

Result: the formula of calcium hydroxide is $\text{Ca(OH)}_2$ — one calcium atom with two hydroxide radicals (two O and two H atoms in total) — and the formula of calcium chloride is $\text{CaCl}_2$ — one calcium atom with two chlorine atoms.

Competitive stretch

For sodium sulphate — sodium (valency 1) and the sulphate radical $\text{SO}_4$ (valency 2) — criss-crossing $\overset{1}{\text{Na}}\ \overset{2}{(\text{SO}_4)}$ gives $\text{Na}_2(\text{SO}_4)_1$ . The subscripts 2 and 1 share no common factor, and the radical's subscript is exactly 1, so its brackets are dropped too: the final formula is $\text{Na}_2\text{SO}_4$ . This shows the bracket rule depends only on the final subscript after simplification, not on the subscript right after criss-crossing.

Common traps

Forgetting to bracket a radical before adding a subscript greater than 1, e.g. writing $\text{CaOH}_2$ instead of $\text{Ca(OH)}_2$ — this misreads the formula as two separate O and H atoms rather than two hydroxide units.
Not simplifying the subscript ratio to lowest terms after criss-crossing, e.g. leaving $\text{Ca}_2(\text{CO}_3)_2$ instead of simplifying to $\text{CaCO}_3$ .
Writing a subscript of 1 explicitly, or keeping brackets around a radical whose final subscript is 1 (as in $\text{Na}_2(\text{SO}_4)_1$ instead of $\text{Na}_2\text{SO}_4$ ).
Confusing the small subscript (how many atoms/radicals are present) with the valency superscript used only as a working step — the valency number itself never appears in the finished formula.

Ask the tutor: Want to practise the criss-cross method on a trickier valency pair, such as aluminium sulphate or ammonium carbonate, or check a formula you're unsure about? Ask the AI tutor for step-by-step help.

Why do the valencies swap places instead of just being added?

The valency of each part is its combining capacity — how many single bonds' worth of connection it can make. Swapping the numbers as subscripts is what makes the total combining capacity balance on both sides: in the final formula, each part appears exactly as many times as the other part's valency demands, so the two totals come out equal. Adding the valencies would not guarantee that balance, which is why the criss-cross swap, not addition, is the rule.

Do I always need brackets around a radical, even when its subscript is 1?

No. Brackets are only needed when a radical's final, simplified subscript is greater than 1, because that is the only situation where leaving them off would be ambiguous — the subscript would otherwise look like it applies to just the last atom of the radical, not the whole group. When a radical's subscript works out to exactly 1, as in sodium sulphate, $\text{Na}_2\text{SO}_4$ , the brackets are dropped along with the subscript, since there is nothing left to bracket.

What if I criss-cross two elements that already have the same valency, like calcium and oxygen?

You still follow the same steps — you just end up needing the simplification step immediately. Calcium (valency 2) and oxygen (valency 2) criss-cross to $\text{Ca}_2\text{O}_2$ , and since 2 and 2 share a common factor of 2, this simplifies straight down to $\text{CaO}$ . Equal valencies always simplify to a 1:1 ratio, which is why compounds like $\text{CaO}$ , $\text{MgO}$ and $\text{NaCl}$ (valencies 1 and 1) end up with no subscripts written at all.

Formulae of compounds

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads