The Criss-Cross Trick That Writes Any Chemical Formula

There is — the criss-cross method. Write the two radicals side by side with their valencies above them, swap the numbers across, and the formula appears.

It works for every compound in the syllabus once you know the valencies. This page covers everything in the ICSE Class 7 Chemistry chapter's second part: radicals and their classification, valency, variable valency, and writing and naming formulae.

A radical, also called an ion, is an atom or group of atoms carrying a positive or negative charge, which acts as a single unit in a chemical reaction.

Radicals are classified in two ways at once.

By number of atoms:

- Simple — a single atom, such as $N{a}^{+}$, $C{l}^{-}$, $M{g}^{2+}$, $O^{2-}$.
- Compound — a group of atoms acting as one, such as $S{O}_4^{2-}$, $N{O}_3^{-}$, $O{H}^{-}$, $C{O}_3^{2-}$, $N{H}_4^{+}$.

By charge:

- Basic (positive) radicals — metals and the ammonium radical: $N{a}^{+}$, $K^{+}$, $C{a}^{2+}$, $A{l}^{3+}$, $N{H}_4^{+}$.
- Acidic (negative) radicals — non-metals and acid groups: $C{l}^{-}$, $O^{2-}$, $S{O}_4^{2-}$, $N{O}_3^{-}$, $C{O}_3^{2-}$, $P{O}_4^{3-}$.

So $S{O}_4^{2-}$ is both compound and acidic, while $N{a}^{+}$ is both simple and basic.

Common salt, washing soda and baking soda in any Indian kitchen are all made of a basic radical joined to an acidic one.

The ammonium radical $N{H}_4^{+}$ is the one that breaks the pattern, and it is examined for that reason. It is a group of atoms, so it is compound, yet it carries a positive charge and behaves like a metal — the only common positive compound radical in the syllabus.

Valency is the combining capacity of an atom or radical — the number of hydrogen atoms it can combine with or displace. It is simply the charge without the sign.

Valency 1: $H^{+}$, $N{a}^{+}$, $K^{+}$, $A{g}^{+}$, $N{H}_4^{+}$, $C{l}^{-}$, $O{H}^{-}$, $N{O}_3^{-}$.

Valency 2: $M{g}^{2+}$, $C{a}^{2+}$, $Z{n}^{2+}$, $B{a}^{2+}$, $O^{2-}$, $S^{2-}$, $S{O}_4^{2-}$, $C{O}_3^{2-}$.

Valency 3: $A{l}^{3+}$, $N^{3-}$, $P{O}_4^{3-}$.

Valency 4: $C$, $Si$.

Valency 0: the noble gases — helium, neon and argon do not combine, which is why they are called inert.

Valency explains why formulae look the way they do. Sodium has valency 1 and chlorine has valency 1, so they pair one to one as $NaCl$. Calcium has valency 2 and chlorine 1, so calcium needs two chlorines: $CaC{l}_2$.

The point students miss is that valency is a property of the radical, not of its size. The whole sulphate group $S{O}_4^{2-}$ has a single valency of 2, which is why it is treated as one unit and given a bracket when more than one is needed.

Because some metals can lose different numbers of electrons, so they combine in more than one way. This is called variable valency, and the four examples in the syllabus are iron, copper, mercury and tin.

Each one is named twice over, by two systems:

- Iron — valency 2 is ferrous or iron(II); valency 3 is ferric or iron(III).
- Copper — valency 1 is cuprous or copper(I); valency 2 is cupric or copper(II).
- Mercury — valency 1 is mercurous or mercury(I); valency 2 is mercuric or mercury(II).
- Tin — valency 2 is stannous or tin(II); valency 4 is stannic or tin(IV).

The rule for the older system is easy: -ous for the lower valency and -ic for the higher one. The modern system simply writes the valency as a Roman numeral in brackets.

So iron and chlorine give two different compounds: $FeC{l}_2$, ferrous chloride or iron(II) chloride, and $FeC{l}_3$, ferric chloride or iron(III) chloride.

The reddish-brown rust on an iron gate contains iron in its ferric state, which is part of why it looks nothing like the grey metal.

And this is why a question must always specify which one. Asking for "the formula of iron chloride" is incomplete — ferrous chloride and ferric chloride are different substances with different formulae.

Four steps, and the same four every time.

1. Write the basic (positive) radical first and the acidic (negative) radical second.
2. Write each valency above its radical.
3. Criss-cross — bring each valency down as the subscript of the other radical.
4. Simplify the ratio if both numbers share a factor, and put a bracket round any compound radical that takes a subscript.

Worked examples.

Aluminium sulphate. $Al$ has valency 3, $S{O}_4$ has valency 2. Crossing over gives $A{l}_2(S{O}_4{)}_3$ — the bracket is needed because the sulphate group is repeated three times.

Calcium hydroxide. $Ca$ is 2, $OH$ is 1. Crossing gives $C{a}_1(OH{)}_2$, written $Ca(OH{)}_2$; a subscript of 1 is never written.

Magnesium oxide. $Mg$ is 2, $O$ is 2. Crossing gives $M{g}_2{O}_2$, which must be simplified by dividing both by 2 to give $MgO$.

Ferric oxide. $Fe$ is 3, $O$ is 2. Crossing gives $F{e}_2{O}_3$.

Naming works backwards. Given $CaC{O}_3$, identify $Ca$ as calcium and $C{O}_3$ as carbonate, and the name is calcium carbonate — the main substance in limestone and in marble.

That simplification step in magnesium oxide is the one most often skipped, and $M{g}_2{O}_2$ is marked wrong. Always check whether the two subscripts share a common factor before writing the final answer.