finding the formula

Higher and foundation tier

Working chemical formula is a valuable skill needed in chemistry. Chemical equations are usually written as either as word or symbolic equations. Symbolic equation are generally more useful than word equations, however in order to write out symbolic equations you will need to be able to workout the chemical formula for compounds. Luckily this is very easy to do.

Working out chemical formula

To workout the chemical formula for a compound all you really need is copy of the periodic table. Using the periodic table we can find out what group any element is in and from this we can easily determine its valency, that is how many chemical bonds it will make. An outline of the periodic table is shown below with groups 1-8 labelled.

periodic table

The number of bonds an element makes it called its valency. The number of bonds an elements makes is simply the number of electrons it needs to lose or gain to achieve a stable octet of electrons, that is a full last shell. The valency or number of electrons is very easily worked from the periodic table.

group in the periodic table where the element is found group 1 group 2 group 3 group 4 group 5 group 6 group 7 group 0 or group 8
valency/number of bonds the element makes 1 2 3 4 3 2 1 0

Using this simple table it is possible to workout the formula for many compounds.

water molecule

Example 1- hydrogen oxide (water)

As a simple example start with a chemical formula that everyone knows- H2O the formula for a molecule of water. The image opposite shows a molecule of water, we can see that the oxygen atom is making two bonds; that is its valency is 2 while each hydrogen atom makes only 1 chemical bond; so its valency is one. Lets imagine that you did not know the molecular formula for water, how would you work it out? The method shown below is often called the cross-over method for obvious reasons, just follow the simple steps to get the chemical formula for a molecule of water.

How to find the formula for water

Using this simple method it is possible to workout the chemical formula for almost all the compounds you are likely to meet in your chemistry course.

Example 2- sodium oxide

Almost everyone knows the chemical formula for water, but if you asked someone for the chemical formula of say sodium oxide the chances are they probably won't know it. However it is easy using the method above to workout its formula:

finding the formula for sodium oxide

Example 3-Phosphorus chloride

What is the formula for the compound formed when phosphorus reacts with an excess of chlorine gas? Well just follow the method above to get the formula for this compound:

finding the formula for PCl5

Example 4- calcium sulphide

Calcium an alkaline earth metal in group 2 reacts with the non-metal sulfur in group 6. What is the formula for calcium sulphide, the compound formed?

finding the formula for calcium sulphide

In this example there is one additional step needed. When the two numbers in the formula are multiples of each other, such as 2 and 4 or 3 and 6 or in this case 2 and 2 we simply cancel down to get the simplest ratio possble for the elements. In this case simply divide by 2 and Ca2S2/2 simply becomes CaS

Finding the formula for compounds containing more than two elements

potassium permanganate is a compound 
 containing 3 elements: potassium, manganese and oxygen

All the compounds we have worked out the formula for so far have all had two elements in them, compounds containing only two elements ends in the letters -ide. However you will no doubt have me other compounds which contain more than two elements and which have different ending to their names e.g

So how do we go about working out the formula for these compounds that contain more than three elements? Well we use the same basic method as above but it is necessary to change it slighly. Many of these compounds which contain multiple elements contain common group ions. You will have met these group ions before and probably not realised it. If you have used compounds which have the following names then these compounds all contain these group ions:

Group ions

Many of the compounds you will meet in chemistry contain these group ions and you should make an effort to learn their names and formula. The most common group ions you are likely to meet are shown below:

group ions

So how do we go about finding the formula for compounds which contain these group ions? As an example consider sodium sulfate. Now sodium sulfate contains sodium ions and sulfate ion;, we can easily find the valency of sodium ions. Sodium is a group 1 metal found in the first group in the periodic table so its valency is 1. However sulfate is a compound and obviously will not be found in the periodic table of elements, so how do we find out how many bond it makes? What is its valency? Thats the easy part, its simply the charge present on the ion. The sulfate ion is SO42-, its charge is simply 2-; so its valency is the same as its charge, that is 2. To find the formula of sodium sulafte simply use the cross-over method from above:

Example 5 - Sodium sulfate

formula for sodium sulfate

As another example of a compound containing one of these group ions consider the alkali calcium hydroxide:

Example 6- Calcium hydroxide

calcium hydroxide formula

You will have noticed that in writing the formula for calcium hydroxide it was necessary to include a set of brackets. Without the presence of these brackets the formula would be wrong e.g. When we worked out the formula for calcium hydroxide using the cross-over rule above it should be noted that calcium hydroxide contains ONE calcium ion and TWO hydroxide ions. That is:

Now simply consider how you would write the formula for this compound. If we write:
CaOH2 then this would be wrong, since it gives us 1 Calcium ion, 1 oxygen and 2 hydrogens. This is not what we want! We want 1 calcium ion and TWO hydroxide ions. So the only way to do this have the hydroxide ion in brackets to indicate how many of these ions we need. So when we write the formula as Ca(OH)2 the "2" after the hydroxide ion means that everything inside the brackets is multiplied by 2, or put another way it means we have TWO hydroxide ions.

Example 7- Magnesium phosphate

The phosphate ion is a group ion with the formula PO43-, it has a valency of 3. Magnesium is a group 2 metal and so has a valency of 2. We can find the formula of magnesium phospahte using the method above:

finding the formula of magnesium phosphate

Magnesium phosphate has 3 magnesium ions and two phosphate ions in its formula. Imaagine how the formula would read if we did not use brackets, we would have Mg3PO42, that is 3 magnesium ions, 1 phosphorus and 42 oxygens- not what we want!

Finding the formula for compounds containing transition metals

Many of the compounds you will use in your chemistry course will contain transition metals, for example you will no doubt have used one or more of the following compounds: copper sulfate, sodium dichromate or potassium permanaganate. Working out the formula for a compound containing a transition metal might seem impossible since the transition metals are found in the middle block of the periodic table and so there is no way you can work out their valencies.

However if you look at the names of many transition metal comounds you will see Roman numerals after the name e.g. iron(III) oxide, copper(II) chloride or copper(I) oxide. These Roman numerals are the valencies of the transition metals in the compound, that is the number of bonds the transition metal is making in the compound. For example what is the formula for copper(II) sulfate?

finding the formula for copper(II) sulfate

Finding the formula for acids and alkalis

All acids contain hydrogen ions (H+) in their formula. The other ion present in most acids are some of the group ions such as sulfate, nitrate and phosphate. Working out the formula of an acid is very staright forward e.g.

What is the formula for sulfuric acid?

working out the formula for sulfuric acid

Sulfuric acid like all acids contains H+ ions and sulfate ions, so we simply use the method above to work out its formula. Similarily:

All alkalis contain the hydroxide ion (OH-) and we simply use the method above to work out the formula for these alkalis.

What is the formula for the alkali sodium hydroxide?

Sodium hydroxide contains sodium ions and hydroxide ions (OH-), the formula for sodium hydroxide is simply: finding the formula for sodium hydroxide

And for the alkali calcium hydroxide we have: finding the formula for calcium hydroxide

Key points

Practice questions

Check your understanding - Questions on formulae