Chemguide: Core Chemistry 14 - 16

How to write symbol equations for simple chemical reactions

This page explains how to work out equations for simple chemical reactions. You have to get this right, because chemistry will be a nightmare to you if you find equations a mystery - it is an essential tool in understanding chemistry.

Learning to write equations can take quite a lot of time when you are starting chemistry. This is one of the major hurdles in the subject. Don't try to rush it - spending time now will save you a lot of problems later on.

You will need to be reasonably competent at writing formulae for ionic compounds and there is no point in continuing with this page until you are.

How writing equations works

You need to know what is actually happening!

You can't just make up an equation - it has to be based on exactly what happened in a chemical reaction. You need to know what you started with and what you ended up with.

Have a look at this YouTube video which is a snippet from a Royal Society of Chemistry lecture, and shows magnesium metal burning in oxygen in the air. It forms magnesium oxide.

The video displayed this as a simple word equation.

magnesium + oxygen     magnesium oxide

The arrow here be translated as "goes to" or "produces" or whatever similar term you want to use.

In the very early stages of a chemistry course, you might be asked to write word equations - usually for reactions slightly more complicated than this one.

But if you are doing chemistry properly, you may never actually write a word equation down, but it has to be in your mind. You have to know what you started with and what you ended up with.

Translating the words into symbols

Still using the example of magnesium burning in oxygen . . .

The next thing you have to do is to translate the names of the substances involved into their formulae.

Mg + O₂     MgO

Don't forget that oxygen (in common with things like hydrogen and chlorine) goes around in pairs.

But this isn't the finished equation.

Balancing the equation

Each symbol you write counts as one atom (or one ion) of that element. (You will later come across another more mathematical way of looking at this, but that is some distance in the future.)

That means that in the equation we have just written, you seem to have started with 2 atoms of oxygen, but only ended up with 1 in the product. You can't just lose an oxygen atom - everything must be accounted for.

Here is the unfinished equation again . . .

Mg + O₂     MgO

So how do you get another oxygen on the right-hand side?

What you absolutely must not do is change the formula of the magnesium oxide. You can't just re-write the formula of magnesium oxide as MgO₂ - that doesn't exist! You must never try to balance an equation by changing a formula.

What you need is to form twice as much MgO. You can do this by writing a big "2" in front of the formula.

A big number in front of a formula multiplies up the whole formula until you get to a break - the end of the equation, a plus sign, or an arrow, for example.

So a revised version would be . . .

Mg + O₂     2MgO

But beware! By writing that 2, you have messed up the balance of the magnesium. If you leave it like that, it seems that you have by magic generated another magnesium atom out of nowhere.

That is easily put right, of course, by re-writing the equation to start with 2 atoms of magnesium.

2Mg + O₂     2MgO

And that is the proper equation - everything is now balanced on both sides of it.

This is a trivial example, of course, and all of this would just be running through your head, but it illustrates the principles.

• You have to start with a word equation, even if that only exists in your head.

• Write down the formulae for everything in your word equation.

• Look for where the equation doesn't balance, and put it right. (I will give you some more help with this in examples to come.)

• At the end, go back and check everything again in case by altering something you have messed up something you have already checked - as, for example, with the magnesium above.

Examples

Example 1

Heptane is one of the hydrocarbons in petrol (gasoline). It has the formula C₇H₁₆, and burns to form carbon dioxide and water. Write the equation for this.

You have all the information you need in the question, so all you need to do is to write the formulae down to start the equation writing process. (I am assuming you know the formulae for carbon dioxide and water.)

C₇H₁₆ + O₂     CO₂ + H₂O

The best way of balancing most equations is to start from the beginning and work through the elements one at a time. However, it is a good idea to leave until the end anything which occurs more than once on either side of the equation - in this case, oxygen.

You will usually find that this will sort itself out easily later on.

So start with the carbon. If there are 7 atoms on the left-hand side, there must be 7 on the right-hand side as well. That means you must have produced 7 molecules of carbon dioxide.

C₇H₁₆ + O₂     7CO₂ + H₂O

Now the hydrogens. There are 16 hydrogens on the left, and so there have to be 16 on the right as well. You must have produced 8 molecules of water.

C₇H₁₆ + O₂     7CO₂ + 8H₂O

Now count the oxygens. There are a total of 22 on the right-hand side. To get 22 atoms, you must have started with 11 molecules of oxygen.

C₇H₁₆ + 11O₂     7CO₂ + 8H₂O

And that's all OK. You wouldn't normally write all these stages down, of course - you just write the original formulae down leaving enough space for the balancing numbers, and then write them in as you work them out.

Example 2

Calcium carbonate reacts with dilute hydrochloric acid to give a solution of calcium chloride, carbon dioxide gas and water. Write the equation for this.

You have to know that dilute hydrochloric acid is a solution of hydrogen chloride in water. For equation purposes, you can just write this as HCl. Obviously, you should know how to work this formula out but, to be honest, you will meet it so many times, that you will just know it.

If you work out the other formulae, you will get . . .

CaCO₃ + HCl     CaCl₂ + CO₂ + H₂O

Working from left to right, the calcium is OK; the carbon is also OK; the oxygen is OK. The hydrogen and chlorine are obviously not OK.

You can put the chlorine right by having two lots of HCl - NOT by turning the HCl into the non-existent HCl₂. This also puts the hydrogen right.

That gives the final balanced equation . . .

CaCO₃ + 2HCl     CaCl₂ + CO₂ + H₂O

Example 3

This is to illustrate how you get around a particular problem that comes up now and then.

If you heat solid copper(II) nitrate, you get copper(II) oxide, nitrogen dioxide and oxygen. The unbalanced symbol equation is . . .

Cu(NO₃)₂     CuO + NO₂ + O₂

Working systematically, the copper is OK.

On the left-hand side, there are 2 nitrogen atoms. The little 2 after the brackets applies to everything inside the brackets. You therefore need 2 nitrogen dioxides on the right-hand side.

Cu(NO₃)₂     CuO + 2NO₂ + O₂

That now leaves a tricky problem with the oxygens. There are 6 (2 lots of 3) on the left-hand side, and 7 on the right. It isn't immediately obvious how to sort that out.

The trick is to allow yourself to have half an oxygen molecule - half an oxygen molecule is just one oxygen atom.

Cu(NO₃)₂     CuO + 2NO₂ + ½O₂

Now there are 6 oxygen atoms on both sides.

You wouldn't normally leave it like this though. Having halves in equations feels wrong, although if you do chemistry to a more advanced level, they aren't uncommon. You can get rid of the half by doubling everything in the equation.

2Cu(NO₃)₂     2CuO + 4NO₂ + O₂

If you count everything up now, it all balances.

The 2 at the beginning means that there are two lots of Cu(NO₃)₂. That is two times 1 copper, 2 nitrogens and 6 oxygens. The 2 after the bracket multiplies everything inside the bracket.

Problems to practise on

Do one set of these questions at a time, and then check your answers. Don't go on to the next set until you are sure you understand any mistakes that you made.

Set 1

Balance these equations where the formulae are given to you.

Mg + HCl     MgCl₂ + H₂

Ba + H₂O     Ba(OH)₂ + H₂

FeSO₄ + NaOH     Fe(OH)₂ + Na₂SO₄

Al + Fe₂O₃     Al₂O₃ + Fe

Na₂CO₃ + HNO₃     NaNO₃ + CO₂ + H₂O

set 1 balancing equations answers

Set 2

Balance these equations where the formulae are also given to you.

Al + H₂SO₄     Al₂(SO₄)₃ + H₂

Fe₂(SO₄)₃ + KOH     Fe(OH)₃ + K₂SO₄

C₄H₁₀ + O₂     CO₂ + H₂O

K + H₂O     KOH + H₂

HNO₃    H₂O + NO₂ + O₂

set 2 balancing equations answers

The rest of these questions are likely to take longer because you are being asked to work out formulae as well as balancing the equation. Take your time to make sure the formulae are right - you can't get the equation properly balanced it it contains a wrong formula.

There aren't any difficult problems here. If you find an equation impossible to balance it is probably because you have got a formula wrong. Don't be surprised if the occasional equation is actually balanced when you have written the formulae - it isn't uncommon.

Set 3

Write balanced equations for the following reactions.

sodium carbonate + hydrochloric acid (HCl)    sodium chloride + carbon dioxide + water

sodium + chlorine    sodium chloride

magnesium + copper(II) oxide    magnesium oxide + copper

sodium hydroxide + sulfuric acid (H₂SO₄)    sodium sulfate + water

copper(II) oxide + hydrochloric acid (HCl)    copper(II) chloride + water

set 3 balancing equations answers

Set 4

Write balanced equations for the following reactions.

potassium + water    potassium hydroxide + hydrogen

iron(III) oxide + nitric acid (HNO₃)    iron(III) nitrate + water

barium chloride + potassium sulfate    barium sulfate + potassium chloride

magnesium + sulfuric acid (H₂SO₄)    magnesium sulfate + hydrogen

sodium + oxygen    sodium oxide

set 4 balancing equations answers

State symbols in equations

I don't want to make too big a deal of this at the moment, because for now you need to concentrate on learning to write the basic equations that we have covered above.

But quite often you will find equations which have state symbols added in brackets after each formula. There are four of these, and they tell you what physical state the substance is in.

So, for example, if you just wrote H₂O in an equation, it isn't always clear whether you are talking about water or steam. Liquid water would be written H₂O(l) and steam would be H₂O(g).

Solid magnesium burns in steam to produce a white powder, magnesium oxide, and hydrogen gas. That would be shown using state symbols as . . .

Mg(s) + H₂O(g)     MgO(s) + H₂(g)

In this case, the state symbols matter, because magnesium has only a very, very slight reaction with cold water, and produces a different product - magnesium hydroxide rather than magnesium oxide.

To take another example, if you write HCl in an equation, it isn't always totally obvious whether you are talking about hydrogen chloride gas, or the solution of hydrogen chloride gas in water, known as hydrochloric acid.

The gas would be HCl(g) and its solution (hydrochloric acid) would be HCl(aq).

We will talk some more about this in places where it really matters.

This has numerous examples of writing formulae and equations, as well as a section on basic atomic structure which you might also want to look at. For now, ignore the part which deals with ionic equations. I prefer to introduce these gently a bit at a time when they are needed, and if you start worrying about them at this point, you will just get confused.

It is important that you read the short User Guide before you begin because the site is correctly fussy about how you enter subscripts (e.g. H₂) and superscripts (e.g. Cu²⁺). You will get reminders about this on the pages where it is relevant. Use the keyboard shortcuts wherever possible - it's a bit tedious otherwise. It is much easier to use the site on a computer with a traditional keyboard rather than a tablet.

You can access a necessary Periodic Table from the title bar on each page. This should open in a new tab, which makes it easy to keep referring to.