Balancing Redox Reactions with the Half-Reaction Method

 

Many redox reactions also fall into another category of reaction. Combustion reactions, single displacement reactions and most decomposition and synthesis reactions all involve electron theft. Because they can be understood as one of the basic types of reactions discussed elsewhere, we can balance them simply.

However, now that we are looking closely at the transfer of electrons within reactions, we will come across electron theft reactions that do not fit one of those old patterns. You will recognize these in several ways. For instance, here is a redox reaction that doesn’t fit anything you’ve seen before:

\(MnO_4^{-1} + Fe^{+2} \rightarrow Fe^{+3} + Mn^{+2}\)

Right away you should see some problems. Here are the big ones that jump out at me:

• Oxygen seems to have disappeared from the reaction, which violates the conservation of matter
• There are ions all over the place and we have only seen ions in reactions as part of acid/base chemistry or as the net-ionic equation of a displacement reaction.
• There is a “connection” issue. Remember that one of the lessons of balancing reactions is that you should balance any element that is alone last. But here, there are two elements that are alone (Fe on BOTH sides of the reaction and Mn on the right). Although it may not seem obvious to you now, this presents a huge problem. - it means that you could have ANY amount of iron and it would seem not to affect the amount of Mn needed.

The Assumptions We’ll Need to Make

To deal with these issues, we’ll need to make a few assumptions

• These reactions occur in aqueous solution. (This will solve the problem of ions, since we know that ions can float freely in water as described here.) In addition, the water will solve our “oxygen problem”
• These reactions generally occur in acidic solution. Although this is not universal, the presence of \(H^{+1}\) ions will also help with our missing matter.
• It's OK to use \(H^{+1}\) instead of \(H_3O^{+1}\)

The Steps of the Half-Reaction Method

We balance redox reactions (that are not also one of the 5 basic types) through a process called the half-reaction method. This involves breaking the redox reaction into the reduction and oxidation, balancing each of those separately and then recombining them by matching the electrons transferred.

Here are the steps we follow:

1. Break the reaction into half-reactions
2. Balance everything except H and O
3. Balance O by adding \(H_2O\)
4. Balance H by adding \(H^{+1}\) ions
5. IF the reaction is in basic solution, add enough \(OH^{-1}\) ions to both sides to combine with the \(H^{+1}\) ions
6. Balance the charge by adding electrons
7. Match the number of electrons between the two half-reactions
8. Add the half-reactions and cancel (if possible)

Let's look at two examples. The first example is relatively straightforward and simple, using only some of the rules. The second is more complex, but uses all of the rules. If you understand these two examples, you should be able to balance anything.