The chemistry of electron transfer – oxidation & reduction

Chemical reactions in which electrons are transferred from one atom/molecule to another are called reduction-oxidation reactions, or redox reactions, for short. Redox reactions are a very important class of chemical reactions in industry, biology and elsewhere.

Oxidation, a loss of electrons by a substace, and reduction, a gain of electrons, always occur together. There aren't any free electrons in a chemical system, so the loss of an electron somewhere has to create a gain somewhere else.

If you need to, you should review the section on oxidation numbers before going on with this section.

In this section we'll learn how to balance redox reactions, a process a little more complicated than our usual mass balancing. In a future section, we'll learn about electrochemical cells – batteries.

There are a few techniques for balancing redox reactions. The one I use is the one I learned from a great teacher of chemistry, Prof. Stephen Thompson at Colorado State University.

Oxidation & reduction

Oxidation is a loss of electron(s)   and   Reduction is a gain of electron(s).

Oxidation and reduction always occur together in any redox reaction.

Balancing redox reactions

Outline of the procedure

Our approach to balancing redox reactions will look like this (There might be some terminology you're not familiar with yet here, but we'll cover it below):

  1. Assign oxidation numbers to each atom.

  2. Separate the reaction into oxidation and reduction "half reactions."

  3. Balance each half reaction with respect to the atoms undergoing oxidation and reduction.

  4. Balance any unbalanced oxygen or hydrogen atoms using water; compensate for added hydrogens by adding H+ to the other side.

  5. Balance the charges by adding electrons to the appropriate side of each half reaction.

  6. If you're working in basic solution, add enough OH- to half-reaction sides containing any H+ (that just wouldn't be hanging around in a basic solution). You'll have to add the same number of OH- to the other side, too.

  1. Multiply the half reactions by coefficients that make the number of transferred electrons the same in each reaction.

  2. Add the half reactions. The electrons should cancel now.

  3. Cancel any atoms or molecules common to both sides, as you would for an algebraic equation.

  4. Reduce to the simplest coefficients.

This can seem like a lot of steps, but once you get the hang of it, it flows pretty naturally, so don't give up. Work through a few examples and you'll see that it gets easier. Also, this isn't the only approach to balancing redox reactions. It's worked for me for a long time. I learned it from Prof. Stephen Thompson, a great chemistry teacher.

The best way to go about learning to balance redox reactions is by example, so let's dive into a couple of them. Here's the first.

Example 1

Balance the reaction:

HCl + KMnO4 → Cl2 + MnCl2 + H2O   in acidic solution.

Now, you'll notice that this reaction isn't even balanced by atoms ("mass balanced"). There is a potassium (K) atom on the left but none on the right. We'll get to that in time.

To better prepare, it's often best to write the net ionic reaction, by assuming that everything in solution, except for the solvent, water, and covalently-bonded species, like Cl2, will ionize. It looks like this:

Cl- + H+ + MbO4- → Cl2 + Mn2+ + H2O

1. Assign oxidation numbers.

Now it's easy to see that chlorine (Cl-) is oxidized (loses electrons) and manganese (Mn) is reduced (gains electrons):

2. Separate into half-reactions

Now we focus only on the chemical species being oxidized and reduced, and write oxidation and reduction half-reactions, respecitvely:

3. Balance the formal charges with coefficients

Only the chlorine ion needs a coefficient here because there is only one Cl on the left and two on the right.

4. Balance any unbalanced oxygen or hydrogen atoms using water; compensate for added hydrogens by adding H+ to the other side.

Now the reduction equation has oxygens on the left but not on the right. To balance them, add four waters to the right, and compensate for the added hydrogens by adding 8 protons on the left. We're working in acid solution, so this is appropriate.

5. Balance the charge on right and left with electrons

In the oxidation reaction, there are two negative charges on the left, and none on the right, so we add two electrons on the right. In the reduction reaction, there are 7 positive charges on the left and 2 positives on the right, so we need to add 5 electrons on the left.

Notice that where we put the electrons makes sense in terms of oxidation (loss of electrons) and reduction (gain of electrons).

6. If necessary, multiply the equations through by coefficients that make the number of electrons the same in both half reactions.

The number of electrons in the respective equations are 2 and 5, so we'll multiply the oxidation reaction through by 5 and the reduction reaction through by 2:

7. Finally, add the equations, cancelling anything that appears on both sides:

Take a look at the result. All of the atoms are mass balanced, and the total charge is the same on the left and right.

Example 2

Balance the reaction:

CN- + MnO4- → CNO + MnO2 + H2O   in basic solution.

First assign oxidation numbers to this net ionic equation. In this case, It's difficult to determine oxidation numbers for the carbon and nitrogen in CN- and CNO, but if we group them as below, it's easy to see that the CN moeity is oxidized (loses electrons).

Now our half reactions are

Both will require addition of water and H+ ions to balance the masses. We're adding water and H+ for now, and we'll reconcile this with the fact that we mean for this reaction to be in basic solution later,

Adding electrons to balance the charge gives

We already have the same number of electrons on both sides, so we won't need to multiply through by anything to balance those. The next step is to understand that in basic solution there won't be any appreciable amount of H+ around, so we add enough OH- to each side of the equation to neutralize any of that (H+ + OH- → H2O)

Now we can cancel anything common on the collective left and right sides of these equations, preparing to add them:

That's the balanced redox equation. It's both mass (number & kind of atoms) and charge balanced.

There are other methods of balancing redox reactions in basic solutions. You don't always have to use this backtracking method — add acid, then base. You can sometimes just add base (as in the next example), but the acid-then-base method will always work. If you work through enough examples, you'll develop an intuition for it and your own style.

Example 3

Balance the reaction:

Cl2 (g) → Cl-(aq) + ClO-(aq)   in basic solution.

Assigning oxidation numbers tells us that in this reaction, chlorine gas (Cl2) is both oxidized and reduced:

The resulting half reactions are then

Balancing the atoms is easy with the reduction half reaction. The oxidation half reaction requires addition of water and H+ ions to balance the oxygens. Remember, we're proceeding as though this reaction were being run in acidic solution, and we'll adjust to basic later.

Adding electrons to balance the charges gives

Now we add four OH- ions to both sides of the oxidation reaction in order to neutralize the 4H+ acidic protons. Adding the hydroxides to both sides maintains our hard-won mass and charge balance.

Converting to water on the right side of the oxidation reaction and cancelling things in common across the arrows of both reactions gives us the sum of the half reactions.

That reaction has coefficients all divisible by two, so we should reduce them to get the final balanced equation:

Practice problems

Balance these redox reactions:

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