Using the McAfoos Rules for Oxidation Numers

Here are the rules in use. Remember that Rule 1 is not only the most important, it is also the LAST thing you do each time.

Rule #1 – The sum of the oxidation numbers = the total charge. 

This rule assigns oxidation numbers to pure elements, and single element ions. Here are some examples:

Rule 1 is also used to assign the "last" oxidation number. That does NOT mean the oxidation of the element on the right (or the left for that matter). It means that once we have assigned oxidation numbers for all but one of the element in the compound or ion, we use math to assign the last.

Let's look at the compound \(CoF_2\). If we know that the F has an oxidation number of -1 (Rule 2 would allow us to know that), we can determine the the Co must have a charge of +2 according to the math below:

\(charge=sum~of~oxidation~numbers\)

The charge on this (or any) compound =  0, and each F is -1. Let's set the oxidation number of Co = x. That gives us:

\(0=x + 2(-1)\)

Rearranging gives us \( x=+2\), so the oxidation number of Co is +2.

For another example, let's look at the compound \(K_2O_2\). We can know (again from rule 2) that the potassium has an oxidation number of +1. We know that the charge is 0, so let's set the oxidation number of oxygen to "y". That gives us:

\(0 = 2(+1) + 2(y)\)

which, when rearranged, gives us \(y=-1\). This is an odd charge for oxygen, but it's common enough that we gave it a name ⎼ this is a peroxide.

Rule #2 – Single charge elements

This rule assigns oxidation numbers to those elements that only have one non-zero charge. The list is short: alkali metals are always +1 (this doesn't include H), alkaline earth metals are always +2, F is always -1. There are some other elements that have only one (non-zero) charge, but you can probably get away without thinking about them. 

Immediately after applying this rule, you should apply Rule #1 (if possible).

Here are some examples:

Rule #3 - Hydrogen is always +1

Remember that this rule is a LOWER priority than the ones above, so we would not apply it for the following:

\(H_2\):    Hydrogen's oxidation # = 0 (Rule 1)

KH:    Hydrogen's oxidation # = -1 (Rule 2)

Now let's look at some examples where Rule 3 does matter:

Rule #4 - Oxygen is always -2

Just like Rule 3, this seems to contradict some of the things we've already done. However, as long as you remember that these rules are in RANKED order, you'll be fine. 

For instance we would NOT use Rule 4 in the following cases:

\(O_2\): Oxygen's oxidation # = 0

\(CaO_2\):    Oxygen's oxidation # = -1

Now, let's look at some examples for which we would use Rule #4:

Rule #5 - The most electronegative element gets its most logical negative charge

This rule is only used occasionally. In fact, you may not even realize that you are using it.

Here's a simple example:

\(NiCl_3\)

None of the previous rules can be applied. We have more than one element (so no Rule 1), Both of these elements have more than one possible charge (Rule 2), there is no Hydrogen (Rule 3) and no Oxygen (Rule 4).

We do know that Chlorine is more electronegative than Ni. The logical charge on Chlorine is -1 (since that makes it isoelectronic with Argon.

That makes our math easy: \(0 = x + 3(-1)\) which gives \(x=+3\). So this is nickel III chloride.

A word of caution: Complex ionic compounds (those with polyatomic ions and especially with polyatomic ions that contain the same element) have to be treated carefully - both in terms of assigning oxidation numbers and physically. This should explain.