Oxidation numbers; what are they?

[lzxnl]

VCE Chemistry, I feel, doesn't do this topic justice and it's something that I feel people rote learn, so here's a quick guide on them.

For most people, oxidation numbers are just some random number that you assign to individual atoms to determine if it's a redox reaction and perhaps to check how many electrons there should be on one side of a redox half reaction. There's nothing wrong with that; it's just not a rather insightful view into what exactly these are.

The oxidation state model assigns numbers to atoms in a compound by making one assumption: that all bonds are ionic. Therefore, the oxidation number is the charge the atom would have under these situations.

What do we do about covalent bonds? Well, logically the atom that is more electronegative is assigned the electrons. This is why, for instance, we assign oxygen as -2 almost all the time as oxygen is the second most electronegative element. Similarly, hydrogen is normally +1 as it's near the bottom of the list in terms of electronegativity amongst the non-metals.

Now, as oxidation numbers count electrons as if they were localised on individual atoms, the sum of all oxidation numbers must be equal to the charge of the molecule or ion. See where that rule comes from now? Also, with something like F2, this is an example of a truly equal covalent bond, so the oxidation state model gives each atom one electron, which is to be expected, allowing each atom to retain their own electron for an oxidation state of 0.

Let's look at some examples. Carbon dioxide, for instance, has carbon forming two double bonds to each oxygen. As carbon is less electronegative than each oxygen, we treat the carbon as having lost each electron it contributes to each covalent bond. It makes four bonds, so its oxidation number is +4. Similarly, each oxygen makes two bonds and receives two electrons, so they each have oxidation number -2.

Similarly, something like K4Fe(CN)6, while ghastly, can be analysed by breaking it down. The four potassium atoms written at the front of the molecular formula are cations with charge +1, so they've just lost one electron to put them in the +1 oxidation state. The Fe(CN)6 bit has charge -4. Now, cyanide, the CN group, has a charge of -1. It consists of a carbon-nitrogen triple bond in which the nitrogen atom has a full octet and the carbon atom only has 4 + 3 = 7 electrons in its valence shell (under the covalent bond, not oxidation state model!), so it gains an electron and has a negative charge. Now, the carbon has formed a triple bond to nitrogen, so nitrogen has, under the oxidation state model, gained 3 electrons. Normally carbon would be considered to have lost those 3 electrons, but it has a negative charge, so its oxidation state is +2, not +3. As the sum of oxidation numbers of C and N is now -1, our intuition that each CN anion with a -1 negative charge can be replaced by a generic anion of oxidation number -1 is confirmed. So, we're attaching 6 anions contributing -1 to the overall oxidation number, which is -4. Clearly the iron must have oxidation number +2, and we're done!

This helps explain some anomalies with some elements too. Normally, oxygen is -2. In peroxides, like H2O2 which is better represented as HO-OH, the oxygen-oxygen bond means each oxygen only gains ONE electron from the hydrogen to give an oxidation state of -1. Similarly, OCl-, the hypochlorite ion, has a chlorine in a +1 oxidation state as it's less electronegative than oxygen, whereas OF2 has oxygen in the oxidation state +2 as it's less electronegative than fluorine. Hydrogen, when combined with metals in hydrides like LiAlH4 or NaH, is more electronegative, so it has an oxidation number of -1, not +1. Be warned.

Finally, let's look at one other aspect of oxidation numbers. If you look at propane, C3H8, you'll see that a standard analysis of oxidation numbers gives hydrogen as +1 and carbon as -8/3. Fractional oxidation numbers?
Propane is H3C - CH2 - CH3. The first carbon is bonded to three less electronegative hydrogens, so it has oxidation state -3. The fourth bond is to another carbon, so that bond counts as an equal covalent bond. Same with the third carbon. The second carbon is bonded to two hydrogens and two carbons, so its oxidation state is -2. If we average -3, -3 and -2, we get -8/3. Thus, the oxidation state of the carbon in C3H8 is really just the average of all of the oxidation states of the carbon atoms.

[alchemy]

Legend.

[Rishi97]

Thanks for that No wonder you got a 50...great job

[hobbitle]

This is a great explanation (even though I still find it complicated!) - thanks for taking the time to write it.

I had heard through Khan Academy about the different way of analysing oxidation states by treating the bonds as ionic and using relative electronegativities, which I think is more intuitive that the weird rote learning way with all the rules.  You provided a really nice explanation.

The problem I had with implementing the ionic bond approach is that you need to know the structural formula for the compound, and being new to Chemistry, sometimes I can't work this out.

So - my first question to you is, if you happen to enjoy doing write-ups like this one, would you perhaps consider doing a write-up on how to determine the structural formula (or Lewis structures I suppose) of more complicated compounds? 
For example, I got super confused when trying to figure out the oxidation numbers for XeOF4 because I thought the O was bound to the Fs and therefore O wouldn't have a 2- oxidation number... but it turns out it does have 2-.... and the dot structure for XeOF4 is crazy (to me) anyway because the Xenon appears to have 12 valence electrons............ I am so confused haha.

I also have another question - not related to oxidation states so much, sorry.  Whilst straightforward compounds are easy (cation first followed by anion etc), it has not been explained to us very well how the formulas for the more complicated compounds are 'created' and how they are structured.  For example: you said in your post that C₃H₈ is actually H₃C - CH₂ - CH₃ in structure.  Why is C₃H₈ written such that the elements are 'grouped' but then in something like vinegar, CH₃COOH, the elements are kind of ordered according to the structure?

Thanks for your time - don't worry about answering if it's too time consuming, I understand they could be lengthy responses.

[lzxnl]

This is a great explanation (even though I still find it complicated!) - thanks for taking the time to write it.

I had heard through Khan Academy about the different way of analysing oxidation states by treating the bonds as ionic and using relative electronegativities, which I think is more intuitive that the weird rote learning way with all the rules.  You provided a really nice explanation.

The problem I had with implementing the ionic bond approach is that you need to know the structural formula for the compound, and being new to Chemistry, sometimes I can't work this out.

So - my first question to you is, if you happen to enjoy doing write-ups like this one, would you perhaps consider doing a write-up on how to determine the structural formula (or Lewis structures I suppose) of more complicated compounds? 
For example, I got super confused when trying to figure out the oxidation numbers for XeOF4 because I thought the O was bound to the Fs and therefore O wouldn't have a 2- oxidation number... but it turns out it does have 2-.... and the dot structure for XeOF4 is crazy (to me) anyway because the Xenon appears to have 12 valence electrons............ I am so confused haha.

I also have another question - not related to oxidation states so much, sorry.  Whilst straightforward compounds are easy (cation first followed by anion etc), it has not been explained to us very well how the formulas for the more complicated compounds are 'created' and how they are structured.  For example: you said in your post that C₃H₈ is actually H₃C - CH₂ - CH₃ in structure.  Why is C₃H₈ written such that the elements are 'grouped' but then in something like vinegar, CH₃COOH, the elements are kind of ordered according to the structure?

Thanks for your time - don't worry about answering if it's too time consuming, I understand they could be lengthy responses.

Yeah, with oxidation numbers you really need to know the structures of these compounds.

For something like XeOF4, you just have to know that the noble gas is bonded to all of the other atoms. There are honestly way too many rules and conventions for working out Lewis dot diagrams I'm afraid; there are guides online, and to be honest, I wouldn't be able to give hard-and-fast rules on these. I just work them out and make sure they make sense.
The thing about Lewis diagrams is that sometimes they can be disputed. For instance, we often think of SO2 as having sulfur double-bonded to two oxygens as it's a period 3 element with d orbitals. Actually, SO2 is a resonance hybrid in which the sulfur has a permanent positive charge and the resonance forms look like O-S=O, with an overall -1/2 charge on each oxygen. Similarly, SO3 may look like having sulfur with three double bonds to each oxygen, but some theories suggest that sulfur here still has an octet of electrons. Lewis diagrams are really weird.

C3H8 is the molecular formula, while CH3CH2CH3 is the semi-structural formula. Generally, people will give you a structural formula or a condensed version of it when discussing molecules, as something like C6H12O6 doesn't do justice to the many isomers of glucose out there. We know C3H8 is CH3CH2CH3, however, because that's the only possibility for a molecule with that formula.

As for ethanoic acid, if you wrote out the formula like C2H4O2, that could actually refer to a few things. For instance, it's not impossible to get HO-CH2-COH, for instance, in which the COH means a C=O with the carbon also bonded to hydrogen. There are multiple isomers; writing the formula as CH3COOH makes it absolutely clear that we're dealing with ethanoic acid.

[hobbitle]

Hey again.
I just wanted to clarify something.
Say for example we have a redox reaction:

2HNO₃ + 3H₂AsO₃ -> 2NO + 3H₃AsO₄ + H₂O

Working out oxidation numbers, we can see that the N goes from 5+ to 2+, and the As goes from 3+ to 5+.

So, do we write specifically that N is reduced and that As is oxidised?  Or is it the whole compound, i.e. HNO₃ is reduced and H₂AsO₃ is oxidised?  So the oxidant is HNO₃... or just N?

[lzxnl]

Hey again.
I just wanted to clarify something.
Say for example we have a redox reaction:

2HNO₃ + 3H₂AsO₃ -> 2NO + 3H₃AsO₄ + H₂O

Working out oxidation numbers, we can see that the N goes from 5+ to 2+, and the As goes from 3+ to 5+.

So, do we write specifically that N is reduced and that As is oxidised?  Or is it the whole compound, i.e. HNO₃ is reduced and H₂AsO₃ is oxidised?  So the oxidant is HNO₃... or just N?

We speak of the entire molecule/compound/ion being oxidised or reduced. For instance, in the reaction 2H2O2 => 2H2O + O2, the hydrogen peroxide is both oxidised and reduced.
In your case, the oxidant is nitric acid.

[hobbitle]

We speak of the entire molecule/compound/ion being oxidised or reduced. For instance, in the reaction 2H2O2 => 2H2O + O2, the hydrogen peroxide is both oxidised and reduced.
In your case, the oxidant is nitric acid.

Cheers for the clarification.

Out of interest, do they teach the "treat it like its an ionic bond" school of thought at VCE?
I have no idea why they are teaching this stuff to us at uni based on like 9 'rules' when its so much easier just to use the method you outlined in your original post, not to mention you actually get the intuition behind it as well as opposed to just being a rote learn monkey.

[lzxnl]

Cheers for the clarification.

Out of interest, do they teach the "treat it like its an ionic bond" school of thought at VCE?
I have no idea why they are teaching this stuff to us at uni based on like 9 'rules' when its so much easier just to use the method you outlined in your original post, not to mention you actually get the intuition behind it as well as opposed to just being a rote learn monkey.

Nope, this isn't taught in VCE funnily enough. I do remember vaguely that first-year uni uses this set of rules as well to work out oxidation numbers (from my hurried review of first year chem last year hahaha；I may be wrong here). Rote-learn monkeys are what VCE want people to be.