I've seen lots of stick and ball models, and taken the basic chemistry class- which entitles one to say 'I have NO idea how that works!'- and it's nice to have you put some meat on those bones.
Why does water- H2O- not follow the seemingly obvious trend and have the two hydrogens straight opposite of one another? And one more that pertains to what we all like to do here; what exactly does H2O2 look like, and does its structure have anything to to with its properties, or are they just strictly a consequence of that molecule being so unstable? I figured I'd start with little molecules- we can work our way up to benzene rings and peptide chains later!
Now these are some questions I can answer!
As I mentioned before electron pairs (called lone pairs) can take up one of these "slots". Oxygen has two of these electron pairs (4 total) in its valence when it has made two bonds. Each electron pair generally represents a place where a bond could be made as a little aside, however Oxygen typically only likes to make 2 bonds, with any further bonds usually being very unstable and short lived. Should be noted that oxygen doesn't particularly like having only one bond either--it tries to have two as hard as it can given a set of conditions.
Moving on.
Because there are two electron pairs, and two bonds (to the hydrogens), what you are seeing is a tetrahedral arrangement with two of the legs missing. The bond angle isn't 120 degrees as you'd see with a trigonal arrangement, it is about 104.5 degrees (the compression from 109.5 is due to the electron pairs, they really don't like to hang out next to each other--a proton (hydrogen) and an electron are equal in charge magnitude, thus because there are more electrons than protons the charge gradient causes the protons to hang out closer than the electron pairs. If oxygen had only one lone pair in its valence we would expect to see 120 degree bond angles, because the repulsion from any one constiuent to the next (including the lone pair ) would be equaled out through the molecule.
A way to figure out if a molecule is "polar" or not is to decide what the geometry is, and then draw vectors in accordance with those degrees (in a 3d plot) facing the most electronegative atoms. In this case we have a vector going up and to the side at 104.5 degrees, and a second coming in the opposite direction to the side but still going up. The vector to the side is cancelled and with end up with a net dipole pointing up and away from the oxygen. If you do this with a nonpolar molecule like CH4 (the carbon is the more electronegative and so lines will be drawn towards it) what you end up with is a net zero vector. The vectors from the "legs" of the tripod cancel each other out in terms of side to side motion (looks like a helix if u draw it out) but leave you 1 unit down below the central atom. The last vector brings you straight back up one. It might seem crazy and tedious--but this is how it works :)
On to H2O2:
This molecule has more than one central atom, so to speak. So the calculation is a bit different. In this case we're looking at two oxygens hooked up to each other in the middle, with each oxygen hanging onto a hydrogen.
For this case we look at the geometry
about each oxygen molecule. Quickly we realize that each oxygen is connected to the same amount of things (and with the same number of lone pairs) as in water, above. This is known as the hybridization state about the central atom. What you're looking at here is a tetrahedral arrangement about each oxygen. the bond angles at each oxygen are again somewhere near 109.5, they are probably lower than in water due to the increased repulsion from two lone pairs. Also, rather than being two Hydrogens bent in the same direction--they will tend to arrange themselves like a staircase, so that each hydrogen points away from the other. When we draw these things, the hydrogens seem far apart--but in reality they are quite close together and don't like to hang out in the same spot. These bonds are ALL free to rotate (in both water and h2o2), so when we're discussing which way is something pointing, we're talking about how most of the molecules would like to be pointing--the probability that any one molecule is in that configuration at any given point in time. As we get into double bonds (or what is called "increasing double bond character" which can be established through resonance)--we start to lose bond rotation, I can explain this--but that's a whole other topic and I'll need to draw something out, let me know if you are interested.
This leads into the reactivity argument.
The oxygen-oxygen bond is highly polarized. Because oxygen is very electronegative, it has the property of being able to stabilize negative charges very well. However, with two of them covalently bonded what you end up with is 4 electrons repelling 4 electrons which are across the bond from them. These electrons not only push at each other in free space, but they also can "talk" to each other through the bond through what are called inductive forces.
This essentially polarizes the bond, like charges repel, opposite attract.
Often when you're looking at molecules it becomes necessary to chase the charge. If you look at a carbonyl ( a C double-bond O) the oxygen is able to leech electron density from that carbon through induction and what you end up with is not this stable, chargeless molecule (that's simply how we draw it, not how we understand it). The oxygen carries a delta-negative charge (less than 1) and the carbon a delta-positive.
If say, h202 were to see such a compound the oxygen would be thermodynamically drawn to not only relieve the repulsion from the bond with its oxygen neighbor--but also to chase after anything positive, like the carbonyl carbon.
This isn't necessarily what we'd call a "high energy bond", it's more of a weak bond really. What ends up happening--contrary to what we'd usually expect (and this is what makes peroxides special) is that one of the Hydrogens is actually pushed off the end of the molecule (with h2o2 acting as a weak acid). You end up with this highly charged up negative oxygen molecule going around looking for something that can stabilize it (and do so better than a proton). This translates to just about anything in the biological world, and thus you have your method of attack.
The HOO- group will usually go after carbons, because carbon is great at stabilizing stuff (has very weird electronic properties that we don't fully understand yet), displacing any bonds that get in its way. This stuff acts as a powerful oxidizer. So much so that its been used in rocket fuels and other such applications where an oxygen rich environment is desirable.
I hope you find all of this cool. Because I do. This is happening along the chain of every molecule in existence right now. Its like all of the substituents want to get away from each other really badly.
Think of the trigonal argument. lets say we have a sphere with rods attached to it (which can somehow move freely along the sphere--but which will not ever become disconnected regardless of the force).
So at the end of three rods we place 3 objects which have
very powerful, but equal, negative charges on them. These negative charges will automatically snap into place at 120 degree angles from each other (with respect to the rods connecting them). If you introduce a fourth negative charge from above--you'll see a the tripod legs flip down and the new charge will stand straight up--the bond angles will be 109.5. Let's say we take the fourth off--the model snaps right back to 120 degree angles and a planar arrangement. If we make the charges so strong that they overwhelm a humans strength to fight them, and you apply a force to one of the objects--all of the objects would spin around the sphere in unison, maintaining their distance from one another at all costs. So this same physical property we see on the macro scale is conserved on the micro scale--it's just done more weirdly, so to speak. A huge amount of this has to do with electrons ability to exist in a "cloud" or valence shell around an atom. When you start combining atoms, you start combining their clouds and some interesting properties emerge.
Have you ever wondered why benzene can be drawn as the ring structure with a circle in the middle of it? It's not because we're lazy and wanted a symbol. It's because all of those bonds are equal and consist of shared electron density throughout the ring--and it's all happening because those electrons want to spread out.
Edit: forgot to mention that for the vector drawing above--the trick is to draw each vector without lifting your pen, tail to tail. As if each vertex is you drawing a vector from (or to, depending on electronegativity) the central atom.
