At it’s most basic, different elements prefer different numbers of things bonded to them. In this case, hydrogen likes to have one thing bonded to it and oxygen likes two. In the case of H20 and H2O2 this is satisfied by the connectivity HOH and HOOH. If it were OHHO or OHOH then you’d get oxygens with one bond and hydrogens with two.
For more complicated molecules where you can have more than one reasonable answers for how things are connected you need to use more complicated techniques such as infrared spectroscopy, NMR spectroscopy or x-ray crystallography. These are just a few of the more common techniques but there are many ways depending on exactly what you’re trying to determine the structure of.
To answer this requires a bit more a background in chemistry but it’s two pieces.
First, we know *why* atoms bond together, which has to do with the number of electrons they have and how they are arranged. In a very simple example, you might understand that electrons repel each other like magnets. So if I have 3 electrons around me in a circle, and they all repel each other, they push themselves in 120^(0) angles. Because 3*120=360, so they evenly push each other apart. Long story short, we now know enough about chemistry to predict the shape of molecules based on our knowledge of each atom’s specific electron situation and how it would interact with another atom’s electron situation.
As a good visualization example, oxygen “wants” to have a 4 electron “situation” (this is another chemistry conversation, let’s agree we know this from a previous school lesson), but it only has 2. So desires bonds with 2 hydrogen atoms which give it the desired 4 electron situation. But in our visual models of water, we wouldn’t draw the 2 electrons oxygen started with, only the 2 new hydrogen atoms. Since 360/4 = 90, we can imagine a water molecule as looking like 2 invisible electrons on the bottom and 2 visible hydrogen atoms on top, all 90 degrees apart, this would be the Micky Mouse Head kind of appearance of water. (Note, this is idealized, there more going on and the hydrogen atoms in water are closer to 110 degrees apart, but that’s tomorrow’s chemistry lesson).
So in the end for basic molecules, we can use our knowledge of electrons, chemistry, and trigonometry to visualize them. This gets much, much more complicated when you get to huge molecules because we’re less sure of how everything connects to together, but we have other, future-lesson complicated type stuff, ways of visualizing those molecules too.
Hydrogen’s electron cloud only has one “connector” for bonding. Oxygen has two.
More specifically, hydrogen’s electron cloud is one electron away from full, while oxygen’s is two. Atoms don’t like to have partially filled electron clouds, and will try to complete them. In the case of hydrogen and oxygen, this means bonding.
When two atoms bond, they each share two electrons, one from each. But, each electron in the bond takes up space in both atoms’ electron clouds. So, forming a bond adds an electron to both atoms’ electron clouds.
Hydrogen bonds with oxygen, and it’s full. But, the oxygen still has one unfilled slot, so it can bond to one more atom. This can be another hydrogen (in the case of water), another oxygen (in the case of hydrogen peroxide), or whatever.
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