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I have recently started learning chemistry, and I've been reading a GCSE (UK high school level) textbook on the stuff :D

Much of it has been fairly straightforward, though there has been a reoccurring theme that has been bothering me.

I've encountered many instances where the author simply presents a reaction with little explanation, as if to suggest that the reason as to why it would occur is obvious.

Let me give you an example I have come across just today. Ethene in bromine water:

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I think to myself, 'why would this happen?'. There are no 'free electrons' that I can see in ethene. OK, bromine is highly reactive, but what will it do? Will it react with H, or C, and how? What about the bromine bond? It's all very uncertain in my mind.

I always try to reduce it to an energy problem. We just want the most stable state, right? But, there are many possible outcomes. Am I supposed to apply some logic, follow some flowchart, or work out all possible outcomes and calculate which has the lowest energy? Do chemists just remember all simple reactions, and reduce problems to those? Or, am I just overthinking it?

A side problem to this is why, if we place an alkane in bromine water, we don't get the same thing happening with ethane.

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There are no 'free electrons' that I can see in ethene

That's correct, but... In ethene there are two bonds between the two carbons that hold the two carbons together. A chemist calls this a "double" bond. The important thing about a double bond (that's not obvious from the drawing) is that the two bonds are not the same. One is a strong sigma bond, just like in ethane; the other is a weaker pi bond. While the electrons in the pi bond are not free, they are not held as tightly

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as the electrons in the sigma bond and are, therefore, more available for reaction. This is why ethene is so much more reactive than ethane.

Am I supposed to apply some logic... Or, am I just overthinking it?

Yes, there is logic and that body of logic is what organic chemistry is all about. In the case of bromine reacting with ethene, the reaction belongs to a class of reactions known as electrophilic additions. Most reactions in organic chemistry involve a molecule that has electrons available to share (a nucleophile) and a molecule that would like more electrons (an electrophile). These two molecules react (form a chemical bond) by the one donating\sharing its electrons and the other molecule accepting\sharing those electrons. Here, the pi bond in ethene has electrons that it is willing to share (they're not free, but they're not tightly held either), while the bromine molecule is highly polarizable, much like $\ce{Br^{\delta +}-Br^{\delta -}}$, with the positively polarized bromine atom wanting electrons. The reaction proceeds as pictured below, to yield 1,2-dibromoethane.

enter image description here

A side problem to this is why, if we place an alkene in bromine water, we don't get the same thing happening with ethane.

I bet you can answer that one now. Ethene has a pi bond with electrons loosely held and available for reaction. Ethane, on the other hand, only has a sigma bond where the electrons are more tightly held and less available for reaction.

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You must learn some basic things in organic chemistry to understand mechanisms for such simple reactions and these are: functional groups, nucleophiles, electrophiles, leaving groups, curly arrows. You should easily find explanations of these in any organic chemistry textbook. Then you could use this link http://www.chemguide.co.uk/mechanisms/eladd/symbr2.html#top to understand what is happening in this reaction. Here are the other basic types of reaction in organic chemistry: http://www.chemguide.co.uk/mechmenu.html#top

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