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Why do reactions with oxygen produce flame (i.e. light), heat and hence a lot of energy? I mean, why only oxygen, why not any other element like nitrogen? What is special about the electronic configuration/arrangement or molecular geometry that confers it with this property?

Maybe you will cite examples of other reactions involving a lot of energy and producing flame, but I am sure there is nothing as familiar to mankind (in terms of the frequency in their occurance) as the reactions involving this compound. Reactions with oxygen are so ubiquitous and vital to life and thus they were classified under a separate category, i.e. combustion.

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    $\begingroup$ Many other materials will undergo rapid oxidation to the point of flaming in halogen atmospheres. $\endgroup$ – Nick T Apr 21 '17 at 18:46
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Your question is quite broad, so I will tackle it in parts.

Element abundance

there is nothing as familiar to mankind (in terms of the frequency in their occurrence) as the reactions involving this compound

This is because frequency depends on abundance. If you have a look to the element abundance on the earth oxygen is the first:

Element Amount      
O   44.8        
Mg  22.
Si  21.5
Fe  5.8 
Ca  2.3 
Al  2.2 
Na  0.3 
K   0.03    
Sum 99.7    

We have then to take care of the "kind" of oxygen you are referring actually to $\ce{O2} $ that is mainly produced by photosynthesis so linked to the evolutionary history of our planet. If you have a look to the atmosphere these are the ratio.

Element        Formula    %    
Nitrogen        N2      78.084
Oxygen          O2      20.946
Argon           Ar      0.9340
Carbon dioxide  CO2     0.04
Neon            Ne      0.001818
Helium          He      0.000524
Methane         CH4     0.000179

Electronegativity

why not any other element like nitrogen?

This is due mainly to the electronegativity, actually, there are other molecules that have greater electronegativity and hence they are good oxidizing agents but because of their abundance, they are not so common.

Periodic table with electronegativity values

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Dioxygen, $\ce{O2}$ is a very special molecule. A good majority of organisms on earth use dioxygen to breathe and survive. Oxygen is also the second most abundant element in the sky, as well as the most abundant elements in the earth's crust. What makes it so special? Its because of its abundance, which is obvious, and also because of it's strong oxidizing power.

If you are a student below 11th grade, you might be taught that oxidation is addition of oxygen or the removal of hydrogen. I will now, introduce a new definition of oxidation.

Oxidation: The loss of electrons from a substance is called oxidation.

The reagents that cause substances to become oxidized are called oxidizing agents. $\ce{O2}$ is an example of an oxidizing agent. A popular oxidizing agent in analytical chemistry is Potassium Permanganate ($\ce{KMnO4}$ ).

Many times, an actual loss of electron doesn't take place, rather a shift of electrons from one element to another within the same molecule occurs, which is also considered as oxidation. To explain such stuff, we introduce the concept of oxidation numbers. An easy way to find oxidation number of an element in a compound is:

Ox.num=(Num. of bonds formed with electronegative atoms)-(Num. of bonds with electropositive atoms)

For example, take carbon dioxide. It's structure is:

O=C=O

Note that bonds made by an atom with a similar atom are not considered (like $\ce{O-O}$ or $\ce{S-S}$).

Carbon makes four bonds with more electronegative atoms (oxygen). So it's oxidation number is +4.

If oxidation number of any atom of a molecule is increased through a reaction, we say that oxidation has taken place. Note that as this happens, the oxidation number of the oxidizing agent will decrease.

Now, finally (with a deep breath), lets come to your question.

Speciality of Oxygen:

Oxygen in nature, as dioxygen has a 0 oxidation number. Since it's so electronegative, it almost always forms bonds with electropositive atoms, and so its oxidation number in compounds is always negative. Oxygen itself has such a high tendency to rip off electrons from other molecules. This is what makes oxygen very special.

There are so many examples of oxidation reactions with oxygen:

Combustion: Burning stuff itself is an oxidation reaction. If you burn coal(carbon), its oxidation number goes from 0 (in pure carbon) to +4 (in carbon dioxide).

Respiration: Even our own bodies have to do an oxidation reaction to keep us with energy to do our daily work, like asking and answering questions on StackExchange. Glucose, which has a oxidation number of 0 (equal number of bonds with oxygen and carbon in its formula of $\ce{C6H12O6}$ ) is oxidized by the oxygen we breathe to carbon dioxide.

Much of the interesting properties of oxygen is due to its oxidizing power. While many oxidizers are known, like fluorine for example; oxygen is, and will always, be the most well known one!

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    $\begingroup$ First of all, good answer. Also notice that I edited you question using the convenient and powerful \ce (for chemical equation) notation. It makes formatting chemical equations easier and formats them correctly according to the meta discussions here and here. Just FYI. Most importantly, keep up the good questions and answers! $\endgroup$ – airhuff Apr 21 '17 at 17:09
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    $\begingroup$ Fluorine is even more oxidizing than oxygen, but we don't see biological reactions centered around fluorination. Might have to do with fluorination being too fast, and oxidation being in the sweet spot of kinetic constants. $\endgroup$ – svavil Apr 21 '17 at 20:08
  • $\begingroup$ @svavil you're absolutely right, fluorine is more oxidizing than oxygen, but oxygen is more commonly around. The reason why you don't observe fluorine oxidations much is because it isn't around much! $\endgroup$ – Pritt says Reinstate Monica Apr 22 '17 at 4:07

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