What is unique about carbon and carbon-based compounds? Why did life evolve around

Answer :

Carbon is the chemical element with the symbol C and atomic number 6 (contains 6 protons in its nucleus). As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds. The most common isotope of carbon has 6 protons and 6 neutrons, and has an atomic mass of 12.0107 amu. Its ground state electron configuration is 1s22s22p2. Its oxidation state ranges from 4 to -4, and it has an electronegativity value of 2.55 on the Pauling scale. It is a solid, and sublimes at 3,642 °C (it has the highest sublimation point of all the elements).

Unique character of carbon :

The ability of carbon to bond to itself to make a host of compounds makes it ideal as a base for the complexities of the chemistry of life. Simple carbon chains can be lengthened and have functionality added to form useful polymers. Even in its elemental form, carbon can form sheets, tubes, complex geodesic structures and crystals. Yes, carbon is special because carbon bonds to itself.

life evolve around carbon

Because carbon is the most flexible light atom.  It has 4 valence electrons.  That allows it to bond to up to 4 other atoms in a molecule, more than any other common element except silicon.

That opens up a world of possibilities: long chains, saturated and unsaturated carbons, bends and kinks, side chains and branches.  There are so many things you can make out of carbon; it's the duct tape of atoms.  Nothing else is as flexible.

The closest you get is silicon, the runner up.  There's certainly plenty of it on the planet.  It's actually a lot more common than carbon, which is actually pretty rare.  It just so happens that carbon is also light, so a lot of it floats to the surface, including in gases like CO2.  More common but heavier elements tend to be bound into rocks, and aren't as available.  

Silicon, for example, is mostly bound into rocks, and doesn't dissolve.  Many carbon compounds are soluble in water, making them much more available for reactions.  (Solids don't react as well as liquids do, since the atoms don't get a chance to meet.)

Silicon has the same valence structure as carbon, and it's almost as flexible.  But it's also heavy, meaning you need more energy to move it around.  And it's bigger, making molecules clunkier and harder to react.

Silicon based life is not impossible, but it's not surprising that it's based on carbon where carbon is available, and where the temperatures are near ours.