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What are the two properties of carbon which lead to the huge number of carbon compounds we see around us?

Answer
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Hint: You can think of some of the most popular carbon-containing compounds i.e. $CO_{ 2 }$, CO, and some long-chain compounds, etc. and observe what is so common in most of them. You can easily get your answer by applying this step.

Complete step by step answer:

The two properties of carbon which lead to the huge number of compounds and show allotropy
(i) Catenation - The property of carbon element due to which its atoms can join one another to form long carbon chains is called catenation. It means carbon atoms have the tendency to link with one another through covalent bonds to form chains and rings.

(ii) Tetravalency - Carbon has a valency of four. So, it is capable of bonding with four other atoms of carbon or atoms of some other mono-valent element.
Compounds of carbon are formed with oxygen, nitrogen, hydrogen, sulfur, chlorine, and many other elements, giving rise to compounds with specific properties that depend on the elements other than the carbon present in the molecule.

Therefore, we explained the two properties of carbon which lead to the huge number of carbon compounds we see around us.

Note: We should also know that carbon has the unique ability to form pπ−pπ bonds with itself and others C=C, C=S, C=O, C=N. This bond makes these structures very stable.