There is a large number of carbon compounds due to (a) tetravalency of carbon (b) strong catenation property of carbon (c) allotropic property of carbon (d) non-metallic character of carbon.

Understanding the tetravalency of carbon is crucial to comprehend the vast diversity of carbon compounds. Tetravalency refers to the presence of four valence electrons in the outer shell of a carbon atom. These four electrons enable carbon to form four covalent bonds with other atoms. Imagine the possibilities like building blocks that can attach on four sides, creating an array of structures. From single, double to triple bonds, carbon can join with other carbon atoms as well as with different elements such as hydrogen, oxygen, nitrogen, forming an assorted range of molecules. This includes everything from simple molecules like methane, \( CH_4 \), to large and complex organic molecules found in living organisms. The versatility due to tetravalency is a foundational principle why carbon is the cornerstone of organic chemistry.

Diving into the catenation property of carbon reveals another layer to its versatile nature. Catenation is the elemental ability to form bonds with itself, creating a chain or network of atoms. Carbon is renowned for its unparalleled catenation capability. It can link with other carbon atoms to form long and stable chains or even intricate structures like rings and branched networks. This property stems from the strong carbon-carbon (C-C) bond which is sturdy and stable. Organic compounds exhibit a rich variety with straight chains, branched chains, and rings, showcasing the incredible impact of catenation. These complex structures are the backbone of many natural substances like proteins, DNA, and synthetic materials like plastics.

Allotropy captures the essence of an element existing in multiple forms in the same physical state. The carbon allotropes exhibit distinctive properties due to the different ways carbon atoms bond with each other. Graphite, diamond, and fullerenes are quintessential examples of carbon allotropes. Graphite is formed by layers of carbon atoms arranged in a hexagonal lattice, leading to its softness and use as a lubricant or in pencils. Conversely, diamonds are renowned for their hardness and brilliance, a result of each carbon atom strongly covalently bonding to four others in a tetrahedral structure. Fullerenes, including molecules like buckyballs, have a spherical shape and distinctive electrochemical properties, opening up uses in materials science and electronics. Through these variations, the allotropes of carbon demonstrate remarkable versatility and a spectrum of properties useful in numerous applications.

The non-metallic character of carbon plays a pivotal role in the formation of carbon compounds. By nature, non-metals tend to accept or share electrons rather than donate them, which aligns with carbon's propensity to form covalent bonds. These bonds are characterized by the sharing of electrons between atoms, which is different from ionic bonds where electrons are transferred from one atom to another. Carbon's ability to form stable covalent bonds facilitates the construction of a myriad of organic molecules, each with unique characteristics and uses, ranging from gases like carbon dioxide \( CO_2 \) to complex polymers and life's very building blocks. The non-metallic character of carbon thereby enriches the chemical world with a platform for a dynamic array of carbon-based molecules.