Final answer:
The term describing the general process of building up chemicals within cells is anabolism, which, along with catabolism, constitutes the broader fabric of an organism's metabolism.
Step-by-step explanation:
The term that most precisely describes the general process of building up chemicals within cells is anabolism. Anabolism is part of metabolism and refers to the sequence of chemical reactions that construct molecules from smaller units. These processes typically require energy. For instance, the assembly of proteins from amino acids is an anabolic process. When comparing anabolism to the broader scope of chemical reactions, it focuses on the synthesis part where small molecules are built up into larger ones - an essential function for growth and repair in organisms.
In a larger sense, the sum of all chemical reactions that occur within an organism is referred to as its metabolism, which includes both anabolic and catabolic processes - where the former is about building up and the latter is about breaking down molecules. When discussing chemical processes in a broader context, one might refer to chemical nomenclature, which is the system for naming the various chemicals involved in these processes, and consider the overall journey of a reactant to becoming a product in a chemical equation. This encompasses all transformations from the initial interaction of reactants through to the final products of a reaction.