Home

Vector Space Chemistry: Elements, Reactions, Tensors and Forms

Ethanol and dimethyl ether have the same molecular formula, C₂H₆O. If we count atoms, the two substances give us the same vector. If we want to follow their amounts during a reaction, we need a separate coordinate for each species. This example introduces the question that runs through the book: which chemical distinctions does a representation preserve, and when do we need a richer one?

Vector Space Chemistry: Elements, Reactions, Tensors and Forms develops an idea I explored at school in 1986–1987: treating chemical elements as basis vectors and stoichiometric coefficients as scalars. Spaces of species and reactions were already part of mathematical chemistry in Aris’s 1965 work. Here we follow the choices that connect these representations, beginning with the elemental inventory in an ordinary chemical formula.

Through worked examples, we balance equations, identify conserved quantities, and check whether a proposed sequence of reactions is feasible from a given inventory. We use dual spaces to describe what a measurement can distinguish, tensor products to retain information about a species and its surroundings, and differential forms to examine thermodynamic change along a path. At each step, the chemical question determines the mathematical structure we need.

ISBN-13: 978-1-906717-55-1
Date: 7 November 2026

PDF Download: https://www.dumpanalysis.org/files/Vector_Space_Chemistry_14.pdf