Arithmetic of mixing

Abstract Often, when a molecular simulation of a complex mixture is to be performed, one runs into the issue of converting complex, experimentally prepared formulations into mole fractions of individual molecular entities. Conversely, in fields such as organic chemistry, there is often a need to convert mole fractions into other compositional units. In common practice, those conversions are performed manually, requiring the writing of the appropriate material balances every time. This work addresses both issues simultaneously by introducing a general matrix formalism that enables conversion between any combination of IUPAC-recognized composition units through the resolution of a simple linear system. The framework can also be used in the reverse direction to convert mole fractions back into any other desired unit of composition. Recursion (i.e., mixtures of mixtures) and the decomposition of complexes into individual molecules or ions are handled consistently. A Python library to perform these calculations is available at https://github.com/TheophileGaudin/chemcalc-lib and can be added to a Python environment with pip install chemcalc_lib .