A model is developed that simulates exchange of one hydrogen isotope with another hydrogen isotope in a spherical metal hydride particle. This is one of the fundamental physical processes operative during isotope exchange in a bed of spherical metal particles and is thus one of the key components in any comprehensive physics-based model of exchange. A critical aspect that must be considered is that the diffusion of one isotope depends not only on its own concentration gradient, but also on the concentration gradient of the other isotope. This coupling arises because the chemical potential of each isotope depends on the concentrations of all isotopes as well as the presence of vacancies within the metal hydride. This thermodynamic coupling is derived from the Gibbs free energy of mixing and the excess chemical potential due to elastic and electronic interactions. Unknown diffusion coefficients appearing in this formulation of isotope transport are determined by fitting to available experimental data. Example calculations illustrate times required for isotope exchange and the asymmetries observed between forward and reverse exchanges due to differences in isotope stoichiometry and diffusivity. Published by Elsevier Ltd.