A new pseudo-component characterization method was developed. It is based on a Gaussian quadrature rule whose weight function is the molar fraction distribution of the complex mixture. Due to its accuracy, this quadrature was shown to be more adequate than the conventional Gaussian quadrature rules to obtain polynomial approximations of any molar fraction distribution function and to calculate any property of the corresponding mixture. A new method was proposed for the solution of continuous thermodynamics flash and mixing operations. It can be applied to continuous or discrete molar fraction distributions and it is adaptive in the sense that the pseudo-component characterization evolves according to the compositional changes. It was shown to be more accurate than the conventional Gaussian quadrature discretization method. Being based on the conservation of the moments of the distributions, it can be called the quadrature method of moments (QMOM) for continuous thermodynamics. (C) 2006 Elsevier Ltd. All rights reserved.