Use of the Laplace transform technique for simple kinetic parameters evaluation. Application to the adsorption of a protein on porous beads

The kinetics of the adsorption of human serum albumin (HSA) onto spherical resin beads (Blue Sepharose CL-6B) in a closed stirred tank have been investigated. The differential equation with appropriate boundary conditions at the grain outer surface may be solved numerically or to various degrees of approxn. Using the Laplace transform technique to solve the equation of interest, we are able to obtain the exact soln. to the problem, in the Laplace domain. We assume that equil. is described by a linear absorption isotherm and that the adsorption rate is very rapid compared to diffusion in the adsorbent particles. A functional description of the exptl. data in the time domain allows us to computer the corresponding Laplace transform and fit it to the exact soln., to obtain the film mass transfer coeff., kf, and the effective diffusion coeff., De. The main advantage of this Laplace transform technique is that time-consuming numerical approaches are not needed. The two parameters are rapidly and easily found via two algebraic fits, one in the time domain followed by another in the Laplace domain. Using the parameters thus obtained, a numerical soln. of the problem is in good agreement with the exptl. data

The second law: statement and applications

The second law of thermodynamics is often expressed as the fact that the entropy of an isolated system increases when a spontaneous change takes place. While this statement is true, a more general formulation can easily be presented to students. Starting from the Kelvin formulation of the second law, one can show that the entropy of a closed adiabatic system increases when an irreversible (spontaneous) process occurs. As a consequence, equilibrium is reached when the entropy of such a system has reached its maximum possible value given the constraints applied to the system. Information on the evolution of systems on which work can be done can be obtained even when temperature and pressure are ill-defined in the system during the process. An isolated system represents only a special case of a closed adiabatic system where no work is done on the system. We use this formulation of the second law to derive the significance of the Gibbs energy and show how it can be used to find the state of equilibrium of monobaric monothermal systems. We then provide one application of this formulation to show that the equilibrium state of a closed adiabatic system corresponds to maximum entropy. Additional examples and applications are provided in the supplemental material

Introductory Thermodynamics

The fundamental aspects of classical thermodynamics are presented in a simple compact way. The equations derived are illustrated by numerous (111) examples, often direct application of the relations just obtained. The (four) laws of thermodynamics are presented and illustrated. The need to define thermodynamic temperature, the meaning of auxiliary thermodynamic functions, the origin, usefulness and use of partial molar quantities are all examined. Gaseous systems, phase equilibriua and chemical reactions are quantitatively treated. It is shown how chemical reactions can provide work. Ideal and non ideal solutions are presented with the various standard states and activity coefficients. This book will be if use to a wide audience of students and professionals in the fields of Chemistry, Chemical Engineering, Materials Science and bio related sciences. "Dr. Infelta has prepared a compact Introductory Thermodynamics book which will serve well for mature students who need a command of this important field. Undergraduate students with confidence in their mathematical background will find the presentation logical, the examples thoughtful, and the coverage thorough. Students and professionals for whom memory or mastery of previous thermodynamics courses have dimmed, will find, in addition to the above virtues, careful derivation of the properties of non-ideal systems and emphasis on when to use these results instead of ideal system results, treatment of multireaction equilibria, and (a personal favorite) a succinct elucidation of that odd proposition of thermodynamics, Le Chatelier's Principle. These students will value this small volume packed with the power of classical thermodynamics." Lynn Melton, Professor of Chemistry, University of Texas, Dallas