Showing papers on "Mass action law published in 2011"

Stochastic thermodynamics of single enzymes and molecular motors

Abstract: For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept of internal energy, intrinsic entropy and free energy for states follows from a microscopic description using one assumption on time scale separation. A first-law energy balance then allows the unique identification of the heat dissipated in one transition. Consistency with the second law on the ensemble level enforces both stochastic entropy as third contribution to the entropy change involved in one transition and the local detailed balance condition for the ratio between forward and backward rates for any transition. These results follow without assuming weak coupling between the enzyme and the solutes, ideal solution behavior or mass action law kinetics. The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.

Mass Transfer Mechanism of Ion Exchange in Fixed Bed Columns

Abstract: In this work, the binary ion exchange of Zn2+−Na+ ions has been studied by a column technique using a NaY zeolite as the cation exchanger. The experimental data (breakthrough curves) for the binary system were obtained at total concentrations of (1, 2, and 3) meq·L−1. The mass action law was used to represent the ion exchange equilibrium. To represent the ion exchange in the column, two models were used. In the first model, the rate-controlling step of mass transfer was considered only in the solid phase. The experimental results were represented by a Linear Driving Force (LDF) model. In the second model, resistance to mass transfer in series in the solid phase and the external liquid film was considered. Both models described ion exchange in the fixed-bed column properly. However, in the initial part of the breakthrough curve, the dual resistance model fit better.