Analysis of Kinetic Langmuir Model. Part I: Integrated Kinetic Langmuir Equation (IKL): A New Complete Analytical Solution of the Langmuir Rate Equation

Abstract

In the article, a new integrated kinetic Langmuir equation (IKL) is derived. The IKL equation is a simple and easy to analyze but complete analytical solution of the kinetic Langmuir model. The IKL is compared with the nth-order, mixed 1,2-order, and multiexponential kinetic equations. The impact of both equilibrium coverage θ(eq) and relative equilibrium uptake u(eq) on kinetics is explained. A newly introduced Langmuir batch equilibrium factor f(eq) that is the product of both parameters θ(eq)u(eq) is used to determine the general kinetic behavior. The analysis of the IKL equation allows us to understand fully the Langmuir kinetics and explains its relation with respect to the empirical pseudo-first-order (PFO, i.e., Lagergren), pseudo-second-order (PSO), and mixed 1,2-order kinetic equations, and it shows the conditions of their possible application based on the Langmuir model. The dependence of the initial adsorption rate on the system properties is analyzed and compared to the earlier published approximate equations.

Direct measurement of the adsorption kinetics of 2-Mercaptobenzothiazole on a microcrystalline copper surface

“…However, the time dependence of this frequency response is the result of the formation of an adsorbed monolayer, therefore the time domain measurements are sensitive to adsorption kinetics of the monolayer and thus, surface coverage information can be extracted from frequency response over time data (Karpovich and Blanchard, 1994). The obtained frequency shift data were fitted to the Langmuir isotherm (Langmuir, 1918;Karpovich and Blanchard,1994;Subramanian and Lakshminarayanan, 2000;Marczewski, 2010;Haerifar and Azizian, 2013):…”

Development of the Wade equation for the description of elution peak profile by using second-order rate equations for the sorption kinetics

“…(9) has been often referred to as the Langmuir kinetics (Kuan et al, 2000;Liu and Shen, 2008;Marczewski, 2010). This equation regards the adsorption as the reversible process between the solute (A) and binding site (L) on the adsorbent surface,…”

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

“…Generalization of the method used in (Marczewski 2010b) may be used to obtain solution for desorption conditions with initial zero concentration as well as a general solution for all possible initial (''o'') and equilibrium (''eq'') adsorption and desorption conditions. In this method coverage, h, and concentration, c, are made dependent on the adsorption progress variable, F, varying from 0 (at t = 0) to 1 (at equilibrium, t ?…”

“…(1) is essentially second order polynomial with respect to coverage or concentration (4) or adsorption progress (3) (Marczewski 2010b). However, by definition the rate becomes zero at equilibrium, i.e.…”

“…(5) was formulated in the way assuring compatibility with IKL (Marczewski 2010b). After integration (for f L \1) and by using initial conditions (t = 0, F = 0) we obtain equation which has the same form as the IKL obtained for adsorption on pure surfaces (h o ¼ 0):…”