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On the applicability of the pseudo-second order equation to represent the kinetics of adsorption at solid/solution interfaces: a theoretical analysis based on the statistical rate theory

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Abstract

It is shown that the empirical pseudo-second order kinetic equation is a very efficient formula to correlate the kinetic data generated by applying theoretical expressions developed from the fundamental SRT (Statistical Rate Theory) approach to the interfacial transport. This is especially true when the most popular linear representation is used in which time/adsorbed amount is plotted vs. time. However, the commonly observed goodness of such linear plots does not necessarily speak for the applicability of the pseudo-second order kinetic equation. A reliable estimation, for instance, of the equilibrium adsorbed amount is possible only when a substantial part of a kinetic isotherms corresponds to the conditions close to equilibrium. Energetic surface heterogeneity increases the goodness of these linear regressions. Then, experimental errors have only little effect on the pseudo-second linear plots.

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Abbreviations

c :

Actual (time-dependent) sorbate concentration in the bulk phase

c in :

Initial sorbate concentration in the bulk phase

c e :

Equilibrium sorbate concentration in the bulk phase

f, f min  :

Coefficients defined in (16) and (21), respectively

k 2 :

Pseudo-second order constant

K L :

The Langmuir constant

K ls ′:

Rate of exchange at equilibrium in the SRT equation

N m :

Monolayer capacity

t :

Time

V :

Volume of the bulk solution

α,γ :

Heterogeneity parameters

ε :

Energy of adsorption

ε m , ε l :

The lowest (l) and the maximum (m) values of the adsorption energy

λ :

Coefficient defined in (7)

μ b , μ s :

Chemical potentials of the sorbate in the bulk (b) and the adsorbed (s) phases

θ, θ(t), θ(τ):

Time-dependent surface coverage

θ e :

Surface coverage at equilibrium

τ :

Dimensionless time defined in (7)

\(\tau_{f},\tau_{f_{\min}}\) :

Characteristic values of dimensionless time defined in (16) and (21)

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Authors and Affiliations

  1. Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239, Cracow, Poland

    Władysław Rudzinski

  2. Department of Theoretical Chemistry, Faculty of Chemistry, UMCS, pl. M. Curie-Sklodowskiej 3, 20-031, Lublin, Poland

    Władysław Rudzinski & Wojciech Plazinski

Authors
  1. Władysław Rudzinski
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  2. Wojciech Plazinski
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Correspondence to Władysław Rudzinski.

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This article is dedicated to Professor Mietek Jaroniec on the occasion of his 60th birthday.

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Rudzinski, W., Plazinski, W. On the applicability of the pseudo-second order equation to represent the kinetics of adsorption at solid/solution interfaces: a theoretical analysis based on the statistical rate theory. Adsorption 15, 181–192 (2009). https://doi.org/10.1007/s10450-009-9167-8

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