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. 2022 Nov 17;7(48):43992–43999. doi: 10.1021/acsomega.2c05386

Table 2. Parameters for Pseudo-First-Order and Pseudo-Second-Order As Well As Weber–Morris Modelsa.

dye/substrate   pseudo-first-order modelb
pseudo-second-order modelc
Weber–Morris modeld
qmax, exp (mg g–1) qmax,cal (mg g–1) k1 (min–1) R2 qmax,cal (mg g–1) k2 (g mg–1 min–1) R2 C (mg g–1) kip (mg g–1 min–1/2) R2
EY/calc. fib. 0.3424 0.2467 0.007 0.88 0.3265 0.089 0.95 0.1138 0.0074 0.66
EY/arag. tab. 0.2801 0.3433 0.002 0.49 0.2726 0.3128 0.91 0.1363 0.0051 0.43
BM/calc. fib. 0.0552 0.0269 0.083 0.72 0.05331 1.6211 0.96 0.026 0.001 0.44
BM/arag. tab. 0.0764 0.0532 0.0086 0.92 0.07584 0.5815 0.93 0.024 0.001 0.26
a

The reaction conditions were based on 0.01 mM EY, 0.07 mM BM, and pH 7.2.

b

The pseudo-first-order model is given by ln (qmaxqt) = ln qmaxk1t, where qmax and qt are the amounts of adsorbed dye (EY or BM) at equilibrium and at time t (mg g–1), respectively. k1 is the equilibrium rate constant of pseudo-first-order kinetics (min–1).

c

The pseudo-second-order model is determined by 1/qt = 1/k2qmax2 1/t + 1/qmax, where k2 is the equilibrium rate constant of the pseudo-second-order kinetics (g mg–1 min–1).

d

The Weber–Morris model is expressed by qt = kipt1/2 + C, where kip is the intraparticle diffusion rate constant (mg g–1 min–1/2) and C (mg g–1) is a constant that reflects the thickness of the boundary layer.