Adsorption Kinetics Study Pseudo First Order Model

Published Date: 02 Nov 2017

Pseudo 1st order equation was applied to the experimental data obtained at a varying dosages of 10−40 g/L and for a fixed initial dye concentration of 50 mg/L and pH 2. The plots for BSD, SHBSD and SABSD are given in Figures 4.19 A−C.

Figure 4. A: Pseudo 1st order modelling for effect of adsorbent dosage−BSD

Figure 4.19 B: Pseudo 1st order modelling for effect of adsorbent dosage−SHBSD

Figure 4.19 C: Pseudo 1st order modelling for effect of adsorbent dosage−SABSD

First order kinetic modelling was also applied to experimental data obtained when the initial dye concentrations were varied at a fixed adsorbent dosage of 30 mg/L and pH 2. The calculated and experimental uptakes together with their respective regression coefficient and rate constant values are given in Table 4.8. The pseudo 1st order plot resulted ina linear plots with a regression coefficient of 0.758−0.983 for BSD, 0.813—0.984 for SHBSD and 0.774−0.984 for SABSD. Very high error percentages were obtained for all three adsorbents. This was mostly due to the underestimation of qe values. The pseudo 1st order kinetic model predicted a significantly lower qe value than the experimental qe, indicating the very poor applicability of this model. The adsorption of RB 221 moelcules onto sepiolite (Alkan et al., 2007) and kaolinte (Karaoğlu et al., 2010) also showed a non conformance to the pseudo 1st order model.

Condition varied

BSD

SHBSD

SABSD

ARE%

ARS %

ARE%

ARS %

ARE%

ARS %

Dosage, g/L

10

49.742

54.287

1.766

9.043

33.633

36.697

20

12.554

20.384

67.656

72.361

71.709

76.717

30

48.606

52.836

28.378

32.243

33.646

37.344

40

48.683

52.656

18.872

22.327

63.906

68.648

Conc, mg/L

25

28.617

31.672

50.672

55.136

56.680

60.948

50

48.606

52.836

28.312

32.180

33.646

37.344

75

16.284

22.338

7.082

9.856

37.085

43.371

100

23.659

27.760

33.824

37.516

19.387

21.437

Table 4.7: Pseudo 1st order error functions at various conditions for BSD, SHBSD and SABSD

Table 4.8: Pseudo 1st order constants at varied conditions for BSD, SHBSD and SABSD

Condition varied

BSD

SHBSD

SABSD

Qe (mg/g)

Qec,

mg/g

K1

R2

Qe (mg/g)

Qec

(mg/g)

K1

R2

Qe (mg/g)

Qec

(mg/g)

K1

R2

Dosage, g/L

10

2.619

1.548

0.0276

0.880

3.541

3.656

0.0576

0.973

3.624

2.574

0.0435

0.984

20

1.488

1.363

0.0364

0.758

1.979

1.208

0.0484

0.963

2.125

1.382

0.0345

0.946

30

1.103

0.644

0.0341

0.945

1.364

1.036

0.0474

0.870

1.484

1.061

0.0435

0.774

40

0.842

0.468

0.0497

0.932

1.107

0.932

0.0560

0.883

1.140

0.464

0.0415

0.856

Conc, mg/L

25

0.582

0.439

0.0493

0.983

0.716

0.402

0.0341

0.813

0.772

0.368

0.0465

0.947

50

1.103

0.644

0.0341

0.945

1.364

1.037

0.0474

0.870

1.484

1.061

0.0435

0.774

75

1.506

1.301

0.0410

0.892

2.025

1.908

0.0578

0.984

2.196

1.421

0.0371

0.958

100

1.682

1.362

0.0426

0.943

2.623

3.464

0.0583

0.858

2.733

2.272

0.0601

0.972

Pseudo Second Order Model

Since pseudo 1st order kinetic model fails to represent the adsorption of RB 221 onto the adsorbents, the pseudo second order kinetic model was applied to the experimental data in order to assess its suitability in defining the rate of adsorption of the system. The Pseudo 2nd order model plots for BSD, SHBSD and SABSD are shown in Figures 4.20 A−C for different adsorbent doses tested.

Figure 4.20 A: Pseudo 2nd order modelling for effect of adsorbent dosage−BSD

Figure 4.20 B: Pseudo 2nd order modelling for effect of adsorbent dosage−SHBSD

Figure 4.20 C: Pseudo 2nd order modelling for effect of adsorbent dosage−SABSD

The graphs for BSD, SHBSD and SABSD showed that the experimental data followed the linear relationship of pseudo 2nd order adsorption model very well. High regressions coefficients of R2 >0.99 were observed for all 3 adsorbents. Pseudo 2nd order kinetic models were also developed for adsorption data obtained when initial dye concentrations were studied and results are summarised in Table 4.9. It may be clearly observed that the calculated qe agreed very well with the experimental qe values. Consequently, the 2nd order model produced data analysis having very low percentage error compared to 1st order model. The low ARE % and ARS % values, as well as higher R2 values obtained for all 3 adsorbents are given in Table 4.10. Therefore, it can be inferred that the sorption of RB 221 molecules onto BSD, SHPBD and SABSD followed the 2nd order kinetic model more accurately. Similar preferences to the second order kinetic models were obtained by Eren and Acar (2006), Alkan et al. (2007) and Karaoglu et al. (2010).

The adsorption rate constant K2 showed a general increase as adsorbent dosage increased from 10 g/L to 40 g/L and a general decrease as the initial dye concentration increased from 25 mg/L to 100 mg/L. A similar trend was observed by Özacar and Senğil (2005), whereby K2 values decreased as the concentration of anionic metal complex dyes increased and increased as the adsorbent dose of pine sawdust increased.

Condition varied

BSD

SHBSD

SABSD

Qe

(mg/g)

Qec,

(mg/g)

K2,

(g/mg.min)

h,

(g/mg.min)

Qe, (mg/g)

Qec

(mg/g)

K2

(g/mg.min)

h

(g/mg.min)

Qe (mg/g)

Qec

(mg/g)

K2

(g/mg.min)

h

(g/mg.min)

Dosage( g/L)

10

2.619

2.643

0.0662

0.462

3.541

3.683

0.0523

0.709

3.624

3.751

0.0536

0.754

20

1.488

1.524

0.0800

0.186

1.979

2.015

0.1740

0.706

2.125

2.176

0.0870

0.412

30

1.103

1.124

0.195

0.246

1.364

1.391

0.177

0.342

1.484

1.503

0.176

0.398

40

0.842

0.854

0.495

0.361

1.107

1.134

0.230

0.296

1.140

1.147

0.478

0.629

Conc. (mg/L)

25

0.582

0.598

0.414

0.148

0.716

0.721

0.357

0.186

0.772

0.783

0.581

0.356

50

1.103

1.124

0.195

0.246

1.364

1.391

0.177

0.342

1.484

1.503

0.176

0.398

75

1.506

1.552

0.100

0.241

2.025

2.100

0.104

0.459

2.196

2.250

0.091

0.461

100

1.682

1.738

0.100

0.302

2.623

2.734

0.056

0.419

2.733

2.815

0.100

0.792

Table 4.9 Pseudo 2nd order constants at varied conditions for BSD, SHBSD and SABSD

Table 4.10: Pseudo 2nd order error functions at varied conditions for BSD, SHBSD and SABSD

Condition varied

BSD

SHBSD

SABSD

R2

ARE%

ARS %

R2

ARE%

ARS %

R2

ARE%

ARS %

Dosage, g/L

10

0.993

1.797

4.932

0.996

2.407

5.523

0.997

2.747

6.007

20

0.983

1.924

7.708

0.999

1.491

2.806

0.996

2.364

4.355

30

0.997

1.753

3.570

0.996

1.155

3.978

0.997

1.557

3.170

40

0.999

0.815

2.728

0.997

1.439

3.703

0.999

0.837

1.542

Conc, mg/L

25

0.998

2.027

3.873

0.996

1.021

3.393

0.999

1.307

2.690

50

0.997

1.753

3.570

0.996

1.155

3.978

0.997

1.557

3.170

75

0.992

2.211

5.636

0.997

2.699

6.004

0.996

2.275

4.118

100

0.994

1.882

5.787

0.993

2.671

5.217

0.998

2.360

5.649

Intra−Particle Diffusion model

Experimental data obtained when different initial dye concentration was varied at a fixed dosage of 30 g/L, were applied to intra−particle diffusion models. The models for BSD, SHBSD and SABSD are represented in Figures 4.21 A−C. The resulting trends gave an insight on the type of diffusion mechanism involved in the sorption process of RB 221 molecules onto the adsorbents.

The plots of all 3 adsorbents showed similar trends. They were non-linear over the whole time range, but could be divided into 3 distinct linear portions. The adsorption of RB 221 molecules onto sepiolite (Alkan et al., 2007), the adsorption of congo red onto acid treated pine powder (Dawood and Sen, 2012), adsorption of brilliant red onto chemically modified sugarcane bagasse lignin (Da Silva et al., 2011) and adsorption of direct brown onto beech wood (Dulman and Cucu−Man, 2009) also yielded such multi−linear plots. In agreement with the latter studies, the multi−linearity observed for the present intra-particle modelling indicated that intra−particle diffusion may not be the only rate controlling mechanism. Actually, the mechanisms involved in the adsorption of RB 221 molecules on the adsorbents may be explained by the 3 linear portions identified onto the plots. The first mechanism may be depicted by the initial sharper portion observed in Figure 4.21. Mane and Babu (2011) related this sharp portion to the boundary layer diffusion of solute molecules on the external surface of adsorbent. Dulman and Cucu−Man (2009) denoted this mechanism as being instantaneous. Dawood and Sen (2012) associated the second less sharp portion with intra−particle diffusion. This corresponded to the second mechanism. In principle, intra−particle diffusion is generally slow as it involves the penetration of dye molecules from the surface of the adsorbent into the internal pores. This would eventually account into a slower uptake of dye molecule and explain the gradual decline of gradient. Mane and Babu (2011) reported that if the boundary diffusion and intra−particle diffusion were independent of each other; their corresponding lines will intercept each other. This could be observed for the present results in Figure 4.21. It can be concluded that these two mechanisms took place separately. Alkan et al.(2007) attributed the final ending plateau observed to the equilibrium stage. Equilibrium was reached due to the increasing occupancy of pores by RB 221 molecules and the concomitant decreasing RB 221 concentration.

3rd Linear Portion

2nd Linear Portion

1st Linear Portion

Figure 4.21 A: Intra−particle modelling for effect of initial dye concentration−BSD

1st Linear Portion

2nd Linear Portion

3rd Linear Portion

Figure 4.21 B: Intra−particle modelling for effect of initial dye concentration−SHBSD

3rd Linear Portion

2nd Linear Portion

1st Linear Portion

Figure 4.21 C: Intra−particle modelling for effect of initial dye concentration−SABSD