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A Graphical Evaluation of the Favorability of Adsorption Processes by Using Conditional Langmuir Constant Chengjun Sun, Lingzhi Sun, and Xianxiang Sun Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie401571p • Publication Date (Web): 23 Aug 2013 Downloaded from http://pubs.acs.org on September 8, 2013

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Industrial & Engineering Chemistry Research

A Graphical Evaluation of the Favorability of Adsorption Processes by Using Conditional Langmuir Constant Cheng-Jun Sun,1 Ling-Zhi Sun,2* Xian-Xiang Sun3 1

2

College of Materials and Textile Engineering, Jiaxing Univesity, Jiaxing, 314001, China.

Institute of Bioscience and Technology, Yancheng Teachers University,Yancheng, 224051, China

3

School of Petrochemical Engineering, Changzhou University, Changzhou, 213164, China.

No conflict of interest is declared. Keywords: Adsorption; Evaluation methodology; Favorable adsorption; Langmuir constant; Graphical evaluation

______________________ *

Corresponding author. E-mail address: [email protected]. Fax:+86-0519-86330167

ACS Paragon Plus Environment

1


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ABSTRACT:

A graphical method for evaluating the Langmuir favorable adsorption is proposed in this work. The conditional Langmuir constant (KLN), a new parameter related to the Langmuir equilibrium constant (KL), can be used to predict the shapes of Langmuir favorable adsorption isotherms. On the dimensionless Langmuir isotherm diagram, all the Langmuir favorable adsorptions (0 1 when θ > 45°, eq 11b indicates that KLN increases with ρ or θ, when θ increases from 45° to 90o. Therefore, the isotherm shapes in the whole range of the Langmuir favorable adsorptions can be predicted through KLN or ρ. In other words, the Langmuir favorable adsorption can be evaluated by using the conditional Langmuir constant KLN. KLN increases faster than ρ with θ (Table 1 ), which suggests that KLN is more sensitive than ρ to evaluate Langmuir favorable adsorption isotherms in the range of 45°< θ < 90°. Thereafter, the essential and methodology of the KLN method are described to evaluate the Langmuir favorable adsorption.

Table 1.Comparison of △K and △ρ θ

ρ

△ρ

KLN *


N

△KL

11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50°

1.192

0.218 0.540

60°

1.732

0.667 0.885

0.274 60°30’

2.006

0.366 1.251

2.999 78°42’

Page 12 of 35

5.005

6.767 8.018

*The values were calculated according to eq 10 in the cases assuming ce =0.10mM and cm =1.0mM.

3. EVALUATION METHODOLOGY When all the values of RL are in the range of 0< RL < 1, the values of cm and qm N for a given set of Langmuir favorable adsorption isotherms can easily be established with the maximum of ce,mi and of qm i, due to cm ≥ ce,mi and qm N ≥qm i. Through the assessment of cm, KLN1 and KLN2, the Langmuir favorable adsorptions can be divided meticulously into three subgroups: favorable adsorption, very favorable adsorption, highly favorable or pseudo-irreversible adsorption. The above three subgroups are shown with three regions on a dimensionless Langmuir isotherm diagram through two Langmuir isotherms of LA with the critical Langmuir constantsKLN1, and LB with KLN2. The values of KLN1 and KLN2, at the maximum concentration cm, can be calculated by using eqs 12 and 13. A part of the critical Langmuir constants are listed in Table 2.

Table 2. The Critical Values of KLN (KLN1 and KLN2) for the Different Concentration (cm,mM). cm

Subgroup I a)

Subgroup II

Subgroup III b)

0.01

KLN＜166.7

166.7≤KLN≤1250

KLN＞1250

0.02

KLN＜83.3

83.3≤KLN≤625.0

KLN＞625.0


12

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0.03

KLN＜55.6

55.6≤KLN≤416.7

KLN＞416.7

0.05

KLN＜33.3

33.3≤KLN≤250.0

KLN＞250.0

0.08

KLN＜20.8

20.8≤KLN≤156.2

KLN＞156.2

0.10

KLN＜16.67

16.67≤KLN≤125.0

KLN＞125.0

0.20

KLN＜8.33

8.33≤KLN≤62.5

KLN＞62.5

0.30

KLN＜5.56

5.56≤KLN≤41.7

KLN＞41.7

0.40

KLN＜4.17

4.17≤KLN≤31.25

KLN＞31.25

0.50

KLN＜3.33

3.33≤KLN≤25.00

KLN＞25.00

0.60

KLN＜2.78

2.78≤KLN≤20.83

KLN＞20.83

0.80

KLN＜2.08

2.08≤KLN≤15.63

KLN＞15.63

0.90

KLN＜1.85

1.85≤KLN≤13.89

KLN＞13.89

1.00

KLN＜1.67

1.67≤KLN≤12.50

KLN＞12.50

3.00

KLN＜0.56

0.56≤KLN≤4.17

KLN＞4.17

5.00

KLN＜0.33

0.33≤KLN≤2.50

KLN＞2.50

10.0

KLN＜0.167

0.167≤KLN≤1.25

KLN＞1.25

50.0

KLN＜0.033

0.033≤KLN≤0.25

KLN＞0.25

100.0

KLN＜0.017

0.017≤KLN≤0.125

KLN＞0.125

a)

KLN＜KLN1, the values of KLN1 can be calculated with eq 12.

b)

KLN＞KLN2, the values of KLN2 can be calculated with eq 13.

1.0

LB

Region III highly favorable

LA

0.8 Region II very favorable

N

0.6

qe/N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


N1

LA with KL

N2

Region I favorable

0.4

LB with KL

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Figure 4. Three regions on a dimensionless Langmuir adsorption isotherm through the graphical KLN method. cm = 50 mM, KLN1=0.033 L (mmol)-1, KLN2=0.25 L (mmol)-1.

The graphical evaluation for a given Langmuir adsorption isotherm is carried out on a dimensionless Langmuir isotherm diagram to compare two Langmuir isotherms (i.e., lines of demarcation between two zones) curve LA with KLN1and curve LB with KLN2, respectively (Fig.4). The initial linear part of each dimensionless Langmuir adsorption isotherm is used to evaluate the favorability. The evaluating criterion of an adsorption isotherm L (KL1N, ce,mi, qm N) is illustrated as follows: (I) A favorable adsorption subgroup for the isotherm curve with KL1N lies in zone I (i.e., KL1N less than KLN1); (II) A very favorable adsorption subgroup for the isotherm curve with KL1N lies in zone II (i.e., KL1N in the range described by KLN1 < KL1N 1, KLN > 0 and the adsorption isotherm should be convex. If ρ < 1, KLN is less than zero and the adsorption isotherm would be concave, due to cm> 0 and ce > 0. If ρ = 1, KLN is zero and the Langmuir adsorption isotherm would be a straight line with the angle between the line and the concentration axis (θ) of 45°. So the Langmuir constant KLN can also be applied to characterize different types of Langmuir isotherms graphically with the same efficiency as the RL parameter. 1.0 0.8

(a) cm=40mM dem o

dem o

dem o

dem o

dem o

dem o

N2

KL dem o

3

dem o

qe/N

dem o

dem o

dem o

N1

dem o

dem o

dem o

KL

2 dem o

N1

KL = 0.0417

N

0.6

N2

dem o

dem o

dem o

0.4 dem o

dem o

dem o

dem o

0.2 0.0 0.0

KL = 0.3125 dem o

Transformed from L1(0.02,20,25)

2d e m o

Transformed from L (0.2,30,40) dem o dem o 2

3

Transformed from L3(0.4,40,40))

dem o

1

0.2

dem o

1

dem o

0.4

dem o

0.6

0.8

1.0

cm/cm

1.0

N2

KL

(b) cm=20 mM

N1

KL

3

0.8

2

0.6

N1

KL = 0.0833

N

qe/N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


N2

KL = 0.625

0.4 0.2 0.0 0.0

1

transformed from L1(0.02,20,25)

2


3


1

0.2

0.4

0.6

0.8

1.0

ce/cm


17


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Figure 5. Effect of cm on the shape of adsorption isotherms. Three transformed adsorption isotherms with EMAA (NN = 50 mmol﹒g-1) are curve 1 from L1 (0.02, 20, 25.0), curve 2 from L2 (0.2, 30, 40.0) and curve 3 from L3 (0.4, 40, 40.0), respectively. (a) cm = 40mM; (b) cm = 20mM.

The highest equilibrium concentration cm is first selected through the KLN method. If cm is set to be too small e.g. smaller than cm/2, relative flat curves for the adsorption isotherms would be plotted and the classification of the favorability sub-group would be inaccurate. Fig.5 shows the effect of cm on the value of KLN and the shapes of adsorption isotherms. The value of KLN for the isotherm curve 3 is larger than the KLN2 when cm =40 mM (Fig.5a), while it falls between KLN1 and KLN2 when cm =20 mM (Fig.5b). To study the effect of qm

N

on the shapes of Langmuir adsorption isotherms, a general

Langmuir adsorption isotherm L (KLi, cm, qm i) is transformed into two different isotherms, L1 and L2, with different maximum adsorption capacities. Let L1 to be L (KLN1, cm, qm N1), L2 to be L (KLN2, cm, qm N2),

the fractions of adsorption capacities of isotherms are

q N2 qm N 1 = a1 and m = a2 , then qmi qm i

a1 ⋅ qe a ⋅q for L1 and 2 N 2e for L2 at the N1 qm qm

concentration ce, respectively. The following stoichiometric relation would be held: a1 ⋅ qe qe a2 ⋅ qe = = qm N 1 qmi qm N 2 This indicates that qm N does not affect the shape of a Langmuir adsorption isotherm .In other words, the selection of qm N does not affect KLN of the Langmuir isotherms with EMAC (KLN1 = KLN2). According to eqs 11 and 17, it is also confirmed that the magnitude of KLN is independent


18

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on qm N. KLN is also not affected by the selection of a , since qm N does not affect KLN of Langmuir isotherms. The maximum ratio factor (a ) is generally between 1 and 2.

5.2. Application of KLN Method. (1) Propr /Propr-IP Adsorption Systems. The Langmuir adsorption isotherm is an ideal adsorption model, which assumes monolayer adsorption of adsorbate on a homogeneous adsorbent surface with finite identical sites, which are energetically equivalent and the interactions among the adsorbed molecules are negligible. In some real adsorptions reported in literature, the interactions of the molecules are not zero and the adsorbate have an intermolecular attraction to the surface of the adsorbent. Since in most cases these interactions are not strong, the Langmuir isotherms can still be applied in these cases. The experimental sorption data of three Propr-IP adsorbents are analyzed through both Langmuir isotherm model and Freundlich isotherm model. The Langmuir constants (qm i and KL) are determined by using eq 15. KF and nF are determined through the intercepts and the slopes of the plots of log qe versus log ce (eq 16). The results including the regression coefficient (R) are listed in Table 3. Fig.6 shows the Langmuir plots of Propr.HCl adsorption on three Propr-IP adsorbents. The linear fitting result through Langmuir model was better than that through Freundlich model. In addition, the results of 1/ nF < 1 from Freundlich model also indicates that the adsorptions obey the Langmuir isotherm. The good fitting result through the Langmuir model suggested that Propr.HCl-IP forms a monolayer coverage on the adsorbent surfaces. Fig.7 shows the dimensionless Langmuir adsorption isotherms and two critical Langmuir isotherms with

Table 3. Langmuir and Freundlich Constants for the Adsorption of Propr.HCl onto MIPs


19


Adsorbent

Langmuir model

Freundlich model KF

nF

r

qm (mmol.g-1)

KL(L.mmol-1)

MIP(A)

0.0356±0.0066

34.38±2.78

0.9864

0.267

0.119±0.006

1.841±0.037

0.9725

MIP(B)

0.0341±0.0011

21.69±2.19

0.9322

0.366

0.158±0.016

1.369±0.064

0.9316

MIP(C)

0.0284±0.0013

13.57±1.71

0.9530

0.496

0.153±0.013

1.133±0.050

0.9320

a)

r

RL a)

c0 = 0.080mM.

5

MIP(A) MIP(B) MIP(C)

-1

ce/qe(g.L )

4

3

2

1 0.02

0.04

0.06

0.08

ce/mM

Figure 6. Langmuir plots for adsorption of Propr.HCl on three MIP adsorbents.

KLN1 and KLN2. Clearly, three adsorption isotherms (B, C and D) belong to favorable N2

1.0

KL

N1

0.8

KL B

0.6

C

qe/N

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 35

D

0.4 B C D

0.2

Propr/Propr IP (A) Propr/Propr IP (B) Propr/Propr IP (C) N1 KL =20.8 N2

KL =156.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

Figure 7. Favorable evaluation of three Propr.HCl / Propr-MIP adsorption systems by using the KLN method. qm N = 0.05 mmol·g-1, cm = 0.080 mM.


20

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adsorption subgroup. While there is a large variation of RL, e.g. for isotherm B for Propr.HCl/Propr-IP(A) adsorption system, ranging from 0.0072 (c0 = 4mM) to 0.267 (c0= 0.08mM),depend on the magnitude of c0. Obviously, the KLN method is more objective than the RL method, whose result is heavily affected by the initial concentrations.

(2) Application of KLN Method to the Adsorption Systems in Literature. Eleven liquid-solid adsorption systems previously reported in literature are chosen as follows: Direct Blue 2B/activated carbon prepared from sawdust carbon ( DB2B / AC prepared from sawdust ),

27

Acid Red 151/modified cetyldimethylbenzylammonium chloride-hectorite (AR151

/ CDBA-hectorite) and Acid Red 151/cetylpyridinium chloride-hectorite (AR151 /CP-hectorite ),28 MB / activated carbon (PAC2)(pH=11),29 Basic Red (BR22) / palm-fruit bunch,30 MB / magnesium silicate (Florisil )(dp 112),10 Acid Red 73(AR) / treated carbon (600△),31 Acid Red 97/activated carbon (AR97 / AC),32 Pb2+ / Chitosan (dp 428 and pH=4.50),33 2,4,6trichlorophenol/coconut husk-based activated carbon (TCP / coconut husk-based AC) 34 and MB / crushed brick .11 All of them obey Langmuir adsorption isotherm. The Langmuir constants (KL and qmi)) or parameters ( RL and nF ) in Table S1 are from the literature. All adsorption systems in Table 4 except the Pb2+ /Chitosan system, clearly belong to favorable adsorption if separation factor (RL) is the only criterion. The experimental data of the equilibrium isotherm graphs are reproduced and re-analyzed through eq 15. The results including the regression coefficient (R) are listed in Table S1 .The reanalyzed Langmuir constants (qm i and KL) are very close to those reported in literature. The graphical evaluations of Langmuir favorable adsorption for the 11 adsorption systems are showed in Fig.8.Based on the graphical KLN method (Table 4), six Langmuir adsorption systems,


21


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Page 22 of 35

Table 4. Comparison of KLN Method with RL and nF Methods for Favorable Evaluation KLN method

Adsorption System

RL method

nF method

subgroup Evaluation

c0(mg.L-1)RL(inlit.) evaluation

AR151/CDBA-hectorite

III highly favorable

(264.6) 0.005

AR151/CP-hectorite

III highly favorable

(223)

DB2B/AC prepared from sawdust

III

highly favorable

(404)

AR/treated (600△)

III

highly favorable

(248)

carbon

a

a

favorable

0.0071 favorable

a

a

Ref.

nF(inlit.) Evaluation 12.30 9.75

0.03

favorable

5.03

0.083

favorable

nF1:1.90

?

28

favorable

28

favorable

27

31

nF2:5.80 favorable ? a

MB/PAC2 (pH=11)

III

highly favorable

(484)

MB/Florisil (dp112)

III

highly favorable

500

0.021

favorable

2000

0.005

favorable

a

0.007

MB/Crushed brick

II

very favorable

(40)

BR22/palm- fruit bunch

II

very favorable

(152.3) 0.023

favorable

6.43

favorable

11.26

0.0237 favorable

2.83

a

nF1:1.91

favorable

?

favorable

29 10

11 30

nF2:8.17 favorable ? a

AR97/AC

II

very favorable

Pb2+/Chitosan

I

favorable

(0.50mM)(0.368)

husk-

I

favorable

25

Propr.HCl/Propr -IP(A)

I

favorable

0.080(mM)0.267 favorable

1.84

favorable

This work

Propr.HCl/Propr-IP(B)

I

favorable


1.31

favorable

This work

Propr.HCl/Propr-IP(C)

I

favorable


1.13

favorable

This work

TCP/coconut based AC

(30)

0.23

favorable b

0.734

favorable

favorable

2.99 0.58 1.20

favorable c c

? favorable

a

The values of c0 in parenthesis were obtained from the values of RL reported in literature by using eq 1.

b

The estimated value of RL is 0.368 by taking c0 = 0.50 mM.

c

The values of nF ,0.58 and 1.20, were obtained from the values 1/nF =1.721 and 1/nF =0.83,respectively.


32 33 34

22

Page 23 of 35

1.0

B

0.8

A

qe/N

N

0.6 0.4

N1

A

KL = 4.17

B

KL =31.25

1

DB2B/AC system

N2

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(a)

1.0 B

1

0.8

2

A

qe/N

N

0.6 0.4

1 2 A

AR151/CDBA system AR151/CP system N1 KL =8.33

B

KL =62.5

N1

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(b) 1.0

1

B

0.8

A

N

0.6

qe/N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


N1

A

KL =1.85

B

KL =13.89

1

MB/PAC2 system

N2

0.4 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(c)


23


1.0

B A

1

0.8

qe/N

N

0.6 0.4

N1

A

KL =0.42

B

KL =3.13

1

MB/Florisil system

N2

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(d) 1.0 1

B A

0.8

qe/N

N

0.6 0.4 0.2 0.0 0.0

0.2

N1

A

KL =5.56

B

KL =41.7

1

AR/treated carbon system

N2

0.4

0.6

0.8

1.0

ce/cm

(e)

B

1.0

A 0.8

1

0.6

qe/N

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 35

0.4 0.2 0.0 0.0

0.2

1 A

BR22/palm-fruit bunch system N1 KL =8.33

B

KL =62.5

N2

0.4

0.6

0.8

1.0

ce/cm

(f)


24

Page 25 of 35

1.0

B A

0.8

1

qe/N

N

0.6 0.4 0.2 0.0 0.0

0.2

N1

A

KL =16.67

B

KL =125.0

1

AR97/AC system

N2

0.4

0.6

0.8

ce/cm

(g)

1.0

B A

0.8 1

qe/N

N

0.6 0.4

N1

A

KL =55.56

B

KL =416.7

1

MB/crushed brick system

N2

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(h) B

1.0

A

0.8 1

N

0.6

qe/N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4 0.2

KL =1.67 KL =12.5

1

0.0 0.0

0.2

N1

A B

0.4

N2

2+

Pb /Chitosan system (dp428)

0.6

0.8

ce/cm

(i)


25


B

1.0

A

0.8

N

0.6

qe/N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 35

N1

A

KL =8.33

B

KL =62.5

1

TCP/coconut hust -based AC system

N2

0.4 1

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

ce/cm

(j)

Figure 8. Graphical evaluation of KLN method for 11 different adsorption systems. (a). Adsorption isotherm (curve 1) for DB2B / AC from sawdust adsorption system: qmN = 0.700 mmol﹒g-1, cm = 0.40 mM, a = 1.083. (b). Adsorption isotherm: curve 1 (■)(a1 =1.435)for AR151/CDBA-hectorite system; curve 2(●) (a2 =1.742)for AR151/CP-hectorite system . qmN =0.700 mmol﹒g-1,cm=0.20mM. (c). Adsorption isotherm (curve 1) for MB / PAC2 adsorption system: qmN = 3.00 mmol﹒g-1, cm = 1.0 mM, a = 1.367. (d). Adsorption isotherm (curve 1) for MB / Florisil (dp112) adsorption system: qmN = 0.500 mmol﹒g-1, cm = 4.0 mM, a = 1.128. (e). Adsorption isotherm (curve 1) for AR / treated carbon (600△) adsorption system: qmN =0.300 mmol﹒g-1, cm = 0.30mM, a = 1.141. (f). Adsorption isotherm (curve 1) for BR22/palm-fruit bunch system: qmN =0.700 mmol﹒ g1

,cm=0.20mM,a =1.008.


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(g). Adsorption isotherm (curve 1) for AR97 / AC adsorption system: qmN = 0.100 mmol﹒g-1, cm = 0.10 mM, a = 1.326. (h). Adsorption isotherm (curve 1) for MB / crushed brick adsorption system: qmN = 0.400 mmol

﹒g-1, cm = 0.03 mM, a = 1.185. (i). Adsorption isotherm (curve 1) for Pb2+ / chitosan adsorption system: qmN = 0.300 mmol﹒g-1, cm = 1.0mM, a =1.007. (j). Adsorption isotherm (curve 1) for TCP / coconut adsorption system: qmN = 4.000 mmol﹒g-1, cm = 0.20 mM, a = 1.188.

DB2B /AC prepared from sawdust, AR / CDBA-hectorite, AR/CP-hectorite, MB / florisil (dp112), AR / treated carbon (600△) and MB / PAC2, are obviously highly favorable adsorption. Two adsorption systems, TCP on coconut and Pb2+ / Chitosan, belong to favorable adsorption. Three other adsorption systems, MB / crushed brick, BR22 / palm-fruit bunch and AR97 / AC, belong to very favorable adsorption, although RL of Pb2+ / Chitosan adsorption system was not provided in the literature. Obviously, as compared with the RL method, the graphical KLN method has the following advantages: (1) The parameter KLN does not depend on the initial adsorbate concentration (co), while RL does; (2) For the favorable evaluation (0 < RL < 1), there are three subgroups of favorable adsorption in the KLN method to be used to further distinguish the favorability; (3) The graphical KLN method is intuitional because of the application of the dimensionless Langmuir adsorption isotherm diagram.

(3) Comparison of the KLN Method to the nF Method .


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The nF of Propr.HCl /Propr-IPs, AR151/CDBA-hectorite etc .adsorption systems are listed in Table 4. Since the nF of AR/treated carbon (600△) and MB/Florisil (dp112) are not reported in literature, they are obtained by re-analyzing the experimental data on the isotherm graphs. According to the KLN method, six adsorption systems (in Table 4), AR151/CDBA-hectorite, AR151/CP-hectorite, DB2B/AC, AR/treated carbon (600△), MB/PAC2 (pH=11), and MB/Florisil (dp112), belong to the highly favorable. On the other hand, the nF of the following systems, i.e., AR/CDBA-hectorite (12.3), MB/Florisil (dp112) (11.26), are larger than 10.0. If based on the nF method, obviously, these adsorptions cannot be classified as favorable adsorption. Two nF values (1.91, 8.17) of BR22/palm-fruit bunch system are obtained from the equilibrium isotherm graph,30 since the plot of log qe versus log ce shows two slopes in two parts. Two nF values of the AR/treated carbon (600△) isotherm system also are shown in Table 4. In these cases, since the nF method may cause the ambiguity for the favorable evaluation, it is not appropriate to evaluate the adsorption favorability through the nF method. The graphical KLN method can used to evaluate any Langmuir favorable adsorption. Another advantage of the KLN method is intuitional and the parameter KLN has a certain physical meaning. Therefore, the mathematical model of the KLN method for the favorable evaluation is superior to those of the RL method and the nF method.

6. CONCLUSIONS This work proposed a graphical method for evaluating the Langmuir favorable adsorption behavior based on the use of the conditional Langmuir constant (KLN) and the dimensionless Langmuir adsorption isotherm. All the Langmuir favorable adsorptions (i.e. 0< RL

Graphical Evaluation of the Favorability of ... - ACS Publications

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