Modelling equilibrium constants_of_multiple_components_in_non-ammoniacal_resin-solution_systems_(abrar_muslim)

1. International Review of
Chemical Engineering
Rapid Communications
(IRECHE)
Contents:
A Very Fast Removal of Orange G from its Aqueous Solutions by Adsorption on Activated Saw Dust:
Kinetic Modeling and Effect of Various Parameters
by Jiwan Singh, Uma, Sushmita Banerjee, Yogesh Chandra Sharma
1
The Process of Non-Dimensionalization Using the Discriminated Dimensional Analysis
by Madrid C. N., Alhama F.
8
Fluidization of Ultrafine Powders
by Jaber Shabanian, Rouzbeh Jafari, Jamal Chaouki
16
Analysis of Liquid Flow in Resin Transfer Molding Using Progressive Injection Strategy
by Chih-Yuan Chang
51
Enhanced Naphthalene Solubilization Using Two Yeast Biosurfactants
by Juliana M. Luna, Raquel D. Rufino, Leonie A. Sarubbo
59
Modeling Equilibrium Constants of Multiple Components in Non-Ammoniacal
Resin-Solution Systems
by Abrar Muslim
65
Evaluation of the Catalytic Potential of the TiO2 Nanomaterials for the Abatement of H2S Gas
at High Temperatures
by N. Shahzad, S. T. Hussain, T. Maggos, M. A. Baig
71
A Comparison between Iron and Aluminum Electrodes on Removal of Chromium
from Wastewater of Electroplating Industry by Electrocoagulation
by Maha I. Al-Ali
76
(continued on outside back cover)
ISSN 2035-1755
Vol. 4 N. 1
January 2012
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved

2. International Review of Chemical Engineering
Rapid Communications
(IRECHE)
Editor-in-Chief:
Prof. Jordan Hristov
Department of Chemical Engineering
University of Chemical Technology and Metallurgy
“KLIMENT OHRIDSKY”, Blvd.
1756 Sofia, 8 – BULGARIA
Managing Editor: Prof. Santolo Meo, FEDERICO II University - 21, Claudio – I80125, Naples – Italy.
Editorial Board:
Abbasov Teymuraz (Turkey) Larachi Faical (Canada)
Al Hayk Yousef (U.S.A.) Levec Janez (Slovenia)
Assael Marc J. (Greece) Luo Lingai (France)
Bennacer Rachid (France) Marengo Marco (Italy)
Coppens Marc-Olivier (U.S.A.) Margulis Raul Bautista (Mexico)
Delichatsios Michael (U.K.) Oron Alexander (Israel)
Denizli Adil (Turkey) Perez Victor Haber (Brazil)
Di Felice Renzo (Italy) Pirozzi Domenico (Italy)
Esfahani Javad A. (Iran) Poletto Massimo (Italy)
Farid Mohammed (New Zealand) Ravi Kumar (India)
Fernandez –Lahore M. (Germany) Saghir Ziad (Canada)
Gonthier Yves (France) Serbezov Atanas (U.S.A.)
Gourich Bouchaib (Morocco) Sharma Yogesh Chandra (India)
Gros Fabrice (France) Sharypov Oleg Vladimirovich (Russia)
Guo Qingjie (China) Tosun Ismail (Turkey)
Hamdy Abdel Salam (Egypt) Valverde Millan Jose-Manuel (Spain)
Ivanova Viara (Bulgaria) Zhu Qingshan (China)
Kosoy Boris (Ukraine) Zhu Jesse (Canada)
Krishnaiah Kamatam (India) Zimparovv Ventsislav (Bulgaria)
Kulish Vladimir (Singapore)
The International Review on Chemical Engineering (IRECHE) is a publication of the Praise Worthy Prize S.r.l..
The Review is published bimonthly, appearing on the last day of January, March, May, July, September, November.
Published and Printed in Italy by Praise Worthy Prize S.r.l., Naples, January 31, 2012.
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved.
This journal and the individual contributions contained in it are protected under copyright by Praise Worthy Prize
S.r.l. and the following terms and conditions apply to their use:
Single photocopies of single articles may be made for personal use as allowed by national copyright laws.
Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or
systematic copying, copying for advertising or promotional purposes, resale and all forms of document delivery.
Permission may be sought directly from Praise Worthy Prize S.r.l. at the e-mail address:
administration@praiseworthyprize.com
Permission of the Publisher is required to store or use electronically any material contained in this journal, including any
article or part of an article. Except as outlined above, no part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,
without prior written permission of the Publisher. E-mail address permission request:
administration@praiseworthyprize.com
Responsibility for the contents rests upon the authors and not upon the Praise Worthy Prize S.r.l..
Statement and opinions expressed in the articles and communications are those of the individual contributors and not the
statements and opinions of Praise Worthy Prize S.r.l.. Praise Worthy Prize S.r.l. assumes no responsibility or
liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or
ideas contained herein.
Praise Worthy Prize S.r.l. expressly disclaims any implied warranties of merchantability or fitness for a particular
purpose. If expert assistance is required, the service of a competent professional person should be sought.

3. International Review of Chemical Engineering (I.RE.CH.E.), Vol. 4, N. 1
ISSN 2035-1755 January 2012
Manuscript received and revised December 2011, accepted January 2012 Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved
65
Modeling Equilibrium Constants of Multiple Components
in Non-Ammoniacal Resin-Solution Systems
Abrar Muslim
Abstract – Since thiosulfate leaching has been applied as an alternative leaching to
cyanidation in gold extraction, the adsorbent of strong based anion exchange resin has been
investigated for the adsorption of thiosulfate, polythionates and gold thiosulfate. Anion exchange
resin simultaneously adsorbs thiosulfate, polythionates and gold thiosulfate, and each component
competes one another in multiple components of non-ammoniacal resin solution systems. The
aim of this work is to develop equilibrium constant models for multiple components in the
systems. Experimental work were conducted to obtain equilibrium constants associated with the
complex reaction in the systems, and compared the values to the ones based on the proposed
model. As the modeling results, the equilibrium constant for trithionate over thiosulfate and
tetrathionate over trithionate was computed to be approximately 90.739 and 1.482, respectively
which was in a good agreement with the experimental result. The model-based equilibrium
constant for gold thiosulfate over trithionate was obtained to be 0.469 with the correlation
coefficient, R2
being 0.9874. In addition, this work also proposed a model reaction mechanism to
obtain the equilibrium constant for gold thiosulfate over tetrathionate with the model-based
equilibrium constant being approximately 0.317. Copyright © 2012 Praise Worthy Prize S.r.l. -
All rights reserved.
Keywords: Adsorption, Equilibrium Constants, Gold Thiosulfate, Polythionates, Modeling,
Resin
I. Introduction
Thiosulfate have been investigated to be one of the
most promising reagents to replace cyanide in the gold
extraction [1]-[2]. In one hand, the use of ammonium
thiosulfate and oxygen under pressure to recover gold
was proposed to improve the leaching of gold [3].
However, other studies concluded that the use of
excessive oxygen increases the oxidative degradation of
thiosulfate [4]-[5]. In the system of ammonium
thiosulfate solutions using anion exchange resin,
tetrathionate, as the product of thiosulfate oxidation,
strongly poisoned the resin in the recovery of gold and
copper [6]. The presence of polythionates affects the
gold recovery using ion exchange resin [7]. On the other
hand, polythionates concentration affects gold adsorbed
on resin in non-ammoniacal resin-solution (NARS)
systems [8]. Degradation of thiosulfate to be
tetrathionate might not occur in the NARS system;
which is contradictory with the thiosulfate degradation
in previous studies [7]-[9]-[10].
Interestingly, kinetics and equilibrium isotherm
adsorption of polythionate and gold thiosulfate in the
NARS system was investigated via experimental work
and modeling.
Dynamic model with the kinetics and capacity
constants for the NARS single component adsorption
was proposed in the study [11].
Because anion exchange resin simultaneously adsorbs
thiosulfate, polythionates and gold thiosulfate with the
charges on the resin’s functional groups with the
opposite charge.
Due to the limited number of charge on resin presented
on the theoretical ion exchange capacity of resin, and
thiosulfate, polythionates and gold thiosulfate competes
one another, modeling equilibrium adsorption would be
a critical aspect to investigate.
Therefore, this work focuses on developing equilibrium
constant model for multiple components in the NARS
systems.
II. Method
Modeling Work
The adsorption of thiosulfate, polythionates and gold
on ion exchange resin in non-ammoniacal resin-solution
(NARS) systems is a heterogeneous process.
The ion exchange mechanism of component from
solution to resin can be expressed as:

4. A. Muslim
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Chemical Engineering, Vol. 4, N. 1
66
   
1 1
1
2 2
2 3 2 3
2 3 2 3
t,k K
Int
t,k
Int
S O S O
R S O R S O
 


       
  
(1)
   
2 2
2
2 2
3 6 3 6
3 6 3 6
t,k K
Int
t,k
Int
S O S O
R S O R S O
 


       
  
(2)
   
3 3
3
2 2
4 6 4 6
4 6 4 6
t,k K
Int
t,k
Int
S O S O
R S O R S O
 


       
  
(3)
   
4 4
4
2 2
5 6 5 6
5 6 5 6
t,k K
Int
t,k
Int
S O S O
R S O R S O
 


       
  
(4)
   
   
5 5
5
3 3
2 3 2 32 2
2 3 2 32 2
t,k K
Int
t,k
Int
Au S O Au S O
R Au S O R Au S O
 


    
   
        
(5)
where Int refers to the initial condition t = 0 s; ∞
represents the equilibrium stage; 1K , 2K , 3K , 4K , and
5K are the equilibrium constant of each component on
resin and in solution for Equations (1), (2), (3), (4), and
(5) respectively; t (s) is time needed to reach the
equilibrium stage; 1k , 2k , 3k , 4k , and 5k are the
kinetics constant of component on resin and in solution
for Equations (1), (2), (3), (4), and (5) respectively; [...]
(M) is the concentration of thiosulfate ( 2
2 3S O 
),
trithionate ( 2
3 6S O 
), tetrathionate ( 2
4 6S O 
),
pentathionate ( 2
4 6S O 
) and gold thiosulfate
(  
3
2 3 2
Au S O

); and [R-...] (M) denotes the
concentration of the component on resin where R
represents the resin backbone and functional group with
the chloride electron as the exchange centre of the resin.
The complex reactions in the multiple components
NARS systems are expressed as Equations (6) to (10):
R2S2O3(s) + S3O6
2−
(aq) <=> R2S3O6(s) + S2O3
2−
(aq) (6)
R2S3O6(s) + S4O6
2−
(aq) <=> R2S4O6(s) + S3O6
2−
(aq) (7)
R2S4O6(s) + S5O6
2−
(aq) <=> R2S5O6(s) + S4O6
2−
(aq) (8)
R2S5O6(s) + S6O6
2−
(aq) <=> R2S6O6(s) + S5O6
2−
(aq) (9)
3R2SxOy(s) + 2Au(S2O3)2
3-
(aq) <=>2R3Au(S2O3)2 (s) +
+3SxOy
2−
(aq)
(10)
where x and y refer to the number of S and O atoms
related to the each component. Because trithionate is
strongly adsorbed on resin compared to other
components, and it can be used as the baseline in the
system [8], hence Equation (10) can be written as:
3R2S3O6(s) + 2Au(S2O3)2
3-
(aq) <=>
2R3Au(S2O3)2 (s) + 3S3O6
2−
(aq)
(11)
Due to the competitive adsorption of multiple
components in the NARS systems, the equilibrium
constants in Equations (1) to (5) can be re-arranged to
be Equations (12) to (15). Term K2,1 represents the
equilibrium constant for trithionate adsorbed over
thiosulfate, K3,2 is the equilibrium constant for
tetrathionate adsorbed over trithionate, K4,3 represents
the equilibrium constant for pentathionate adsorbed over
tetrathionate, and K5,2 denotes as the equilibrium
constant for gold thiosulfate adsorbed over trithionate.
The power signs in Equations (12) to (15) is to express
the mole balance in Equations (6) to (11):
    
 
    
 
3 6 3 6
2 2
2 3 2 3
2 1
2 3 2 3
2 2
3 6 3 6
Int
Int
,
Int
Int
R S O R S O
S O S O
K
R S O R S O
S O S O

 


 

    
 
          
    
 
          
(12)
    
 
    
 
4 6 4 6
2 2
3 6 3 6
3 2
3 6 3 6
2 2
4 6 4 6
Int
Int
,
Int
Int
R S O R S O
S O S O
K
R S O R S O
S O S O

 


 

    
 
          
    
 
          
(13)
    
 
    
 
5 6 5 6
2 2
4 6 4 6
4 3
4 6 4 6
2 2
5 6 5 6
Int
Int
,
Int
Int
R S O R S O
S O S O
K
R S O R S O
S O S O

 


 

    
 
          
    
 
          
(14)
 
 
 
    
 
 
3
2 3 2
2 3 2
2
2 2
3 6 3 6
5 2 2
3 6 3 6
3
2
2 3 2
2
2 3 2
Int
Int
,
Int
Int
R Au S O
R Au S O
S O S O
K
R S O R S O
Au S O
Au S O

 





                
 
          
    
 
 
   
           
(15)

5. A. Muslim
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Chemical Engineering, Vol. 4, N. 1
67
The concentration of each component in Equations
(12) to (15) for the component on resin can be measured
via experimental work using the same method of single
component, typically Equation (28) in previous study
[11]. Meanwhile, the concentration of thiosulfate or
polythionate in solution at the time t can be obtained
using Equation (16) where the kinetic constant, k (M/s)
of each component is available in the literature:
 
 
2 2 2
2
x y x y x y
t Int
x y
S O S O S O
exp kt S O
  



            
   
 
(16)
Because the component concentration in solution at
the equilibrium time te, [SxOy
2−
]te is equal to [SxOy
2−
]∞,
consequently, the absolute error (AE) value for the
deviation of initial and equilibrium concentrations is
applied in the modeling method. Equation (16) could be
presented as follows:
 
 
 
2
2
x y
Int
x y
S O exp kte
ABS
AE exp kte
S O
exp kte



      
       
(17)
The same Equations (16) and (17) can be also
derived for the concentration of gold thiosulfate in
solution at the equilibrium time te. The AE (M=gr/L)
value increases with the increase in the initial
concentration following an exponential growth trend
with a magnitude M proposed in previous study [11].
However, terms M is now replaced with terms AEmax
meaning a maximum AE value. The AE value which is a
function of initial concentration of component, can be
modelled as:
 1 IntC / cf
Int maxAE( C ) AE e
  (18)
where CInt (M) is the initial concentration of component;
and cf is a correction factor.
It is needed to incorporate another initial
concentration of component in order to work on the
equilibrium constants in Equations (12)-(15). The AE
value for multiple components in the NARS system is
modelled as follows:
 1 2
1 1 2 1
1
1 2
1 1 2
1 Int ,C
Comp Int , Comp max
Int
Int ,
Int ,
AE (C ) AE e ,
C
C
C cf
 
 
(19)
 2 1
2 2 1 2
2
2 1
1 2 1
1 Int ,C
Comp Int , Comp max
Int
Int ,
Int ,
AE (C ) AE e ,
C
C
C cf
 
 
(20)
where AEComp1 and AEComp2 are the AE values of
component 1 and component 2, respectively; AEComp1max
and AEComp2max are the maximum AE values of
component 1 and component 2, respectively which are
found from the model simulation of experiment data;
CInt1 and CInt2 are the initial concentration of component
1 and component 2, respectively; and cf1,2 and cf2,1 the
correction factors related to Equations (19) and (20),
respectively which are also obtained from the models
simulation of experiment data. Both Equations (19) and
(20) are simultaneously used to predict an equilibrium
constant in Equation (12), (13), (14) or (15). This model
is called as an AEMC (Absolute Error Multiple
Components) model. In obtaining the parameters in
modeling works, Levenberg-Marquardt method [12] was
applied to minimize the sum of weighted deviation
square between the experimental results and model
results.
Experimental Work
To generate a set of equilibrium data for the
equilibrium constants of thiosulfate, polythionates and
gold thiosulfate adsorbed on resin in the multiple
components NARS systems, the same material and
method in previous study [13] were taken into account
for loading and stripping processes with 0.333 gram
resin. The thiosulfate and polythionates samples were
analyzed using HPLC. The initial trithionate
concentration at the range 1-5 mM and the initial
thiosulfate concentration at the range of 1-50 mM were
used to generate a set of equilibrium data for the
equilibrium constant of trithioante over thiosulfate.
Synthetic polythionates mixture was diluted with DI
water to prepare loading solution consisting of about 1.5
mM thiosulfate, 1.3 mM trithionate, 2.5 mM
tetrathionate and 0.9 mM pentathionate with the initial
concentration of gold thiosulfate in the range 0.2-10
mg/L with 0.5 gram resin. Then, the diluted mixture
was used in the experiments to generate a set of
equilibrium data for the equilibrium constant of
tetrathionate and pentathionate reaction on resin in the
multiple components NARS systems. The gold
thiosulfate samples were analyzed using an inductively
coupled plasma-optical emission spectrometer (ICP-
OES).
III. Results and Discussion
Absolute Error (AE) Values
To compute the AEMC model-based AE values, the
kinetic constant k for each component in the multiple
components NARS systems were taken from the
previous study [11] where k for thiosulfate, trithionate,
tetrathionate and gold thiosulfate is approximately
0.0579, 0.0359, 0.0199 and 0.0331 minute-
1,
respectively. The equilibrium time was assumed to be 5

6. A. Muslim
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Chemical Engineering, Vol. 4, N. 1
68
hrs. The AE values of trithionate based on the AEMC
model with the AEComp1mas value of 1.4801 mM and the
cf1,2 value of 0.035 found via the model simulation, are
1.0011, 0.8666, 0.9374, 1.1346, 0.8727, 0.9465, 1.1388,
0.6566, 1.2855, and 1.3976 mM (see Fig. 1) for the
ratio values of [Int. Trithionate]/[Int. Thiosulfate] being
0.0395, 0.0308, 0.0351, 0.0509, 0.0312, 0.0357, 0.0514,
0.0205, 0.0711 and 0.0101 respectively.
Meanwhile, the HPLC-based AE values are about
1.0031, 0.8863, 0.9153, 1.1534, 0.8634, 0.9581, 1.1213,
0.6803, 1.2875 and 1.3897 mM, respectively with the
deviation within these AE values and the first model-
based AE values being varied from 0.1525 to 3.4918%.
The AEMC model-based equilibrium concentrations
of trithionate in loading are 0.9733, 0.6746, 0.8185,
1.4116, 0.6860, 0.8388, 1.4287, 0.3694, 2.2654 and
3.6546 mM, respectively for the same ratio values of
[Int. Trithionate]/[Int. Thiosulfate].
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 0.02 0.04 0.06 0.08 0.1 0.12
[Int.Trithionate]/[Int.Thiosulfate]
AEofTrithionate(mM)
The AEMC-based
The HPLC-based
Fig. 1. The AEMC-based AE values of trithionate versus the ratio of
initial concentrations of trithionate and thiosulfate
Meanwhile, the experiment-based equilibrium
concentrations of trithionate in loading solution are
0.9713, 0.655, 0.8406, 1.3928, 0.6953, 0.8272, 1.4463,
0.3456, 2.2634 and 3.6625 mM, respectively. The
deviation within the model-based and experiment-based
equilibrium concentrations is varied at the range of
0.0867-6.8730%. Fig. 2 shows The AEMC model-based
AE values of trithionate the with the AECopm2mas value of
1.5999 mM and the cf2,1 value of 58.0010 found via the
model simulation, are 0.5660, 0.6854, 0.6207, 0.4595,
0.6796, 0.6127, 0.4563, 0.9094, 0.3449 and 0.2509,
respectively for the same ratio values of [Int.
Trithionate]/[Int. Thiosulfate] in the previous results.
The highest deviation within these AE values and the
HPLC-based AE values is approximately 12.1586%. As
a result of the AEMC model at the pair initial
concentrations of trithionate and tetrathionate in the
loading solutions of being 1.0119 and 1.0119 mM,
2.0565 and 0.9087 mM, 3.0538 and 1.0242 mM, 1.0353
and 2.0563 mM, 2.0563 and 2.0480 mM, 3.0684 and
2.0529 mM, 1.0353 and 3.0938 mM, 2.0597 and 3.0739
mM, and 3.0700 and 3.0834 mM with the AEComp1mas
value of 1.1415 mM and the cf1,2 value of 0.969, the AE
values of trithionate are approximately 0.7348, 1.0311,
1.0889, 0.4626, 0.7365, 0.8974, 0.3334, 0.5691 and
0.7329 mM based on the ratio value of initial
concentration of trithionate and the initial concentration
of tetrathionate as plotted in Fig. 3.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60
[Int.Thiosulfate]/[Int.Trithionate]
AEofThiosulfate(mM)
The AEMC-based
The HPLC-based
Fig. 2. The AEMC-based AE values of thiosulfate versus the ratio of
initial concentrations of thiosulfate and trithionate
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3 3.5
[Int.Trithionate]/[Int.Tetrathionate]
AEofTrithionate(mM)
The AEMC-based
The HPLC-based
Fig. 3. The AEMC model-based AE values of trithionate versus the ratio
of initial concentrations of trithionate and tetrathionate
As shown in Fig. 3, the AEMC model-based results
are also quite close to the HPLC-based ones with the
deviation within the two results at the range of 0.6640 to
5.2620%. Fig. 4 shows the AE values of tetrathionate
based on the AEMC model, the AECopm2mas value of
1.2481 mM and the cf2,1 value of 0.8415. As can be seen
in Fig. 4, the AECM model-based AE values of
tetrathionate is in a consistent trend with the AE values,
and the AE values of tetrathionate are approximately
0.8678, 0.5098, 0.4103, 1.1303, 0.8659, 0.6845, 1.2123,
1.0369 and 0.8698 mM. The deviation within the
AEMC and HPLC results are varied from 2.1986 to
9.2892%.
Therefore, from the AEMC model-based results
discussed above, it is worthy to predict equilibrium
constants the multiple components NARS systems using
the proposed AEMC model.

7. A. Muslim
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Chemical Engineering, Vol. 4, N. 1
69
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2 2.5 3 3.5
[Int.Tetrathionate]/[Int.Trithionate]
AEofTetrathionate(mM)
The AECM-based
The HPLC-based
Fig. 4. The AEMC-based AE values of tetrathionate versus the ratio of
initial concentrations of tetrathionate and trithionate
Model-based Equilibrium Constants
The equilibrium constant for trithionate over
thiosulfate, K2,1 of Equation (12) in the NARS system is
calculated based on the AEMC model and both loading
(LB) and stripping (SB). In general, the loading affinity
of thiosulfate (thiosulfate on resin over thiosulfate in
solution, Thio-R/Thio-Sol.) linearly increases with the
increase in the loading affinity of trithionate (trithionate
on resin over trithionate in solution, Tri-R/Tri-Sol.) as
shown in Fig. 5.
y = 90.739x - 35.427
y = 100.65x - 51.208
y = 99.468x - 50.857
0
100
200
300
400
500
600
0 1 2 3 4 5 6
Thio-R/Thio-Sol.
Tri-R/Tri-Sol.
Loading-based
Stripping-based
Model-based
Linear (Loading-based)
Linear (Stripping-based)
Linear (Model-based)
Fig. 5. The equilibrium constant for trithionate over thiosulfate based on
model, experiment both loading and stripping
The slope of the line in Fig. 5 represents the value of
equilibrium constant for the trithionate over thiosulfate
in the NARS system. The model-based K2,1 is
approximately 99.468, which is very close to the one by
stripping, 100.65 with the deviation within the two
results being approximately 1.1883%. Meanwhile, the
loading-based K2,1 is 90.739 which is not really far from
the results by the Model and stripping with
approximately 9.6199% deviation from the model-based
result. From the equilibrium constant value being much
more than 1, it can be concluded that trithionate is very
much strongly adsorbed on resin than thiosulfate leading
to the loading affinity of trithionate is very much higher
than the loading affinity of thiosulfate. As can be seen in
Fig. 6, the model-based equilibrium constant for
tetrathionate over trithionate, K3,2 of Equation (13) in
the NARS system is almost the same as the ones by
loading and stripping which is approximately 1.482. The
equilibrium constant based on loading and stripping is
approximately 1.415 and 1.428 respectively. Overall, the
model-based results are in good agreement with
experimental results.
y = 1.415x + 13.545
y = 1.428x + 1.7485
y = 1.482x - 30.163
0
100
200
300
400
500
600
700
100 150 200 250 300 350 400 450 500
Tri-R/Tri-Sol.
Tetra-R/Tetra-Sol.
Loading-based
Stripping-based
Model-based
Linear (Loading-based)
Linear (Stripping-based)
Linear (Model-based)
Fig. 6. The equilibrium constant for tetrathionate over trithionate based on
model, and experiment both loading and stripping
Using the loading affinity model, the equilibrium
constant for gold thiosulfate over trithionate, K5,2 can be
obtained to be 0.4693 with the correlation coefficient, R2
being 0.9874 as viewed in Fig. 7. Compared to the result
of equilibrium constant for gold thiosulfate over
trithionate being 0.53 in previous study [13], the model-
based value is smaller than 0.53. However, the model-
based value is still in a good agreement with the
reference value wherein the deviation is approximately
11.453%.
y = 0.4693x
R2
= 0.9874
0.00E+00
2.00E+07
4.00E+07
6.00E+07
8.00E+07
1.00E+08
1.20E+08
0.00E+00 5.00E+07 1.00E+08 1.50E+08 2.00E+08 2.50E+08
(Tri-R^3/Tri-Sol.^3)
(Au-R^2/Au-Sol.^2)
Fig. 7. The model-based equilibrium constant for gold thiosulfate over
trithionate
Since tetrathionate is an attractive component in
multiple components NARS system because it is
adsorbed stronger than trithionate (K3,2 is more than 1),
modeling the equilibrium constant of gold thiosulfate
over tetrathionate would be worthy to know. This is also
a challenge because the equilibrium constants should
connect one another. Hence, the gold thiosulfate over
tetrathionate reaction with the equilibrium constant K5,3

8. A. Muslim
Copyright © 2012 Praise Worthy Prize S.r.l. - All rights reserved International Review of Chemical Engineering, Vol. 4, N. 1
70
can be expressed as below:
3R2S4O6(s) + 2Au(S2O3)2
3-
(aq) <=>
2R3Au(S2O3)2 (s) + 3S4O6
2−
(aq)
(21)
The reaction mechanism to obtain the K5,3 value is:
3R2S4O6(s) + 3S3O6
2−
(aq) <=>
3R2S3O6(s) + 3S4O6
2−
(aq)
(22)
3R2S3O6(s) + 2Au(S2O3)2
3-
(aq) <=>
2R3Au(S2O3)2(s) + 3S3O6
2−
(aq)
(23)
3R2S4O6(s) + 2Au(S2O3)2
3-
(aq) ) <=>
2R3Au(S2O3)2(s) + 3S4O6
2−
(aq)
(24)
where K5,3 is equal to 1/K3,2 times K5,2. The equilibrium
constant for Equation (22) is not equal to 1/( K3,2)3
due
to multiplying all the coefficient reaction (R2S4O6(s) +
S3O6
2−
(aq) <=> R2S3O6(s) + S4O6
2−
(aq) ) by three. This is a
special case because of the entire coefficient in the
original reaction being one, and this case is described on
some specific examples in the available literature [14].
As a result, the model-based equilibrium constant of
gold thiosulfate over tetrathionate, K5,3 is approximately
0.317.
IV. Conclusion
Strong based anion exchange resin has been
investigated for the adsorption of thiosulfate,
polythionates and gold thiosulfate in non-ammoniacal
resin solution (NARS) systems. Experiments and
modeling work were conducted to obtain equilibrium
constants associated with the complex reaction in the
NARS systems. As the modeling results, the equilibrium
constant for trithionate over thiosulfate was obtained to
be approximately 90.739. Meanwhile the equilibrium
constant for tetrathionate over trithionate was
approximately 1.482. These model-based results were in
a good agreement with the experimental results. The
model-based equilibrium constant for gold thiosulfate
over trithionate was obtained to be 0.469 with the
correlation coefficient, R2
being 0.9874. A model
reaction mechanism to obtain the equilibrium constant
for gold thiosulfate over tetrathionate was proposed, and
the model-based equilibrium constant was obtained to be
approximately 0.317.
Acknowledgements
The author is grateful to Curtin University in
Australia, The A. J. Parker Cooperative Research Centre
(CRC) for Hydrometallurgy and CSIRO Mineral in
Australia for financial and technical support.
References
[1] Muir D. M., Aylmore M. G. (2004), Thiosulphate as an alternative
to cyanide for gold-processing issues and impediments. Mineral
Processing and Extractive Metallurgy, 113, 2-12.
[2] Hilson D., Monhemius A. J. (2006), Alternatives to cyanide in the
gold mining industry: what prospects for the future? Journal of
Cleaner Production, 14, 1158-1167.
[3] Berezowsky R. M., Sefton V. B., Gormely L. S. (1978), Recovery
of precious metals from metal sulfides. US Patent 4070182. Sherritt
Gordon Mines Limited.
[4] Hemmati M., Hendrix J. L., Nelson J. H., Milosavljevic E. B.
(1989), Study of the thiosulphate leaching of gold from
carbonaceous ore and the quantitative determination of
thiosulphate in the leached solution. London, UK, The Institution
of Mining and Metallurgy.
[5] Langhans, J. W., JR., Lei, K. P. V., Carnahan T. G. (1992), Copper-
catalyzed thiosulfate leaching of low-grade gold ores.
Hydrometallurgy, 29, 191-203.
[6] Zhang H., Dreisinger D. B. (2002), The kinetics for the
decomposition of tetrathionate in alkaline solutions.
Hydrometallurgy, 66, 59-65.
[7] Nicol M. J., O'Malley G. (2002), Recovering gold from thiosulfate
leach pulps via ion exchange. JOM, 54, 44-46.
[8] Muslim A. (2009), Gold loading on ion exchange resins in non-
ammoniacal resin-solution systems. Journal of Chemical
Engineering and Environment (Jurnal Rekayasa Kimia dan
Lingkungan), 7(4), 158-162.
[9] Wan R. Y. (1997), Importance of solution chemistry for
thiosulphate leaching of gold. Carlton, Vic, The Australasian
Institute of Mining and Metallurgy.
[10] Jeffrey M. I., Brunt S. D. (2007), The quantification of thiosulfate
and polythionates in gold leach solutions and on anion exchange
resins. Hydrometallurgy, 89, 52-60.
[11] Muslim A., Pareek V. K., Tadé M. O., Jeffrey M. I., Zang H. (2010)
Dynamic Models for Isotherm Adsorption of Thiosulfate,
Polythionates and Gold in Non-Ammoniacal Resin-Solution
Systems. Annual Bulletin of the Australian Institute of High
Energetic Materials, Vol. 1.
[12] Williams H. P., T., S. A. Williams, T. V., Brian P. F. (2002),
Numerical Recipes in C++, Cambridge, United Kingdom,
Cambridge University Press.
[13] Muslim A., Pareek,V. K., Tadé M. O., Jeffrey M. I., Zang H.;
Adsorption of Polythionates and Thiosulfate on Strong Base Anion
Exchange Resins. Proceeding of Chemeca 2009 Conference in
Perth-Western Australia 27-30 September, Published by
Engineers Australia, Paper No. 247/615.
[14] Clark J. (2002), Le Chatelier's Principle. Available at:
http://www.chemguide.co.uk/physical/equilibria/lechatelier. html
Authors’ information
Chemical Engineering Department, Faculty of Engineering,
Syiah Kuala University, Darussalam – Banda Aceh
Indonesia 23114.
Abrar Muslim is a lecturer at Chemical
Engineering Department of Engineering Faculty,
Syiah Kuala University, Indonesia. He received an
M.Eng. (Chem. Eng.) in 2007 and a PhD (Chem.
Eng.) in 2010 from Curtin University of
Technology, Western Australia. He is a
Professional Engineer awarded by Engineers
Australia in 2009, AMIChemE, UK since 2008
and member of International Association Engineers since 2011. He has
focused his research on the area of chemical and mineral processes, and
simulation, modeling and control of the processes. Among others, his
researches and studies have been published and available at
http://en.scientificcommons.org/abrar_muslim.
E-mail: abrar.muslim@che.unsyiah.ac.id

9. International Review of Chemical Engineering
Rapid Communications
(IRECHE)
Aims and scope
The International Review of Chemical Engineering (IRECHE) is a peer-reviewed journal that publishes original
theoretical and applied papers on all fields of the Chemical Engineering. The topics to be covered include, but are not
limited to:
Biochemical and biomolecular engineering; Bioreactors ; Process Fluid dynamics (pipe flow, mixing, rheology-experiments, Multi-
phase flow and so on); Flows with phase change; Coating processes and technology; Computer aided process engineering; Heat
transfer (both modelling and experimental results pertinent to problems in chemical engineering, mechanical engineering and
biotechnology); Heat and mass transfer (modelling, equilibrium, adsorption, absorption, extraction, etc); New reactors,
thermodynamics and thermodynamic optimization of reactors, catalysts, devices and processes; Entropy and Energy analysis of
chemical and biotechnological process and optimization; Transport phenomena and process analysis and synthesis, Scale-up,
scale-down , modelling and simulation; Fluidization-broad aspect: Gas-solid, Liquid-solid, Gas-liquid-Solid; Fluidized ed
combustion processes Separations processes (sedimentation, filtrations, membrane filtration, etc.); Process safety and physics of
accidents in chemical technology, Risk analysis; Powder mechanics in both models and experiments; Alternative fuels (such as new
developed ones and utilization of wastes: derivation, analysis and combustion performance); Combustion, pyrolysis, gasification,
etc.; Environmental chemical and biotechnological engineering; External field assisted process including applications of electric
fields, magnetic fields, ultrasound, vibrations, etc.; Physical metallurgy and micro-metallurgy; New materials, Polymers and
composites; Process Control, Process Design, Process Development and Process intensification; Wastes: new material based on
waste conversion; engineering methods for waste treatment and management; New and important applications and trends.
Instructions for submitting a paper
Contributions may consist of invited tutorials or critical reviews; original scientific research papers (regular paper);
letters to the Editor and research notes which should also be original presenting proposals for a new research,
reporting on research in progress or discussing the latest scientific results in advanced fields.
All papers will be subjected to a fast editorial process.
Any paper will be published within two months from the submitted date, if it has been accepted.
Papers must be correctly formatted, in order to be published.
Formatting instructions can be found in the last pages of the Review.
An Author guidelines template file can be found at the following web address:
www.praiseworthyprize.com/Template_of_IRECHE.doc
Manuscripts should be sent via e-mail as attachment in .doc and .pdf formats to:
info@praiseworthyprize.it or santolo@unina.it (Managing Editor)
The regular paper page length limit is defined at 15 formatted Review pages, including illustrations, references and
author(s) biographies.
Pages 16 and above are charged 10 euros per page and payment is a prerequisite for publication.
Subscription rates:
on Cd-Rom, per year: Print copy, per year:
Institutional: 270*
(euros) 300**
(euros)
Individual: 270*
(euros) 300**
(euros)
Individual Article: 30 (euros) 40**
(euros)
*
To be downloaded
**
Shipment costs to be charged
Abstracting and Indexing Information:
Academic Search Complete - EBSCO Information Services
Cambridge Scientific Abstracts - CSA/CIG
Index Copernicus (Journal Master List): Impact Factor 6.42
Autorizzazione del Tribunale di Napoli n. 15 del 25/02/2008

10. (continued from outside front cover)
SPECIAL SECTION ON
3RD
CEAM 2011 - VIRTUAL FORUM
Jerusalem Artichoke and Pea Hulls Based Substrates as Raw Material for Ethanol Production
by Saccharomyces cerevisiae
by Petya Gencheva, Georgi Dobrev, Naiden Delchev, Jordan Hristov, Viara Ivanova
84
Functional Copolymer/Organo-MMT Nanoarchitectures. XIII. EPDM Rubber/Poly[(MA-alt-1-
octadecene)-g-PEO]/Organoclays Nanocomposites Through Reactive Extrusion
by Mostafa A. Dilmani, Zakir M. O. Rzayev, Erdoğan Alper
91
Control of Metal Dispersion, Chemical Composition and Texture of Palladium-Zinc Catalysts
on Mesoporous Titania
by Lyudmila B. Okhlopkova, Mikhail A. Kerzhentsev, Zinfer R. Ismagilov
105
Designing an Fuel Cell Autonomous Energy System for Residential Use
by A. Cancela, A. Sanchez, R. Maceiras, D. Fernandez, S. Urrejola
115
Evaluation of Paper Industry Compliance with Air Quality Emissions
by Abdulkareem A. S., Afolabi A. S., Mokoena S. N., Fungura N., Muzenda E.
119
2035-1755(201201)4:1;1-A
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved