Journal of Minerals and Materials Characterization and Engineering, 2012, 11, 730-734
Published Online July 2012 (http://www.SciRP.org/journal/jmmce)
Model for Prediction of the Concentration of Extracted
Tin during Leaching of Cassiterite in Potassium
Hydroxide Solution
Onyedika Gerald1*, Ugwu Priscilla1, Ogwuegbu Martin1, Ejike Emmanuel1,
Nwoye Chukwuka2, Jiann-Yang Hwang3
1Mineral Processing Unit, Department of Chemistry, Federal University of Technology, Owerri, Nigeria
2Department of Metallurgical and Materials Engineering, Nnamdi Azikiwe University, Awka, Nigeria
3Materials Science and Engineering, Michigan Technological University, Houghton, USA
Received May 8, 2012; revised June 19, 2012; accepted July 10, 2012
ABSTRACT
Model for prediction of the concentration of tin extracted during potassium hydroxide leaching of cassiterite has been
derived. The model: A = Nt1.53, indicates that the concentration of tin extracted is dependent on the residence time. It
was found that the validity of the model is rooted in the expression LogA = Log(Nt1.53). Tin extraction per unit time as
obtained from experiment and derived model are 2.6666 and 2.6268 mg/min respectively. The maximum deviation of
the model-predicted concentration of dissolved tin from the corresponding concentration obtained from the experiment
was found to be less than 8%, which is quite within the acceptable deviation limit of experimental results and hence,
impacting about 92% confidence coefficient on the model.
Keywords: Model; Tin; Potassium Hydroxide; Cassiterite; Leaching
1. Introduction
Tin presently finds extensive use in industrial and do-
mestic applications. As a result of this, extraction of tin
from ores has continued to attract considerable attention.
Extraction of metals from their ores and recovery from
their various industrial wastes are a major step towards
judicious utilization and conservation of our mineral re-
sources. Various works have been done to extract metals
from their ores [1-4]. Cassiterite, otherwise known as tin
ore is the only tin mineral from which tin can be ex-
tracted in a commercial quantity. Matell [5] studied the
extraction of tin from its ores by reduction of cassiterite
to tin metal and then extracting the tin with aqueous in-
organic acids.
Models are of central importance in many scientific
contexts, useful for testing, analysis or training where
real-world systems or concepts can be represented by a
model [6,7]. One of such models as reported by Hwang
et al. [7] is a numerical simulation of heat transfer during
the microwave heating process of a two dimensional,
magnetic dielectric, magnetite, subjected to heat conduc-
tion, convection and radiation. The heat transfer process
was modeled using an explicit finite difference approach
and the temperature profile for different heating parame-
ters was generated through developing a code in mathe-
matica 7.0.
The derivation of models for the evaluation of the
concentration of some metal values leached in some ores,
concentrates, calcine or other solid materials containing
metal(s) in some aqueous solutions of acids, bases, com-
plexing agents, etc has gained very wide interest among
researchers in recent time. Many models have been evalu-
ated involving the use of different acids for the leaching
of some ores. One of such works as reported by Nwoye
[8] is the model for the computational analysis of the
solution temperature during leaching of iron oxide ore in
hydrochloric acid solution. The model is expressed as:
N
Te

(1) 

8.9055
Te

(2) 
where T is the solution temperature (˚C) during leaching
of iron oxide ore using hydrochloric acid; N = 8.9055 (pH
coefficient for hydrochloric acid solution during leaching
of iron oxide ore) determined by Nwoye et al. [9];

is
the final pH of the leaching solution at the time t when the
solution temperature is evaluated.
Nwoye [10] also derived a model for computational
analysis of the concentration of dissolved haematite and
*Corresponding author.

O. GERALD ET AL. 731
heat absorbed by oxalic acid solution used during leach-
ing of iron oxide ore. The models are:
23
OK%Fe





c
QK
(3)

(4) 
where
%Fe2O3 = Concentration of dissolved haematite in ox-
alic acid solution;

= Final pH of the leaching solution at time t at which
%Fe2O3 was obtained;
µ = Weight of iron oxide added into the oxalic acid
leaching solution (g);
K = Constant of proportionality associated with heat
absorption;
Q = Quantity of heat (J) absorbed by oxalic acid solu-
tion during the leaching process (J).
Successful attempt has also been made [11] to derive a
model for computational analysis of heat absorbed by
hydrogen peroxide solution relative to the weight of iron
oxide ore added. It is of the form:

16
23
e O
%Fe
%F



(5)
where µ is the weight input of iron oxide ore (g); %Fe2O3
and %Fe are the concentrations of dissolved haematite
and iron respectively in hydrogen peroxide solution dur-
ing leaching. The model is rooted on the expression
13
%Fe 
23
%Fe O where both sides of the relation-
ship are correspondingly almost equal.
The aim of this work is to develop a model for pre-
dicting the concentration of extracted tin during leaching
of cassiterite in potassium hydroxide solution.
2. Materials and Methods
2.1. Materials
The sample of cassiterite ore concentrate used for this
study was obtained from Jos, Plateau State, Nigeria.
2.2. Methods
2.2.1. Leaching Experiment
The ore was crushed to particle size of −212 µm. Con-
ventional leaching experiments were carried out in glass
vessels which were put in a temperature-controlled water
bath. Stirring was carried out using an overhead mecha-
nized stirrer and a glass impeller. 250 ml of the leaching
solution was heated to the desired temperature and then
1.0 g of cassiterite ore was added. Periodic sampling of 5
ml of liquor was drawn for chemical analysis using ICP-
OES (Inductively Coupled Plasma—Optical Emission
Spectrometer).
2.2.2. Model Formulation
Experimental results shown in Table 1 were used for the
model derivation. Computational analysis on the experi-
mental data in Table 1 using C-NIKBRAN (Nwoye,
2008) as shown in Table 2 resulted to Table 3 which
indicates that



1.53
Log LogapproximatelyANt
1.53
(6)
A
Nt
1.53
0.1898
(7)
Introducing the value of N into Equation (7),
A
t (8)
where
A = Concentration (mg) of tin dissolved during leach-
ing of cassiterite ore using potassium hydroxide solution;
N = 0.1898, interaction factor between ore and leach-
ing solution);
1.53 = The leachability of the leaching solution.
Equation (8) is the derived model.
2.2.3. Model Validation
This model was validated using the correlation coeffi-
cients (CORREL), sum square techniques (SSQ) and
Table 1. Experimental result of the variation of the concen-
tration of tin obtained with time (conditions: 4 M KOH,
temperature: 80˚C, agitation speed: 500 rpm, particle size:
−212 µm).
Time (min) Aexp (mg)
10 7.2
30 30.8
45 68.9
60 112.0
90 199.3
110 257.6
120 286.8
Table 2. Analysis table showing variation of LogA with 1.53
Logt.
Time (min)Aexp (mg)LogA 1.53 Logt Log0.1898
10 7.2 0.8573 1.5300 −0.7217
30 30.8 1.4886 2.2600 −0.7217
45 68.9 1.8382 2.5294 −0.7217
60 112.0 2.0492 2.7206 −0.7217
90 199.3 2.2995 2.9900 −0.7217
110 257.6 2.4109 3.1233 −0.7217
120 286.8 2.4576 3.1812 −0.7217

O. GERALD ET AL.
732
Table 3. Variation of (LogA) with (Log0.1898 + 1.53 Logt).
Time (min) LogA Log0.1898 + 1.53 Logt
10 0.8573 0.8085
30 1.4886 1.5383
45 1.8382 1.8077
60 2.0492 1.9989
90 2.2995 2.2683
110 2.4109 2.4016
120 2.4576 2.4595
statistical cum graphical methods.
2.2.4. Correlation Coefficients
The correlation coefficient is a measure of the degree of
interaction between process parameters acting as de-
pendent and independent variables.
2.2.5. Sum Square Deviational Method
The sum square deviation is the measure of the goodness
of fit for each point. The difference between the predic-
tion by the model and the observed is value squared
given by the expression:

2
12 exp
,,
!
kkY
n



SSQ Ya  (9)
It is a direct measure of the accuracy of the average
observation when divided by the number of observations
and the square root taken. The smaller the average dis-
tance, the better the fit.
2.2.6. Statistical and Graphical Method
The validity of the model was established by comparing
the model-predicted values and the experimental values.
Comparison between these two values reveals deviations
which were due to the physiochemical interactions be-
tween the ore and the leaching solution and also due to
the surface properties of the ore, which were found to
have played vital roles during the leaching process [11].
It is then expected that a correction factor be added to
the model-predicted values to make up for those factors
neglected during the model formulation.
The deviation, Dv (%), of model-predicted A values
from the experimental values is expressed as:
mo
Dv d exp
exp
100
AA
A


Cf Dv
(10)
where
Amod is the model-predicted concentration of tin leached
out, and Aexp is the corresponding experimental value.
Correction factor (Cf), if expressed as the negative of
the deviation, then,
(11)


and
mod exp
exp
100 AA Cf A


 


(12)
Addition of the corresponding Cf values obtained from
Equation (12) to the model-predicted values of the con-
centration of tin leached gives the exact experimental
values.
3. Results and Discussion
3.1. Results
The results of the experiment on the variation of concen-
tration of tin obtained with time is shown in Table 1,
while that of the analysis of the variation of the model
variables are presented in Tables 2, 3 and 4 respectively.
The effects of residence time on the concentration of tin
dissolved from experiment and as predcted by the derived
model are presented in Figures 1 and 2 respectively. The
graph of the comparison of the results obtained from the
experiment and the derived model is as in Figure 3.
3.2. Discussion of Results
The correlation coefficients R between concentration of
tin extracted and residence time as obtained from the
experiment and derived model (Table 4) were calculated
using Microsoft EXCEL as 0.9942 and 0.9916 respec-
tively. Comparison of these proximate correlation coeffi-
cients indicates validity of the derived model.
The obtained value of the sum squared technique (SSQ)
from Equation (9) and Table 4 is compared with average
sum of the experimental results. The value is 5.92% de-
viation. This confers a high degree validity of 92% con-
fidence coefficient.
The derived model is Equation (8). The comparison of
Table 4. Comparison between concentrations of tin re-
moved as predicted by model and as obtained from experi-
ment.
Time (min)Aexp Amod Dv (%) Cf (%)
10 7.2 6.4313 −10.68 +10.68
30 30.8 34.5376 +12.14 −12.14
45 68.9 64.2261 −6.78 +6.78
60 112.0 99.7396 −10.95 +10.95
90 199.3 185.4758 −6.94 +6.94
110 257.6 252.1314 −2.12 +2.12
120 286.8 288.0338 +0.43 −0.43

O. GERALD ET AL. 733
020 40 60 80
0
50
100
150
200
250
300
100 120
Aexp ( mg )
Time ( mi n )
Figure 1. Effect of residence time on the concentration of
dissolved tin as obtained from the experiment.
0 20406080
0
50
100
150
200
250
300
100120
Amod ( mg )
Time ( mi n )
Figure 2. Effect of residence time on the concentration of tin
dissolved as predicted by the derived model.
the concentrations of dissolved tin as predicted by the
model (Amod) with those obtained from the experiments
show insignificant positive and negative deviations, hence,
depicting the reliability and validity of the model.
The data on deviations are shown in Table 4. The av-
erage deviation is calculated to be 7.15%, which is quite
within the acceptable deviation limits from experimental
results. The validity of the model is found to be rooted in
Equation (8) where both sides are correspondingly ap-
proximately equal. Table 3 is also in agreement with
Equation (6) where the values of logA is approximately
equal to the value of log (Nt1.53).
The rate of dissolution (concentration of tin dissolved
per unit time) (mg/min) was determined using the ex-
perimental values and the model-predicted values as per
the following equation:
tA
A
c
t (12)


Equation (12) therefore, implies that a plot of concen-
tration of tin dissolved against residence time should give
a straight line (Figure 1) with a slope equal to S, where S
is:
A
St

 (13)
and ∆A = change in the concentration of tin dissolved (A1,
A2) at times t2, t1.
Figure 1 gives a slope of 2.6666 mg/min, which is the
concentration of tin removed per unit time during the
actual experimental leaching process. Also, a similar plot
(Figure 2) using the model-predicted values gave a slope
equal to 2.6268 mg/min. This is the model-predicted
concentration of dissolved tin per unit time of the leach-
ing process. A comparison of these two rates shows a
proximate agreement, indicating a high degree of validity
for the model. Figure 3 showed that both the values of
the dissolved tin from experiment (line Aexp) and the de-
rived model (line Amod) in relation to residence time are
generally quite close, indicating proximate agreement
and validity of the proposed model.
4. Conclusion
The model predicts the concentration of tin dissolved
during leaching of cassiterite in potassium hydroxide
solution. The validity of the models is rooted on the ex-
pression LogA = Log0.1898 t1.53 where both sides of the
relationship are correspondingly approximately equal. Tin
extraction per unit time as obtained from experiment and
0 20406080100120
0
50
100
150
200
250
300 Aexp
A mod
Concentration of tin removed (mg)
time
(
min u tes
)
Figure 3. Comparison of the concentration of dissolved tin
in relation to the residence time as obtained from experi-
ment and derived model.

O. GERALD ET AL.
734
derived model are 2.6666 and 2.6268 mg/min respec-
tively. The average deviation of the amount of the model-
predicted concentration of tin from the corresponding
experimental values was found to be less than 8%, which
is quite within the acceptable range of deviation limit of
experimental results. Also, the rate of dissolution as ob-
tained from experiment and derived model show proxi-
mate agreement, and hence, indicates a very high degree
of validity for the model.
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