Simulation of aqueous system is important in order to get better understanding of the chemical phenomena in a predictable way. Thermodynamic simulation is believed to be the most efficient way to derive aqueous phenomena without undergoing troublesome experiments. Chemical modeling has achieved tremendous development over the years and is being widely used in various branches of chemistry and chemical processes. Model assumption is a very powerful tool to predict and understand the behavior of complex aqueous systems and equally powerful in educational aspect as well.
The model simulation is being widely used in various branches of chemistry and chemical technology. An extensive literature review was done on simulation model used in chemical researches. A number of articles were found in solution chemistry including metal separation, ionic characterization, kinetic of reaction and mass transfer (Martín et al., 2007; Sabaté et al., 2006; Rooklidge et al., 2005; Al-hamdan and Reddy, 2005). Model analysis or simulations involving chemical reactions have so far been made in many aspects. Some of them were made to determine the constants related to chemical reaction, such as equilibrium constant, solubility constant, reaction rate constant, reaction order etc. (Christov, 1998; Thomsen and Rasmussen, 1999; Berlot et al., 1999).
Ions in aqueous solutions are very important in maintaining the pH and other
chemical behavior. So the qualitative and quantitative analyses of them in aqueous
solution play an important role in appropriate use in chemical, environmental
and industrial processes. Various ions are present in water, nonetheless, the
presence of some ions beyond the tolerance limit in water would contaminate
the aqueous system and become dangerous for drinking and irrigation purposes.
A simple, economically feasible and ecologically sustainable model simulation
process for the detection and separation of ions in aqueous system is very important
to avoid troublesome experiments. Recently model simulation technique is being
used in aqueous system to have a complete scenario of the chemical phenomena
that can be difficult to achieve in an experiment.
This study presents a mathematical modeling for Na(I)-K(I)-HCl-H2O
system, which was developed to predict chemical phenomena of ions in the aqueous
system at 25°C.
MATERIALS AND METHODS
Preparation of solutions: The solutions of NaOH and KOH were prepared separately at a concentration of 0.2 mol dm3and standardized using standard oxalic acid solution. Thus standard solutions of NaOH and KOH were set at concentrations of 0.01, 0.05 and 0.1 mol dm3 separately in different volumetric flasks. Dissolving the HCl (BDH Co. Ltd.) was also made 0.2 mol dm3 concentration of HCl solution and the solution was then standardized with standard NaOH solution. 0.01, 0.05 and 0.1 mol dm3 concentrations of HCl solutions were made from the standardized HCl solution.
Fifty milliliter of 0.01 mol dm3 HCl was titrated against 0.1 mol
dm3 NaOH and KOH solutions separately by continuous mixing using
a magnetic stirrer. pH was continuously measure using a pH meter. This procedure
was repeated several times until more than 90 mL of total alkaline solutions
were added. The whole experimental apparatuses were set inside a chamber under
nitrogen gas atmosphere. The box was equipped with gas inlet and outlet to maintain
the gas pressure inside the box. Nitrogen gas was supplied from out side of
the box and gas flow was controlled so as to maintain 1 atm atmospheric pressure
inside the box. Same procedures were repeated for the other two sets of concentrations
of acid and alkaline solutions and they were 0.05 and 0.1 mol dm3.
A set consisted of same concentration of an acid and two alkali metals hydroxide.
The pH increases slowly initially with increasing metal ions concentrations, then it increases sharply and finally it reaches almost constant with increasing metal ions concentrations. These three figures show the similar tendency. The pH increases sharply near the equivalence point, from a pH of about 3 to a pH about 11. The equivalence point was attained in different metal ions concentrations at 0.01, 0.05 and 0.1 mol dm3 initial concentrations of HCl solutions, respectively (Fig. 1-3) .
Simulation model: The significance of the present research is to assume a suitable model for an aqueous system containing common metal ions, i.e., sodium and potassium and only one anion, chloride ion for developing an adequate model to characterize sodium and potassium ions in aqueous system and reaction phenomena that take place.
Lee et al. (2003) has developed a chemical model of ZnSO4-Na2SO4-H2SO4-NaOH-H2O
system to predict the hydrogen ion activity at 25°C. The study showed that
the experimental pH values were in good agreement with the predicted pH values.
In view of this, Na(I)-K(I)-HCl-H2O system in the present study is
described considering the chemical equilibria with mass and charge balance equations.
Hydroxides of sodium and potassium and hydrochloric acid reagents are supplied
to a reaction vessel containing water and they were mixed at a constant temperature
and pressure. Various chemical species would be generated in the aqueous system
due to chemical reactions. The model did not consider any precipitation or complex
ion formation reaction and assumed only the association between H+
and OH¯ ions. However, the hydration of ions is very common phenomena (Ebbing,
1996). The energy of attraction between an ion and a water molecule is due to
an ion-dipole force.
between metal ions concentration and pH for 0.01 mol dm3 initial
concentration of HCl solution at 298K
between metal ions concentration and pH for 0.05 mol dm3 initial
concentration of HCl solution at 298K
between metal ions concentration and pH for 0.1 mol dm3 initial
concentration of HCl solution at 298K|
Water molecules are polar, so they tend to orient with
respect to nearby ions. In the case of positive (Na+ and K+),
water molecules orient with their oxygen atoms (the negative ends with the molecular
dipoles) toward the ion. In the case of a negative ion (Cl¯), water molecules orient with their
hydrogen atom (the positive ends of the molecular dipoles) toward the ion. However,
the hydration of ions was not considered as it as has no or less significant
effect on the simulation results. The charge balance equation, mass balance
equation and chemical reactions in the aqueous system were taken into consideration
in this model. The equilibrium reaction between H+ and OH¯ ions
played a vital role in maintaining ionic equilibrium in the aqueous system and
that the ionic product of water was used in the model. The present model also
assumed different equilibrium states among various ions in aqueous phase under
isothermal and isobaric conditions i.e., temperature at 298K and 1 atmospheric
pressure. A numerical programme was made based on model assumption.
Various species were assumed to be generated in the reaction vessel and their concentrations were calculated in the numerical programme using the following equations:
Where, Ci(x) and C(x) are the initial concentration and concentration
of a given species, x. Vi, and Vtotal are the initial
volume, added volume of alkaline metals hydroxide solutions and total volume
of aqueous solution in the vessel.
Chemical reactions: HCl, NaOH and KOH are assumed to be completely dissociated in water and they produce the ions of H+, CI¯, Na+, K+, OH-. The reactions are as follows:
The ionic product of water is as follows:
Mass balance equations are
Charge balance equation
The literature value for the ionic product of water, Kw = 1.0x1014 (mol dm3)2 (Chang, 1996) was used in the model assumption. All physical and chemical conditions were considered the same in as was done in the experiment. The values thus determined, concentrations of various chemical species were computed. pH was derived by using the equation pH = - logαH + = -log (χH+ + [H+]), where χH+ = 1 as the dilute solutions were considered in the model simulation. H+ ion doesnt exist in aqueous solutions as an independent species, it combines with H2O to form H3O+ and net ionic equation in acid bases reaction in water is (Sevenair and Burkett, 1996):
The existence of H+ or H3O+ ion in aqueous system considered to be the same in this model assumption. Hence H+ was used in calculating pH values in the numerical program.
A numerical programme was made using Microsoft Quick Basic to compute the concentrations of different ionic species in the aqueous system.
COMPARISON OF SIMULATION RESULTS WITH EXPERIMENT
The simulation results have to compare the experimental data to check the validity
of model assumption. A number of literatures were found on model simulation
of aqueous system where simulation results were compared with the experimental
data. A simulation model for the Co(NO3)2-Na2CO3-H2O
system based on a thermodynamic model which predicted possible equilibrium states
attained among gas, aqueous and solid phases under isothermal and isobaric conditions
were made by Mostafa et al. (2000). A theoretical and experimental result
on the speciation of the Fe(II)-Fe(III)-H2SO4-H2O
system in concentrated solutions was studied by Casas et al. (2005).
of pH between simulation and experiment for 0.01 mol dm3 initial
concentration of HCI solution at 298K|
of pH between simulation and experiment for 0.05 mol dm3 initial
concentration of HC1 solution at 298K|
Model simulations indicated that anions, cations and neutral complexes coexisted
in the studied system, where the dominant species were HSO4¯,
H+, Fe2+ and FeH(SO4)2. A study
was carried on extraction of Zn(II) from its aqueous hydrochloric acid solutions
into Alamine 336-m-xylene systems by Sayar et al. (2007). It was observed
that the increase in acidic molarity slightly increases the extractability of
Zn(II). The mathematical model simulating metal extractability in terms of organic
phase Alamine volume content, aqueous phase acidic molarity and initial metal
concentration were developed.
of pH between simulation and experiment for 0.1 mol dm3 initial
concentration of HC1 solution at 298K|
of various species H+ OH-and CI- in aqueous
system with metal ions concentration for 0.1 mol dm3 initial
concentration of HC1 solution at 298K
Liu and Papangelakis (2005) presented a model the chemistry of high temperature
aqueous processing systems. Monometallic sulphate solutions like Al2(SO4)3-H2SO4,
Fe2O3-H2SO4 were used to fit new
thermodynamic parameters which were verified on progressively more complex solution
mixtures. In all the above studies, simulation results were compared with available
experimental data and very good agreement was found.
Both the simulation results and the experimental data show similar tendency.
pH increases slowly with increasing metal ions concentrations in aqueous system
initially until it researches the equivalence point. At the equivalence point,
pH increases rapidly and finally, it again increases slowly with increasing
metal ion concentrations. An overall very good agreement between the simulation
results and experimental data were found (Fig. 4-6).
The simulation results of Fig. 7 showed the concentrations
of different ionic species in aqueous system with mathematical precision that
would be difficult to realize in an experiment.
A complete scenario of the chemical phenomena was thus obtained in the present model. Thus the model assumption about the chemical reactions without considering complex formation is valid.
Recently the model simulation of an aqueous system has widely been used to avoid complicated experimental procedure. In this study a good agreement between the simulation results and the experimental data was found. The complex formation among various cations and anions were not considered in the model and thus the comparison results justify the validity of the model assumption. However, the hydration of ions and attraction between opposite ions are very common phenomena in an ionic aqueous system and it has no significant interference in assuming the model. Moreover, the comparison results suggest that there is no metal complex ion formed in this aqueous system. The simulation results show various ions concentration in aqueous system with mathematical precision.
A well judged simulation model would provide a number of information, which would be very difficult to realize in experiments. This study could be helpful to predict the concentrations of chemical species under any stated conditions of an aqueous system. The model can be used on ionic characterization in aquifers by adapting more ions and parameters.
The author thanks Mr. Iqbal Bahar, Fellow in the Institute of Environmental Science, University of Rajshahi, Bangladesh for his assistance to the experiments.