Kinetics analysis of the forward extraction of cerium(III) by D2EHPA from chloride medium in the presence of two complexing agents using a constant interfacial area cell with laminar flow

2.1 Reagents and apparatus

D2EHPA (H₂A₂) extractant with sulfonated kerosene was brought from Luoyang ZhongDa Chemical Industry Co., Ltd. (China) A certain known amount of D2EHPA is first diluted until it has reached the required concentration having appropriate sulfonated kerosene; for a situation like this, the D2EHPA will have the ability to form a dimer H₂A₂, e.g. 2HA⇄Kd H2A2. As the dimerization is constant (K_d) and is defined as: K_d=[H₂A₂]/[HA]², log K_d=4.42 [22], its dissociation reaction goes like this: HA⇄Ka H++A−, when the dissociation constant (K_a) will be defined as: K_a=[H⁺][A⁻]/[HA], pK_a=1.27, at T=25°C [22].

The stock solution of aqueous phase is prepared by dissolving CeCl₃ (Chengdu Aikeda Chemical Reagent Co., Ltd., China) (purity >99.9%) using distilled water, and diluted to the required volume, and then analyzed by titration using a standard solution of EDTA (Tianjin Fengchuan Chemical Reagent Technologies Co., Ltd., China) at pH 5.5 using xylenol orange (Shanghai Xinshengshi Chemical Science Co., Ltd., China) as an indicator. A 1.0 mol l⁻¹ of NaCl is used to maintain a constant ionic strength. Lactic acid (HLac, pK_a=3.86, at T=25°C [23]) and citric acid (H₃Cit, pK_a1=3.13, pK_a2=4.76, pK_a3=6.40, at T=25°C [23]) are obtained from the Sinopharm Chemical Reagent Co. Ltd (China). All the chemicals are of analytical reagent grade.

A model of pHS-3C digital pH meter (Shanghai Rex Instruments Factory, China) is employed to measure the acidity. The cerium concentrations during extraction process are all determined using the Prodigy high dispersion inductively coupled plasma spectrometer (Leeman Labs, USA).

2.2 Experimental procedure

The constant interfacial area cell with laminar flow is used to conduct the kinetic experiment based on the principle found in the literature [24]. Figure 1 shows the schematic diagram for this constant interfacial area cell. It shows that there are two stirring impellers, one located on one side of the pool and the other at the opposite end of that impeller, the guide plates actions make the fluid reverse the laminar flow keeping the interface stable and at a smooth pace, resulting in there being no flow going towards the interface.

Figure 1:

Experimental devices of kinetics (A) and the structure of constant interfacial area cell with laminar flow (B).

1: Sampling aperture; 2: motor; 3: guide plate; 4: electro-thermostatic water bath; and 5: stirring paddle.

Unless it is otherwise stated, the area of the interface will be 15 cm². An aliquot of the aqueous phase (84 ml) followed by another aliquot of organic phase are added carefully to the cell chambers using a syringe, and stirring started. Unless otherwise stated, in most experiments, the speed of the stirring in both the phases (in most experiments) will constantly stay at 300 rpm. There will be 0.2 ml taken from the aqueous phase, once the stirrer has started, and an interval every 10 min to take a sample to be analyzed. Unless otherwise stated, there will be a kinetic experiment performed at 298 K.

Equal volumes of (20 ml for everyone) the aqueous and organic phases for equilibrium experiments are mixed well by shaking for 30 min at 298±1 K.

2.3 Treatment of rate data

According to the method used by Danesi and Vandegrift [25], the experimental data were processed. Assuming the mass transfer process is considered as a pseudo-order having a reaction that is nonreversible with respect to cerium(III):

where a and o are aqueous phase and organic phase, respectively. k_ao (cm · s⁻¹) and k_oa (cm · s⁻¹) represent the forward and backward mass transfer coefficients, respectively. k_ao and k_oa have been evaluated with the use of the theoretical treatment that had been developed in the literature.

The rate of change of the number of moles, n, with respect to time entering into the organic phase, dn/dt, is given by Eq. (2) [26]:

where n represents the number of moles of Ce(III) in the organic phase; V and Q represent one or the other between the aqueous and the organic phase, as well as the interfacial area cell, respectively.

At the state of being stable, either hand will be equal to zero in Eq. (3). That is:

According to the law of conservation of mass, after logarithm fetch on either side of the equality, it follows that:

All the slopes in the plots in ln{1−([Ce3+](o)/[Ce3+](o)e)}and against t have been used for the elevation of k_oa and k_ao. The value of distribution ratio K_d has been evaluated by determining Ce³⁺ concentrations that follow the contact of the two phases (20 ml each) for a time of 30 min.

3.1 Extraction studies

From the experiments of extraction kinetics, it is common to identify the extraction rates using criterion by stirring speed. When diffusion process takes control of the extraction, the rate of extraction is increased with an increased stirring speed, while there is without an effect on the extraction rate governed by chemical reactions [27]. Within this system, the plot (Figure 2) for log k_ao versus stirring speeds in the range of 100–400 rpm provided an increased trend, thus indicating that extraction rates are dependent on stirring speeds. Meanwhile, the linear relations of stirring speeds and log k_ao indicate that mass transfer process continues to be influenced by the agitation, even with 400 rpm. Therefore, mass transfer process is mostly controlled by diffusion instead of chemical process. The reason may be that chemical reaction rates are quicker than the diffusion rates, thus chemical reaction effect only possesses a small portion [15].

Figure 2:

Effect of stirring speed on mass transfer rate.

Aqueous phase: [CeCl₃]=0.10 mol l⁻¹, pH=2.00, [HLac]=0.3 mol l⁻¹, [H₃Cit]=0.03 mol l⁻¹; organic phase: [H₂A₂]=0.60 mol l⁻¹; Q=15 cm², T=298 K.

Additionally, if the diffusion-controlled extraction rate has a temperature effect that is more pronounced compared to rates controlled by chemical processes, the activation energy in this case does not generally exceed 20.9 kJ mol⁻¹ [27], [28]. The method of expressing influences on temperature that are most satisfactory with extractions of Ce(III) by D2EHPA in ranges of 20°C–55°C is derivable by plotting values of log k_ao against the absolute temperature 1/T reciprocal. Figure 3 shows results that are represented by a straight line that obeys Arrhenius equation kao=A⋅e−Ea​/​RT​, where R is the gas constant, T represents absolute temperature, and A represents frequency factor or pre-exponential factor. The activation energy E_a is calculated using this line as the slope, determined as 13.82 kJ mol⁻¹, indicating that the extraction of Ce(III) within the diffusion controlled investigated system, takes place in either the interface or the bulk phase.

Figure 3:

Effect of temperature on mass transfer rate.

Aqueous phase: [CeCl₃]=0.10 mol l⁻¹, pH=2.00, [HLac]=0.3 mol l⁻¹, [H₃Cit]=0.03 mol l⁻¹; organic phase: [H₂A₂]=0.60 mol l⁻¹; Q=15 cm², stirring speed=250 rpm.

The effects on the interfacial area have been studied by utilizing various interfacial regions within the range of 5.4–15 cm² while each phase was fixed with a volume of 84 ml. Meanwhile, the plots (Figure 4) of various values of k_ao versus certain corresponding interfacial regions a̅ (a̅=interfacial area/volume of the phase) have indicated an increase in reaction rates with increases in certain interfacial area, indicating that the extraction rates of Ce(III) are dependent on variations of interfacial area, and the reaction rates takes place at the interface instead of the bulk phase, which is based on the criterion as follows: if the bulk phase encounters slow chemical reactions, initial rates are independent of certain interfacial areas. Otherwise, reactions occurring in the interfacial zone indicate direct proportionality between the certain interfacial area and rate.

Figure 4:

Effect of specific interfacial area on mass transfer rate.

Aqueous phase: [CeCl₃]=0.10 mol l⁻¹, pH=2.00, [HLac]=0.3 mol l⁻¹, [H₃Cit]=0.03 mol l⁻¹; organic phase: [H₂A₂]=0.60 mol l⁻¹; stirring speed=250 rpm, T=298 K.

3.2 Extraction rate equation

In addition, our previous investigation indicates that the complexing agents lactic acid and citric acid do not involve the extraction process, on the contrary, they retain in the raffinate. Based on general kinetic equations for formation of metal chelates [22], the rate R_f reaching the extraction equilibrium is expressed as Eq. (6):

where HL, k_f, λ, and K_HL are acidic extractant, rate constant, partition ratio of extractant between the interface and organic phase, and ionization constant, respectively.

Based on the experimental results, plots for ln{1−([Ce3+](o)/[Ce3+](o)e)} versus time (t) yield straight lines every time, which indicates that first-order reactions are mass transfers being pseudo-first-order reversible reactions.

The effects of pH values and the concentration of the extractant H₂A₂ on the rate of extraction are investigated separately (Figures 5 and 6). Results indicate that the extraction rate increases as the pH values and H₂A₂ concentrations increases, with a slope of 0.9800≈1.0 and a slope of 1.086≈1.0, respectively. Furthermore, the line slopes show that the extraction of Ce(III) is inverse first-order dependent on [H⁺] as well as first order with respect to H₂A₂ concentration. The rate constant of extraction can be calculated in accordance with the intercepts shown in Figures 5 and 6, k_f=10^−2.31. Based on the experimental results, the rate equation of Ce(III) extraction with H₂A₂ can be written as follows:

Figure 5:

Effect of pH value in the aqueous phase on extraction rate.

Aqueous phase: [CeCl₃]=0.10 mol l⁻¹, [HLac]=0.3 mol l⁻¹, [H₃Cit]=0.03 mol l⁻¹; organic phase: [H₂A₂]=0.60 mol l⁻¹; Q=15 cm², stirring speed=250 rpm, T=298 K.

Figure 6:

Effect of extractant concentration on extraction rate.

[CeCl₃]=0.10 mol l⁻¹, pH=2.00, [HLac]= 0.3 mol l⁻¹, [H₃Cit]=0.03 mol l⁻¹, stirring speed=250 rpm, Q=15 cm², T=298 K.

3.3 Extraction mechanism and kinetic model

According to the above-mentioned analysis, the stoichiometry of the complex formation reactions between H₂A₂ and Ce shows the following formula of CeA₃ · 3HA_(o). Also, the complex agents H₃Cit and HLac are not extracted in the organic phase in the extraction process, which has been certified in the prior studies [18].

The stepwise metathetical reaction mechanism has been applied for analyzing the rate controlling phase (Table 1). Therefore, the following equations can be used to represent the process of extraction.

According to Eq. (8), the following equation can be obtained:

If the instantaneous state is assumed, while the k₋₂ rate constant is ignored, the concentration of [CeA(i)2+]can be calculated from Eq. (14):

By assuming interfacial is a steady state that is instantaneous, i.e.d[CeA(i)2+]dt=0.

It follows that:

By assuming that Eq. (10) is the rate-controlling step, the following rate law is obtained:

By assuming that Ce³⁺ rate transfers from aqueous to the organic phase, it could be faster than the reverse rate, k₋₁[H⁺]>>k₂[HA_(i)], therefore, the extraction rate equation can be written as:

where k₁k₂K₁K₂/k₋₁=k_f.

The above mechanism is in accordance with Eq. (7) that is obtained by experimental results. The identity of the reaction zone and extraction regime confirms that liquid–liquid interface reaction zones and diffusion control regime occur under these conditions. Thus, the rate-controlling phase takes place in the liquid-liquid interface.

The extraction process of Ce³⁺ results in diffuses from the bulk of aqueous to reaction zones that are located within the layer of aqueous diffusion that adheres to the organic/aqueous interface. Additionally, the dimeric D2EHPA extractant (H₂A₂) diffuses from organic to interface reaction zones while ionizing into monomeric acid. Then, CeA(i)2+ species are formed firstly at the interface, and the CeA_3(i) species are formed last, step by step. Meanwhile, three hydrogen ions are released. The CeA_3(i) species is extracted using H₂A₂ within the organic phase from the last CeA₃·3HA_(o) complex, meanwhile, the hydrogen ions are released and combined with H₂Cit⁻ and Lac⁻ for forming HLac and H₃Cit for buffering effects of higher acidy changes on extraction.

According to the expression above, Figure 7 shows the interface geometry model.

Figure 7:

Model of the extraction interface.