Article pubs.acs.org/IECR
Extraction Kinetics of Phosphoric Acid from the Phosphoric AcidCalcium Chloride Solution by Tri‑n‑butyl Phosphate Yang Jin, Da Zou, Shiqin Wu, Yuqing Cao, and Jun Li* Department of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065, People’s Republic of China ABSTRACT: The design and enlargement of extraction equipment require kinetic data on the extraction system. In this study, the extraction kinetics of phosphoric acid from the phosphoric acidcalcium chloride solution by tri-n-butyl phosphate (TBP) was investigated using a constant-interfacial-area cell with laminar flow. The extracted complexes were demonstrated to be H3PO4·TBP, H3PO4·2TBP, and H3PO4·3TBP by equilibrium studies. The effects of stirring speed, temperature, and interfacial area on the extraction rate were investigated. The results indicate that the extraction process is under mixed control by the extraction reaction at the interface and the diffusion of the reactant in the aqueous phase. The extraction rate is first-order with respect to H3PO4 and TBP with a rate constant of 10−5.34 L·mol−1·s−1. A mixed-control regime model is proposed. The forward extraction rate constant and the diffusion coefficient of the reactant in the aqueous phase were calculated to be 6.86 × 10−6 and 6.47 × 10−5 L·mol−1·s−1, respectively.
1. INTRODUCTION Phosphoric acid is a type of widely used basic raw material in many areas such as fertilizers, food additives, and detergents. It is mainly manufactured by a wet process, involving decomposition of phosphate rock with either sulfuric acid, hydrochloric acid, or nitric acid. Although the sulfuric acid route is widely used, it suffers from the fact that a large amount of gypsum is produced and the use of gypsum is difficult and expensive. These problems can be solved by dissolving phosphate rock with hydrochloric acid with no byproduct gypsum. The HCl-route phosphoric acid contains phosphoric acid with calcium chloride and some other impurities that is usually purified by solvent extraction. Tri-n-butyl phosphate (TBP) can serve as an effective extractant for extracting phosphoric acid from HCl-route phosphoric acid because of its immiscibility with the aqueous solution, good selectivity to phosphoric acid, and easy recovery.1−3 In a previous work, we investigated the equilibrium in the system phosphoric acid/water/tri-n-butyl phosphate/calcium chloride.3 However, a thorough study on the extraction kinetics of phosphoric acid from phosphoric acidcalcium chloride solution by TBP is not available. Jin et al. studied the extraction kinetics of phosphoric acid from phosphoric acidchloride solution by TBP using the single-drop and constant-interfacialarea-cell methods.4,5 The effects of the specific interfacial area and the concentrations of phosphoric and hydrochloric acids on the extraction rate were studied. However, the control type and kinetic model of the extraction process, which are essential for the design and enlargement of extraction equipment, have not been revealed. Several techniques are available for the study of extraction kinetics such as constant-interfacial-area cells,5−9 single drops,4,10 and highly stirred vessels.11 A constant-interfacialarea cell with laminar flow developed by Zheng et al. is a type of revised constant-interfacial-area cell12,13 that has already been used by many researchers in their investigations.14−16 In this apparatus, the flows of both the organic and aqueous phases near the interface flow parallel to the interface. As a result, the © XXXX American Chemical Society
interface is smooth and stable, which makes it a good apparatus for investigating extraction kinetics. The main aim of the present work was to study the extraction rate of phosphoric acid from phosphoric acidcalcium chloride solution by TBP using a constant-interfacial-area cell with laminar flow. The effects of the stirring speed, temperature, and interfacial area on the extraction rate were investigated to determine the extraction regime and reaction zone. The stoichiometry of phosphoric acid complexes formed in the organic phase are also discussed. Moreover, an extraction reaction model is proposed for the determination of some factors limiting the extraction process of phosphoric acid in this system.
2. EXPERIMENTAL SECTION 2.1. Materials. TBP and kerosene were provided by Sichuan Zhongcui Chemical Co. (Sichuan, China). TBP (purity ≥98.5%) was used without any further purification. Kerosene was washed with concentrated sulfuric acid, then neutralized with 5% Na2CO3 solution, and finally washed with water until the pH was neutral and distilled at 185−255 °C. Cyclohexane, phosphoric acid, and calcium chloride, supplied by Kelong Co. (Sichuan, China), were of analytical reagent grade. Toluene of analytical reagent grade supplied by Changlian Co. (Sichuan, China) was distilled before the measurements. Doubly distilled water was used only in interfacial tension determination experiments. Deionized water was used in the other experiments in the preparation of aqueous solutions. 2.2. Equilibrium Studies. Experiments were carried out at T = 298.15 ± 0.1 K in a water thermostat. Certain amounts of aqueous phase (phosphoric acidcalcium chloride solution) Received: August 19, 2014 Revised: December 3, 2014 Accepted: December 9, 2014
A
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in the organic phase as a complex of the form pH3PO4·qTBP,18 the extraction of phosphoric acid from phosphoric acid calcium chloride solution by TBP can be described as
and organic phase (TBP diluted in kerosene or cyclohexane) were mixed in a separatory funnel. The mixture was shaken for 2 h until euquilibrium was reached and then left to settle for 2 h for the complete separation of the two phases. The concentrations of phosphoric acid in the two phases were determined by the quinoline phosphomolybdate gravimetric method.17 FT-IR spectroscopy (NICOLET 7100, Madison, WI) was used for the analysis of the organic phase. 2.3. Kinetic Studies. The constant-interfacial-area cell with laminar flow that was used in this work was described by Zheng and Li.12 A schematic diagram of the apparatus is shown in Figure 1. It was made of glass with a jacket to maintain the
pH3PO4(a) + qTBP(o) = pH3PO4 ·qTBP(o)
(1)
where the subscripts a and o stand for the aqueous and organic phases, respectively. p and q are the stoichiometric coefficients of phosphoric acid and TBP, respectively, in the reaction. The equilibrium constant (Keq) of the extraction reaction in eq 1 is Keq =
[pH3PO4 ·qTBP](o) [H3PO4 ](a) p [TBP](o)q
(2)
The distribution coefficient of phosphoric acid is calculated as Dc =
[H3PO4 ](o) [H3PO4 ](a)
=
p[pH3PO4 ·qTBP](o) [H3PO4 ](a)
(3)
where [H3PO4](o) and [H3PO4](a) are the analytical concentrations of phosphoric acid in the organic and aqueous phases, respectively, at equilibrium. An indirect approximation method based on slope analysis was used to verify the stoichiometry of the extracted species.19 Inserting eq 3 into eq 2 and then taking the logarithm of both sides of the resulting equation leads to the expression
Figure 1. Schematic diagram of the constant-interfacial-area cell with laminar flow: (1,2) sampling hole, (3) water input, (4) water output, (5,6) stirrer, (7) thermostatic jacket, (8,9) flow deflector, (10) interfacial plate.
log Dc = log pKeq + (p − 1) log[H3PO4 ](a)
required temperature. The organic phase containing TBP was saturated with water before being used to avoid changing the aqueous-phase volume during the extraction process. Identical volumes (305.5 mL) of both phosphoric acidcalcium chloride solution and organic phase were maintained at the set temperature for 30 min, as was the apparatus. The aqueous phase was first added into the apparatus. Then, the organic phase was added carefully without disturbing the interface. The impellers were simultaneously started at the set speed. A stopwatch was employed to measure the time. Samples (1 mL) of the aqueous phase were withdrawn from sampling hole 1 for analysis at fixed intervals. Each time after sampling, 1 mL of the initial aqueous phase was added to the apparatus through sampling hole 1 with syringes to maintain the interface level. The phosphoric acid concentration in the aqueous phase was determined by the quinoline phosphomolybdate gravimetric method.17 The amount of phosphoric acid transferred into the organic phase was calculated according to the change in phosphoric acid content in the aqueous phase. 2.4. Interfacial Tension Determination. The interfacial tension was measured by the Wilhelmy plate method with a tensiometer (Fangrui BZY-201, Shanghai, China). TBP diluted in toluene was used as the organic phase, and doubly distilled water was used as the aqueous phase. Equal volumes (50 mL) of the two phases were mixed and shaken for 2 h at 298.15 ± 0.1 K until euquilibrium was reached. The mixture was left to settle for 2 h, and then, the two phases were separated before the measurements, abandoning layers at least 1 cm thick of both phases near the interface.
+ q log[TBP](o)
(4)
Inserting eq 3 into eq 4 gives log[H3PO4 ](o) = log pKeq + p log[H3PO4 ](a) + q log[TBP](o)
(5)
The relationship between the phosphoric acid distribution coefficient and the TBP concentration is illustrated in Figure 2. The concentrations of phosphoric acid and CaCl2 in the initial aqueous phase remained 1.45 and 2.80 mol/L, respectively. The results show that an increase of TBP concentration from 0.37 to 3.65 mol/L in the organic phase led to a considerable increase in the phosphoric acid distribution coefficient. In addition, there was no apparent difference in distribution
3. RESULTS AND DISCUSSION 3.1. Equilibrium Studies. Before studying the extraction kinetics of the system, it is very important to know the stoichiometry of the extracted complex, which can be determined by equilibrium studies. Assuming that phosphoric acid transfers into the organic phase in a neutral form and exists
Figure 2. Effect of TBP concentration on the phosphoric acid distribution coefficient at 298.15 K: (□) TBP in kerosene, (▲) TBP in cyclohexane. B
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coefficient between the TBP−kerosene system and the TBP− cyclohexane system, which indicates that the impact of nonpolar diluent types on the extraction process can be ignored. Using regression analysis, the following relations can be established from the obtained data:
15% CaCl2 in the initial phosphoric acid solution
TBP−kerosene system
20% CaCl2 in the initial phosphoric acid solution
log Dc = − 1.17 + 2.06 log[TBP](o) ,
R = 0.998
log[H3PO4 ](o) = −0.45 + 1.55 log[H3PO4 ](a) , R = 0.999
for [H3PO4 ](a) < 1.17 mol/L,
(6)
log[H3PO4 ](o) = −0.26 + 1.53 log[H3PO4 ](a) ,
TBP−cyclohexane system log Dc = − 1.22 + 2.09 log[TBP](o) ,
(11)
R = 0.999
R = 0.998
(7)
where R is the correlation coefficient. According to eq 4, the stoichiometric coefficient of TBP (q) in eq 1 is suggested to be 2. The relationship between the phosphoric acid concentrations of the organic and aqueous phases at equilibrium was studied by varying the concentration of phosphoric acid and CaCl2 using pure TBP. The data used here were from our previous work.3 Plots of [H3PO4](o) versus [H3PO4](a) are shown in Figure 3. The results indicate that [H3PO4](o) increases with
(12)
for [H3PO4 ](a) > 1.17 mol/L, log[H3PO4 ](o) = −0.25 + 0.93 log[H3PO4 ](a) , R = 1.000
(13)
25% CaCl2 in the initial phosphoric acid solution for [H3PO4 ](a) < 0.79 mol/L, log[H3PO4 ](o) = −0.04 + 1.27 log[H3PO4 ](a) , R = 0.998
(14)
for [H3PO4 ](a) > 0.79 mol/L, log[H3PO4 ](o) = −0.09 + 0.60 log[H3PO4 ](a) , R = 0.999
According to eq 5, the stoichiometric coefficient of H3PO4 (p) in eq 1 is suggested to be 1.5 for the conditions of 0−15% CaCl2 and lower phosphoric acid concentrations in 20% and 25% CaCl2. The extracted complex is suggested to be 3 /2H3PO4·2TBP, which indicates that there might be two types of the extracted complex: H3PO4·TBP and H3PO4·2TBP. The ratio of the two complexes is 1:1. The stoichiometric coefficient of H3PO4 reduces to about 1 when [H3PO4](a) exceeds 1.17 mol/L in the presence of 20% CaCl2. The extracted complex is suggested to be H3PO4·2TBP. The stoichiometric coefficient of H3PO4 becomes even smaller, ∼0.6, when [H3PO4](a) exceeds 0.79 mol/L in the presence of 25% CaCl2. The extracted complex is demonstrated to be H3PO4·3TBP. The results obtained suggest that the mole ratio of TBP to phosphoric acid participating in the reaction increases as the concentration of H3PO4 and CaCl2 increases. Previous studies also reported these three species with the TBP/H3PO4 stoichiometries 1:1, 2:1, and 3:1.18,20,21 A comparison of the IR spectra of TBP obtained before and after extraction of phosphoric acid is presented in Figure 4. The IR spectrum of TBP shows a band at 1280 cm−1 corresponding to the PO bond stretching vibration. The band at 1030 cm−1 is assigned to the stretching vibration of POC. As the material TBP contains a little water, the spectrum also shows the band at 3500 cm−1 corresponding to the OH bond vibration and the band at 1690 cm−1 ascribed to the OH bond deformation vibration. The main difference between the spectra of phosphoric acid loaded TBP and pure TBP is the appearance of broad bands at about 3400, 2650, and 2150 cm−1 representing O−H bond vibrations. The intensity of the band at 1690 cm−1 also increases slightly. The band at 1030 cm−1 broadens because of the superposition of the vibrations of P OC and POH. Based on these changes, it was concluded that phosphoric acid had been extracted into the
Figure 3. Equilibrium isotherms between the analytical concentrations of the organic phase ([H3 PO4] (o) ) and the aqueous phase ([H3PO4](a)) for the extraction of phosphoric acid by TBP at 298.15 K: (■) 0%, (□) 5%, (▲) 10%, (Δ) 15%, (●) 20%, and (○) 25% CaCl2.
increasing [H3PO4](a) and calcium chloride concentrations. Using regression analysis, the following relations can be established from the obtained data: 0% CaCl2 in the initial phosphoric acid solution log[H3PO4 ](o) = −0.92 + 1.53 log[H3PO4 ](a) , R = 0.997
(8)
5% CaCl2 in the initial phosphoric acid solution log[H3PO4 ](o) = −0.78 + 1.55 log[H3PO4 ](a) , R = 0.999
(9)
10% CaCl2 in the initial phosphoric acid solution log[H3PO4 ](o) = −0.64 + 1.55 log[H3PO4 ](a) , R = 1.000
(15)
(10) C
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Figure 4. Comparison of the IR spectra of TBP (A) before and (B) after extraction of phosphoric acid.
Figure 5. Effect of stirring speed on the extraction rate of phosphoric acid. Conditions: [H3PO4] = 1.45 mol/L, [CaCl2] = 2.80 mol/L, [TBP] = 3.40 mol/L, S = 45 cm2, Vo = Va = 305.5 cm3, T = 298.15 K.
organic phase after extraction. Moreover, the peak at 1280 cm−1 shifted to lower frequency at 1250 cm−1, which indicates that a hydrogen bond (PO···H) formed between the oxygen atom of the phosphoryl group of the TBP molecule and the hydrogen atom of the phosphoric acid molecule. 3.2. Kinetic Studies. The extraction rate (r) can be expressed as the change in concentration of phosphoric acid per unit time. At the beginning of the extraction process, backextraction can be ignored. Therefore, the extraction rate can be expressed as r=
d[H3PO4 ](o) dt
=−
d[H3PO4 ](a) dt
the following stirring conditions: (1) The stirring speed was separately 0 and 300 rpm in the aqueous and organic phases, respectively (0, 300 rpm). (2) The stirring speed was separately 300 and 0 rpm in the aqueous and organic phases, respectively (300, 0 rpm). (3) The stirring speed was 300 rpm in both phases (300, 300 rpm). A plot of [H3PO4](a) versus the extraction time is shown in Figure 6. The changes in the
= k[H3PO4 ]b [TBP]c (16)
where k is the extraction rate constant and b and c are the reaction orders with respect to H3PO4 and TBP, respectively. Taking the logarithm of both sides of eq 16 gives log r = log k + b log[H3PO4 ] + c log[TBP]
(17)
3.2.1. Effect of Stirring Speed. The effect of the stirring speed on the extraction rate was studied to determine the contribution of diffusion resistance. The stirring speed was varied from 50 to 400 rpm. A plot of the extraction rate versus the stirring speed is shown in Figure 5. The extraction rate increased linearly as the stirring speed was increased from 50 to 300 rpm and then increased sharply at stirring speeds of 350 and 400 rpm. The sharp increase in the extraction rate is because of the disturbance of the interface caused by the high stirring speed and vibration of the motors. There were slight waves at the interface at stirring speeds of 350 and 400 rpm. Under these conditions, the area of the interface was no longer fixed. In contrast, the interface was always smooth and stable at stirring speeds ranging from 50 to 300 rpm. Further experiments were carried out at a stirring speed of 300 rpm to keep the interface stable and maintain the same hydrodynamics. At this stirring speed, the Reynolds number was about 960 (calibrated with water at 298.15 K). As the extraction rate was found to depend on the stirring speed in the range from 50 to 300 rpm, the extration might be controlled by diffusion. However, the possibility of a mixed-control regime cannot be excluded.16 3.2.2. Diffusion Resistance Zone. To determine the diffusion resistance zone, experiments were carried out under
Figure 6. Effect of different stirring conditions on the extraction rate of phosphoric acid. Conditions: [H3PO4] = 1.45 mol/L, [CaCl2] = 2.80 mol/L, [TBP] = 3.40 mol/L, S = 45 cm2, Vo = Va = 305.5 cm3, T = 298.15 K. (●) (0, 300 rpm), (▲) (300, 0 rpm), (■) (300, 300 rpm).
phosphoric acid concentration in the aqueous phase under stirring conditions 2 and 3 were almost the same. However, in comparison, the changes in the phosphoric acid concentration under stirring conditions 1 were very small and could almost be ignored. These results indicate that the diffusion resistance in the aqueous phase is much higher than that in the organic phase. That is, the diffusion resistance was mainly in the aqueous phase. 3.2.3. Effect of Temperature. The effect of temperature on the extraction rate was studied within the range from 293.15 to 308.15 K. A plot of log r versus 1/T is shown in Figure 7. The D
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3.2.4. Reaction Zone. The effect of the interfacial area was studied in the range from 26 to 45 cm2 to determine whether the extraction reaction takes place in the bulk phase or at the interface. A linear relationship between the extraction rate and the interfacial area is shown in Figure 8. A previous study
Figure 7. Effect of temperature on the extraction rate of phosphoric acid. Conditions: [H3PO4] = 1.45 mol/L, [CaCl2] = 2.80 mol/L, [TBP] = 3.40 mol/L, S = 45 cm2, Vo = Va = 305.5 cm3, n = 300 rpm.
extraction rate increased with increasing temperature. The experimental data can be treated according to the Arrhenius equation22 Ea log k = − + log A 2.303RT
Figure 8. Effect of interfacial area on the extraction rate of phosphoric acid. Conditions: [H3PO4] = 1.45 mol/L, [CaCl2] = 2.80 mol/L, [TBP] = 3.40 mol/L, Vo = Va = 305.5 cm3, n = 300 rpm, T = 298.15 K.
(18)
where R is molar gas constant, Ea is the apparent activation energy, and A is pre-exponential factor. Inserting eq 18 into eq 17 leads to the expression log r = −
showed that the extraction rate is independent of the interfacial area when the extraction reaction occurs in the bulk phase.23 By contrast, the extraction rate increases with increasing interfacial area when the reaction occurs at the interface. In this system, the extraction rate of phosphoric acid was found to be dependent on the interfacial area, which indicates that the extraction reaction possibly occurs at the interface. Furthermore, because of the structure of the TBP molecule, a monolayer forms at the interface with the phosphoryl dipoles pointing toward the aqueous phase and the alkyl chains more or less in the organic phase.24 This results in the strong absorption of TBP at the interface, supporting the possibility of an interfacial reaction. The interfacial tension isotherm for TBP at the toluene/water interface is presented in Figure 9. The experimental data were fitted by the Szyszkowski equation25
Ea + log A + b log[H3PO4 ] 2.303RT
+ c log[TBP]
(19)
As the concentrations of H3PO4 and TBP were fixed, the apparent activation energy was calculated from the slope of log r versus 1/T plot; its value was found to be 39.16 kJ/mol. The value of Ea is an important criterion for determining the reaction regime. If the reaction rate is controlled by a chemical reaction, Ea is greater than 42 kJ/mol, whereas for a diffusioncontrolled process, Ea is less than 20 kJ/mol. Ea values in the range of 20−42 kJ/mol are expected for mixed-control regimes.16 The Ea value together with the conclusions of section 3.2.1 indicate that the extraction of phosphoric acid in the investigated system is under mixed control. According to Biswas et al.10 and Wang et al.,14 specific rate theory can be expressed as log
rh ΔH ΔS =− + + log([H3PO4 ]b [TBP]c ) k′T 2.303RT 2.303R (20)
where h is Planck’s constant; k′ is the Boltzmann constant; and ΔH and ΔS are the enthalpy and entropy of activation, respectively. The plot of log rh/(k′T) versus 1/T yielded a straight line, as shown in Figure 7, from the slope of which the enthalpy of activation was calculated to be 36.66 kJ/mol. The entropy of activation was calculated to be −225.09 J/(mol·K) from the intercept of the line. The Gibbs free energy of activation (ΔG) at a particular temperature can be calculated as ΔG = ΔH − T ΔS
(21)
Thus, the Gibbs free energy of activation at 298.15 K (ΔG298.15) was calculated to be 103.77 kJ/mol.
Figure 9. Interfacial tension isotherm for TBP at the toluene/water interface at 298.15 K. E
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(22)
where γ0 is the interfacial tension for concentration c′ = 0. A′ and B are the adsorption coefficients and are calculated by the Levenberg−Marquardt algorithm. The surface excess at the saturated interface (Γ∞) and the Gibbs free energy of adsorption (ΔGads) can be calculated according to the equations Bγ Γ∞ = 0 (23) RT ΔGads = RT ln A′
(24)
These values were determined as follows: A′ = 5.31 × 10−4 mol/L, B = 8.89 × 10−2, Γ∞ = 1.28 × 10−6 mol/m2, and ΔGads = −18.44 kJ/mol. The surface excess at the saturated interface determined in this work is slightly lower than the value reported in the literature (1.67 × 10−6 mol/m2).25 In addition to the surface activity of TBP, its low solubility in the aqueous phase also supports the possibility of an interfacial reaction. Our previous work showed that the concentration of TBP in the aqueous phase is very low (∼0.1%).3 The solubility of TBP in the aqueous phase reported in the literature is even lower (
