1036
Anal. Chem. 1989, 61, 1036-1040
Investigation of Fast Mass Transfer Kinetics in Solvent Extraction Using Rapid Stirring and a Porous Membrane Phase Separator Lawrence Amankwa a n d Frederick F. Cantwell*
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
An improved apparatus Is descrlbed for performing llquldllquld extraction rate studies under turbulent condltlons. The contribution to band broadenlng of various Instrument components Is measured. I t Is shown that the resulting absorbance versus time proflle for an extractlon experlences severe dlstortlon due to Instrument band broadening and that this dlstortlon can be mathematically ellmlnated via deconvolution In order to obtaln the mass transfer coefflclent, Studies on the extraction of o-nltroanlllne from the dlspersed aqueous phase Into chloroform and on the extraction of onitrophenolate from the contlnuous phase Into the dispersed phase show that Is about the same for both processes = 2 X 1 0 - ~cm/s).
8.
(B
8
In many of the solvent extraction systems that are important in analytical (I),synthetic (2),and hydrometallurgical (3)applications a chemical reaction accompanies the transfer of solute from one bulk liquid phase to the other. The rate of solvent extraction in such systems may be governed by the rate of the chemical reaction, by the rate of mass transfer between the phases, or by some combination of both chemical and mass transfer rates (4, 5 ) . Considering only the mass transfer rate, the overall resistance to mass transfer for extraction of solute from phase Y into phase X is the sum of resistances in each of the two liquid phases X and Y and at the interface itself, the last usually being negligible (4, 6). When the equilibrium distribution coefficient for extraction of solute strongly favors the X phase, then the resistance to mass transfer in the Y phase is much larger than that in the X phase. Under these conditions, the mass transfer rate constant k , (9-l) is given by the equation ~ M = T (A/Vy@y (1) where A (cm2)is the interfacial area between the two liquid phases, V yis the volume of the liquid phase Y, and & (cms-'), the overall mass transfer coefficient, is equal to the mass transfer coefficient in the Y phase. p y is often taken as a constant under fixed hydrodynamic conditions (4-6). When a chemical reaction accompanies mass transfer, the experimentally observed rate constant kobd is related to the chemical rate constant k , and mass transfer rate constant as follows: - 1- - - 1+ - 1 (2) kobsd
k,
kMT
Provided that the chemical reaction does not involve a reactant that is adsorbed at the liquid-liquid interface, k, is independent of both A and By. If a reactant is interfacially adsorbed, then the k , in eq 2 is still independent of Py, but it is dependent on A and is related to the true chemical reaction rate constant by the factor A / V , ( 4 ) . Regardless of whether the chemical reaction occurs in the liquid phase or a t the interface or both, in designing in extraction experiment to 0003-2700/89/0361-1036$01.50/0
measure a chemical reaction rate the goal is to make kMT larger than k,. Of the techniques used to measure solvent extraction rates (4, 7,8),the rotating diffusion cell (7,9),the single drop apparatus (7,10,1 I), and the rapid-stir cell can produce large enough values of p y and km to permit the measurement of relatively fast chemical reactions. An advantage of the rapid-stir experiment is the fact that the entire concentration versus time profile for the extraction is obtained in a single experiment ( 5 ) . A disadvantage is the fact that hydrodynamic conditions are ill-defined (4, 7). However, drop size (and thus A / V y ) can be measured experimentally (4, 12, 13), and both drop size and & can be estimated from theoretical models (IO,12-16) to yield an order of magnitude accuracy for the estimated value of.,k If the theoretically predicted km is much larger than the chemical reaction rate constant to be measured, one can be reasonably sure that the observed extraction rate is free from partial mass transfer control and that k o b d is equal to k,. In fact, in rapidly stirred systems where ~ M isT large, systematic errors in measured chemical reaction rate constants are more likely to arise from instrumental artifacts such as band broadening in the phase separator, detector, and connecting tubing ( 5 ) ,than they are from failure to recognize partial mass transfer control of the overall extraction rate, as will be shown below. The goals of the work reported here have been as follows: (i) design a rapid-stir cell employing remote sample injection and a porous membrane phase separator, in which instrument band broadening effects are minimized; (ii) measure the contribution of instrument components to band broadening; (iii) eliminate instrument band broadening effects by mathematical deconvolution using an algorithm based on fast Fourier transform (FFT)in order to measure the actual mass transfer rates for extraction of solute both out of aqueous droplets and into aqueous droplets. EXPERIMENTAL SECTION Apparatus. An overall schematic diagram is shown in Figure 1,and an enlarged view of the. extraction cell is shown in Figure 2. The main componenta are the extraction cell (E), a variable wavelength photometric detector (D)with an 8-pL flow cell (UV 50, Varian Associates), a strip chart recorder (R) (Recordall 500, Fisher Scientific), an IBM-XT microcomputer (C) interfaced to the detector via a Lab Master ADC Interface Board (TM-40-P6L, Tecmar, Cleveland, OH), and a variable speed peristaltic pump (P) (Minipuls 2, Gilson, Ville-le-Belle,France). The stainless steel extraction cell has a volume of 270 mL. It is stirred at 2300 r-rnin-l by a high-speed stirring motor (M) (Model HST 20N No. 447401 G.K., Heller Corp., Floral Park, NY) and a 3 cm diameter Teflon impeller (I). There are four 8 mm wide baffles (H). The impeller shaft (S) passes through a combination of Rulon (No. 9127, Johnston Industrial Plastics) and Teflon bearings (W) in the lid, which, purposely, are not made airtight in order to allow pressure equalization between the extraction cell and the airtight aluminum cylinder (A) that surrounds it. This aluminum cylinder is pressurized at 20 psig with nitrogen from tank T1, which creates a constant-pressure pumping device that causes chloroform phase to flow out of the extraction cell through 0 1989 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989
A
Figure 1. Diagram of the extraction apparatus: A, aluminum pressure cylinder; E, stainless steel extraction cell; M, high-speed stirring motor; B, circulating constant temperature bath; T, and T,, tanks of pressurized nitrogen; D, spectrophotometer detector; C, microcomputer; R, strip chart recorder; P, peristaltic pump; V,, solenoid valve, V, manual valve.
l
n nl
1
S
c
Diagram of the stainless steel rapid-stir extraction cell: S, stirrer shaft; F, filter probe tube; I, impeller; K, injector; H, baffle; W, Teflon and Rulon bearings; X, Teflon plug; Z, Teflon plunger. Flgure 2.
the membrane phase separator. The extraction cell is immersed in water in the aluminum cylinder, which is held at 20 f 0.1 O C by means of copper coils (not shown) that are connected to a circulating constant-temperature water bath (B) (Fisher Scientific). Threaded into the lid of the steel extraction cell is a removable injection capsule (K). Injection is made pneumatically by electrically actuating the solenoid valve (V,) (skinner V520V2100, Honeywell Ltd., Scarborough, ON). This causes nitrogen pressure (80 psig) from tank T2to drive the Teflon plunger (Z) down in the injection capsule, thereby forcing the small Teflon plug (X) to pop out and expelling the solution from the capsule into the extraction cell. The "filter probe" (F) is made of a 12 cm long by 0.25 in. 0.d. by 0.5 mm i.d. stainlesssteel tube with either of two sizes of porous Teflon membrane phase separators fitted on the end, similar to what has previously been described (17, 18). The small probe had a membrane area of 0.28 cm2, and the large probe had a membrane area of 1.32 cm2. The chloroform phase passes from the probe tube through a piece of Teflon tubing (54 cm long by 0.3 mm i.d.) to the flow
1037
cell of the photometric detector and then through a similar Teflon tube from the detector cell to an Acidflex peristaltic pump tube (12.7 cm long by 0.88 mm i.d.) (Technicon Corp., Tarrytown, NY). The pumping rate was 1.00 mlamin-', unless otherwise specified. The three-port valve V2 (Model No. CAV 3031, L E ) either directs the chloroform to waste or returns it to the extraction cell via 60 cm of 0.5 mm i.d. Teflon tubing. Flow to waste was used only when extraction times were under 1 min, since the volume of organic phase lost represented a change in organic to aqueous phase ratio of less than 1%. Reagents and Solvents. All water was demineralized, distilled, and finally distilled over alkaline permanganate. All solvents and chemicals were of reagent grade. Chloroform (Caledon Labs, Ltd.) was washed with distilled water prior to use. Aqueous pH 6.5 buffer at ionic strength of 0.050 was prepared from Na2HP04and NaH2P04. Stock solutions of o-nitroanilinewere prepared in pH 6.5 buffer of ionic strength 0.050 and in chloroform. A stock solution of o-nitrophenol was prepared in chloroform. Extraction of o-Nitroaniline from Water. Initially, 100 mL of chloroform and 99 mL of pH 6.5 phosphate buffer were placed in the extraction cell. Absorbance of chloroform was monitored at 396 nm. After a steady base line was established, 1.00 mL of M o-nitroaniline in aqueous buffer was injected to initiate the experiment. Another experiment was performed in which 99 mL of chloroform and 100 mL of aqueous buffer were initially in the extraction cell and 1.00 mL of M o-nitroaniline in chloroform was injected. Data from this latter experiment were used to generate both the instrument variance, u?, and the impulse response function (IRF). Extraction of o-Nitrophenol from Chloroform. Initially, 100 mL of a 10"' M solution of o-nitrophenol in chloroform and 99 mL of aqueous pH 6.5 buffer were placed in the extraction cell. Absorbance of chloroform was monitored at 354 nm. After a steady base line was established, 1.00 mL of aqueous sodium hydroxide (0.4, 1.0, 4.0, and 6.0 M) was injected to initiate the experiment. Another experiment was performed in which the extraction cell contained 99 mL of chloroform and 100 mL of aqueous pH 6.5 M solution of o-nitrophenol buffer and in which 1.00 mL of a in chloroform was injected. Data from this latter experiment were used to generate the IRF. Evaluation of Band Broadening. Each sigmoidal extraction profile of chloroform absorbance ( A ) versus time ( t ) was mathematically converted to a peak by taking the first derivative. The variance of the A vs t profile, u* (in units of s2), was calculated as the second statistical moment of this peak (19). Calculations were performed on an IBM-XT microcomputer using programs written in ASYST (MacMillan Software Co., New York) (20). Experimentally, variances were measured as follows. For the overall variance, u:, an aqueous solution of o-nitroaniline was injected. For the instrument variance, u t , a chloroform solution of o-nitroaniline was injected. For the parts of the instrument variance associated with the small membrane phase separator, probe tube, connecting tubing, detector, and computer, uI12,the pump was turned on only after extraction equilibrium had been reached. For the variance associated with the probe tube, connecting tubing, detector, and computer, u12, the only liquid in the extraction cell was a chloroform solution of o-nitroanilineand the membrane phase separator was removed from the end of the probe tube. For the variance associated with the detector and computer, a slider type sample injection valve was placed in the Teflon tubing line immediately before the detector. Five different sliders were used to inject 1,2,5,10,and 20 pL of an o-nitroaniline solution in chloroform, respectively, into a chloroform flow stream at each of three different chloroform flow rates, 0.66,1.0, and 1.5 rnl-min-'. Deconvolution. For a large number of data points, deconvolution is best performed by using the "fast Fourier transform" algorithm (21). Deconvolution was achieved as follows. First, the sample A vs t profile (e.g. Figure 3A) was differentiated and smoothed to obtain a peak. This operation significantlyreduced the deleterious effect of signal noise on the final result. Next, the IRF was obtained from the A vs t profiles in the second part of the experiment (e.g. Figure 3B) as previously described (5). FFTs were taken of the peak-shaped sample function and of the
1038
ANALYTICAL CHEMISTRY, VOL. 61, NO. 9, MAY 1, 1989 1.o
Table I. Variances Associated with Instrument Components and Mass Transfer for Extraction of o -Nitroaniline from Water into Chloroform component or process
injection and mixing
0.36 f 0.09
small phase separator probe tube and tubing detector and computern
0.41 f 0.26
mass transfer
0.31 f 0.10 3.56 f 0.49
overall (I
TIME (S)
Flgure 3. Absorbance of the chloroform phase vs time: (A) for
injection of o-nitroaniline in a water solution (includes extraction from water into chloroform); (B) for injection of o-nitroaniline already in chloroform; (C) after deconvolution of curve A with the IRF from curve 0.
IRF, the former was divided by the latter, and an inverse Fourier transform was performed to yield the peak-shaped derivative of the desired result. Integration then yielded the desired A vs t profile (e.g. Figure 3C). RESULTS AND DISCUSSION The overall variance, 62, for a system in which a chemical reaction accompanies mass transfer is the sum of contributions due to chemical reaction (gR2), mass transfer (a&, and instrument band broadening ( ~ 1 ~ ) .
=
+
+
(3) For the systems described in this work either no chemical reaction occurs or the accompanying chemical reaction is very fast (k,is large). For such systems ffR2
