The extraction (liquid/liquid and solid/ liquid) is very common in the treatment of ores but also in the food, pharmaceutical and cosmetic industry and in the production of essential oils, as well as the purification of effluent streams in order to remove unwanted contaminants and toxic, which already exist in very small amount, for example The liquidliquid extraction of the weak base B is governed by the following equilibrium reactions: \[\begin{array}{c}{\mathrm{B}(a q) \rightleftharpoons \mathrm{B}(org) \quad K_{D}=5.00} \\ {\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\rightleftharpoons \mathrm{OH}^{-}(a q)+\mathrm{HB}^{+}(a q) \quad K_{b}=1.0 \times 10^{-4}}\end{array} \nonumber\]. A. Note that D is related to the G of the extraction process[clarification needed]. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. 2 For instance, if the distribution ratio for nickel (DNi) is 10 and the distribution ratio for silver (DAg) is 100, then the silver/nickel separation factor (SFAg/Ni) is equal to DAg/DNi = SFAg/Ni = 10.[5]. A Low-Cost Aqueous Two Phase System for Enzyme Extraction. LLE is a basic technique in chemical laboratories, where it is performed using a variety of apparatus, from separatory funnels to countercurrent distribution equipment called as mixer settlers. Traditionally, the polysaccharide used is dextran. Stripping is the opposite of extraction: Transfer of mass from organic to aqueous phase. Absorption and stripping employ special contactors for bringing gas and liquid phases into intimate contact. Note the position of point \(M\). To plan a liquidliquid extraction we need to know the solutes distribution ratio between the two phases. Experimental Procedure 3. Two types of extraction units may be provided - liquid liquid extraction and solid liquid extraction. LLE is also widely used in the production of fine organic compounds, the processing of perfumes, the production of vegetable oils and biodiesel, and other industries. Locate point \(R_N\) on the ternary phase diagram. There are two solvents involved and a solute which is transferred from one to . [28] Cobalt can be extracted also using Ionquest 290 or Cyanex 272 {bis-(2,4,4-trimethylpentyl) phosphinic acid}. where CHL is the ligands initial concentration in the organic phase. Table 7.7.1 Department of Chemical Engineering Illinois Institute of Technology. . [4], The separation factor is one distribution ratio divided by another; it is a measure of the ability of the system to separate two solutes. This page titled 7.7: Liquid-Liquid Extractions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. \[D=\frac{K_{\mathrm{D}}\left[\mathrm{H}_{3} \mathrm{O}_{aq}^{+}\right]}{\left[\mathrm{H}_{3} \mathrm{O}_{aq}^{+}\right]+K_{a}} \label{7.11}\]. \(N\) = Final stage. Solid-phase extraction offers a range of benefits over liquid-liquid extraction such as the removal of possible emulsion formation and the ability for quantitative recovery. Liquid-liquid extraction is an important unit operation used to separate liquid components when distillation is difficult and/or expensive. Using solvent extraction it is possible to extract uranium, plutonium, thorium and many rare earth elements from acid solutions in a selective way by using the right choice of organic extracting solvent and diluent. A solution of solute (A) in diluent (B) is mixed with a solvent (S). The intersection of these two lines is mixing point \(M\). The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. , explain how we can separate the metal ions in an aqueous mixture of Cu2+, Cd2+, and Ni2+ by extracting with an equal volume of dithizone in CCl4. When the pH is 1.00 the distribution ratio is, \[D=\frac{\left(2.5 \times 10^{16}\right)\left(7.0 \times 10^{4}\right)\left(5.0 \times 10^{-5}\right)^{2}\left(1.0 \times 10^{-4}\right)^{2}}{\left(1.0 \times 10^{4}\right)^{2}(0.10)^{2}+\left(2.5 \times 10^{16}\right)\left(5.0 \times 10^{-5}\right)^{2}\left(1.0 \times 10^{-4}\right)^{2}} \nonumber\], or a D of 0.0438. Determining minimum feasible solvent mass ratio (\(S_{\rm min}/F\)) when (1) feed composition; (2) incoming solvent composition; and (3) outgoing raffinate composition have been specified/selected. This is where the fresh solvent S enters the system and the final raffinate \(R_N\) leaves the system. This is where the fresh solvent \(S\) enters the system and the final raffinate \(R_N\) leaves the system. On a fresh copy of the graph, with plenty of blank space on each side of the diagram, note the location of points \(F\), \(S\), and \(R_N\) (specified/selected) and \(E_1\) (determined in step 3). Extend to both sides of the diagram. Liquid-Liquid Extraction Column: Selection, Scale-up and Design. shows how we can use Equation \ref{7.6} to calculate the efficiency of a simple liquid-liquid extraction. The first step of an extraction process is mixing for an intensive contact of both liquid phases to enable the mass transfer of the product (white dots) from the (blue) feed . Gangue material is removed by the milling and floats on the water-immiscible liquid to be removed without further processing. Ionic liquids systems. A classic example is the extraction of carboxylic acids (HA) into nonpolar media such as benzene. One obtains high-purity single metal streams on 'stripping' out the metal value from the 'loaded' organic wherein one can precipitate or deposit the metal value. or by a correlation process of experimental data.[21][22][23][24]. In solvent extraction, a distribution ratio is often quoted as a measure of how well-extracted a species is. Examples of other reactions that affect extraction efficiency include acidbase reactions and complexation reactions. 1000 kg/hr of 30 wt% acetone and 70 wt% water is to be extracted with 1000 kg/hr of pure MIBK. Note the intersection of these two lines and label as \(P\). One phase usually is an aqueous solvent and the other phase is an organic solvent, such as the pentane used to extract trihalomethanes from water. 1 Introduction. \(M\) = Composition of the overall mixture. Source with confidence. Extraction [edit | edit source] Extraction is the general practice of taking something dissolved in one liquid and forcing it to become dissolved in another liquid. The two phases enter the mixing section where they are mixed using an impeller. shows the relevant equilibrium reactions (and equilibrium constants) for the extraction of Mn+ by the ligand HL, including the ligands extraction into the aqueous phase (KD,HL), the ligands acid dissociation reaction (Ka), the formation of the metalligand complex (\(\beta_n\)), and the complexs extraction into the organic phase (KD,c). [not verified in body]. Before their analysis by gas chromatography, trihalomethanes are separated from their aqueous matrix using a liquidliquid extraction with pentane [The Analysis of Trihalomethanes in Drinking Water by Liquid Extraction,EPAMethod501.2 (EPA 500-Series, November 1979)]. (a) The fraction of solute that remains in the aqueous phase after the extraction is given by Equation \ref{7.6}. This is often done to aid further separations, such as distillation, by putting the compound of interest into a solvent with a greater difference in boiling temperature. Ionic Liquids for Aqueous Two-Phase Extraction and Stabilization of Enzymes. Methods to improve the demixing include centrifugation, and application of an electric field. Liquid-liquid extraction, also known as solvent extraction, is a method to separate compounds based on their relative solubilities in two different immiscible liquids, usually water and an organic solvent. From Table 7.7.1 Solving Equation \ref{7.2} for (mol Sorg)1 and substituting into Equation \ref{7.4} leave us with, \[\left[S_{o r g}\right]_{1} = \frac{\left(\operatorname{mol} \ S_{a q}\right)_{0}-\left(\operatorname{mol} \ S_{a q}\right)_{1}}{V_{o r g}} \label{7.5}\], Substituting Equation \ref{7.3} and Equation \ref{7.5} into Equation \ref{7.1} gives, \[D = \frac {\frac {(\text{mol }S_{aq})_0-(\text{mol }S_{aq})_1} {V_{org}}} {\frac {(\text{mol }S_{aq})_1} {V_{aq}}} = \frac{\left(\operatorname{mol} \ S_{a q}\right)_{0} \times V_{a q}-\left(\operatorname{mol} \ S_{a q}\right)_{1} \times V_{a q}}{\left(\operatorname{mol} \ S_{a q}\right)_{1} \times V_{o r g}} \nonumber\], Rearranging and solving for the fraction of solute that remains in the aqueous phase after one extraction, (qaq)1, gives, \[\left(q_{aq}\right)_{1} = \frac{\left(\operatorname{mol} \ S_{aq}\right)_{1}}{\left(\operatorname{mol} \ S_{a q}\right)_{0}} = \frac{V_{aq}}{D V_{o r g}+V_{a q}} \label{7.6}\], The fraction present in the organic phase after one extraction, (qorg)1, is, \[\left(q_{o r g}\right)_{1}=\frac{\left(\operatorname{mol} S_{o r g}\right)_{1}}{\left(\operatorname{mol} S_{a q}\right)_{0}}=1-\left(q_{a q}\right)_{1}=\frac{D V_{o r g}}{D V_{o r g}+V_{a q}} \nonumber\]. The extraction of cobalt from hydrochloric acid using Alamine 336 (tri-octyl/decyl amine) in meta-xylene. We intend that the raffinate contain no more than 5.0 wt% acetone. , a quantitative separation of Cu2+ from Cd2+ and from Ni2+ is possible if we acidify the aqueous phase to a pH of less than 1. -page10 There are two types of extraction, liquid-liquid extraction also known as solvent extraction as well as solid-liquid extraction. Liquid-Liquid Extraction Lab 05 Unit Operations Suppose you have this Data Collected from some Literature:- EXPERIMLNT A EXPERIMENT B Waier Raw rate = 031 L minin Organie flow race = 0.3 L / min Packing dimension: length = 1.2 m Dianceter = 50 mar Ending distriturion woefficicat: K = Y OX Whicre-Y concetcatios of ickete in extrat phine. The organic phase may then be treated to make it ready for use again.[19][20]. In its simplest form, this involves the extraction of a solute from a binary solution by bringing it into contact with a second immiscible solvent in which the solute is soluble. In that case, a soluble compound is separated from an insoluble compound or a complex matrix. Assume that the extract is the continuous phase, a residence time of 5 minutes in the mixing vessel, standard sizing of the mixing vessel and impeller. We take a liquid which is called a solvent and contact it intimately with the solid in order to extract the solute from the solid and bring it into the liquid thus effecting a separation. In a simple liquidliquid extraction the solute partitions itself between two immiscible phases. From here, one can determine steps for optimization of the process.[6]. Ionic liquids are ionic compounds with low melting points. The two phases would then be separated. It is possible by careful choice of counterion to extract a metal. The best way to understand the success of an extraction column is through the liquidliquid equilibrium (LLE) data set. Figure 7.7.6 For the conditions in Example 7.7.1 Number of Transfer Units Method (NTU Method) To determine number of transfer units (N OL) and K x a, develop a table as follows. The transfer is driven by chemical potential, i.e. A mixer settler consists of a first stage that mixes the phases together followed by a quiescent settling stage that allows the phases to separate by gravity. \((x_i)_n\) = Mass fraction of species \(i\) in the raffinate leaving stage \(n\), \((y_i)_n\) = Mass fraction of species \(i\) in the extract leaving stage \(n\). Aqueous Two-Phase Extractions in Bioseparations: An Assessment. The I3 anion is an example of a polyhalide anion that is quite common. In this case the distribution ratio and the partition coefficient are equal. Filter By category Extraction Systems Liquid or Solid Extraction Devices brands Biotage (1) Chemglass Life Sciences (14) Corning (5) Connect point \(E_N\) to operating point \(P\) with a straight line, mark the location of \(R_{N-1}\). Solid-liquid extraction processes, both traditional ones (maceration and percolation) and those introduced more recently (e.g., supercritical fluid extraction (SFE) and accelerated solvent extraction (ASE), are based on two fundamental principles: diffusion and/or osmosis. When a solvent is extracted, two immiscible liquids are shaken together. Follow the tie-lines from stream \(R_{N-1}\) to \(E_{N-1}\). The last two examples provide us with an important observationfor any extraction efficiency, we need less solvent if we complete several extractions using smaller portions of solvent instead of one extraction using a larger volume of solvent. Points (\(F\) and \(S\)) and (\(E_1\) and \(R_N\)) are connected by a straight line passing through \(M\). Thus, polymersalt systems are not as useful for purifying proteins. Because a ligands ability to form a metalligand complex varies substantially from metal ion to metal ion, significant selectivity is possible if we carefully control the pH. One important application of a liquidliquid extraction is the selective extraction of metal ions using an organic ligand. Liquid-Liquid Extraction: Sizing Mixer-settler Units C = volume fraction occupied by the continuous phase D = volume fraction occupied by the dispersed phase C = viscosity of the continuous phase (mass time -1 length -1) D = viscosity of the dispersed phase (mass time -1 length -1) M = viscosity of the mixture (mass time -1 length -1) At a pH of 9, most of the weak base is present as HB+, which explains why the overall extraction efficiency is so poor. Dechema Chemistry Data Series, Dortmund Data Bank, etc.) Background: Liquid-Liquid Extraction (LLE) is a unit operation that uses mass transfer as the driving force for separation. This quantitative measure is known as the distribution ratio or distribution coefficient. This is a charged species that transfers another ion to the organic phase. Chemical Engineering Separations: A Handbook for Students (Lamm and Jarboe), { "1.01:_Performance_Metrics_for_Separation_Processes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.02:_Mass_Transfer_in_Gas-liquid_Systems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.03:_Liquid-liquid_Extraction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.04:_Absorption_and_Stripping" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.05:_Distillation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.06:_Membranes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.07:_Sorption_and_Chromatography" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Chapters" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "license:ccbync", "licenseversion:40", "authorname:lamm-jarboe", "source@https://iastate.pressbooks.pub/chemicalengineeringseparations" ], https://eng.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Feng.libretexts.org%2FBookshelves%2FChemical_Engineering%2FChemical_Engineering_Separations%253A_A_Handbook_for_Students_(Lamm_and_Jarboe)%2F01%253A_Chapters%2F1.03%253A_Liquid-liquid_Extraction, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Staged Liquid-Liquid Extraction and Hunter Nash Method, Hunter Nash Method for Finding Smin, Tank Sizing and Power Consumption for Mixer-Settler Units, Staged LLE: Hunter-Nash Method for Finding the Minimum Solvent to Feed Ratio, Liquid-Liquid Extraction: Sizing Mixer-settler Units, Modeling Mass Transfer in Mixer-Settler Units, Hunter Nash Method 1: Mixing and Operating Points, source@https://iastate.pressbooks.pub/chemicalengineeringseparations, status page at https://status.libretexts.org. Liquid-liquid extraction (also called solvent extraction) was initially utilized in the petroleum industry beginning in the 1930's. It has since been utilized in numerous applications including . This pH is greater than the minimum pH for extracting Cu2+ and significantly less than the minimum pH for extracting either Cd2+ or Ni2+. Liquid-liquid extraction is a fundamental material transfer operation in chemical engineering based on the varying . Including a Thermodynamic Review and a Graphical User Interface (GUI) for Surfaces/Tie-lines/Hessian matrix analysis, https://en.wikipedia.org/w/index.php?title=Liquidliquid_extraction&oldid=1141347921, All articles with bare URLs for citations, Articles with bare URLs for citations from March 2022, Articles with PDF format bare URLs for citations, Wikipedia articles that are too technical from August 2022, Short description is different from Wikidata, Articles with unsourced statements from May 2014, Articles needing additional references from May 2014, All articles needing additional references, Wikipedia articles needing clarification from December 2019, Articles needing additional references from March 2014, Articles with unsourced statements from October 2020, Creative Commons Attribution-ShareAlike License 3.0, B.L. [31], Dialkyl sulfides, tributyl phosphate and alkyl amines have been used for extracting palladium and platinum. Temperature swing solvent extraction is an experimental technique for the desalination of drinking water. Instead, water is reduced to hydrogen. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. \(\Delta \rho\) = density difference (absolute value) between the continuous and dispersed phases (mass volume-1), \({\rm HETS}\) = height of equilibrium transfer stage (length), \(m^*_C\) = mass flowrate of the entering continuous phase (mass time-1), \(m^*_D\) = mass flowrate of the entering dispersed phase (mass time-1), \(N\) = required number of equilibrium stages, \(u_0\) = characteristic rise velocity of a droplet of the dispersed phase (length time-1), \(U_i\) = superficial velocity of phase \(i\) (C = continuous, downward; D = dispersed, upward) (length time-1), \(V^*_i\) = volumetric flowrate of phase \(i\) (volume time-1), \[U_i = \dfrac{4V_i^*}{\pi D_T^2} \tag{7.1}\], \[\dfrac{U_D}{U_C} = \dfrac{m_D^*}{m_C^*} \left( \dfrac{\rho_C}{\rho_D} \right) \tag{7.2}\], \[(U_D + U_C)_{\rm actual} = 0.50(U_D + U_C)_f \tag{7.3}\], \[u_0 = \dfrac{0.01 \sigma \Delta \rho}{\mu_C \rho_C} \tag{7.4} \], for rotating-disk columns, \(D_T\) = 8 to 42 inches, with one aqueous phase, \[D_T = \left( \dfrac{4m_D^*}{\rho_D U_D \pi} \right)^{0.5} = \left( \dfrac{4m_C^*}{\rho_C U_C \pi} \right)^{0.5} \tag{7.5}\]. A 43.8 to 31.1 kJ mol1 = 12.7 kJ mol1 of additional energy is given out by the reaction when compared with energy if the reaction had been done in nitrobenzene using one equivalent weight of a tetraalkylammonium acetate.[15]. Often there are chemical species present or necessary at one stage of sample processing that will interfere with the analysis. [citation needed], The PEGNaCl system has been shown to be effective at partitioning small molecules, such as peptides and nucleic acids. [7] This process is done by injecting small amounts of an appropriate extraction solvent (C2Cl4) and a disperser solvent (acetone) into the aqueous solution. Mixer-settlers are used when a process requires longer residence times and when the solutions are easily separated by gravity. An organic soluble uranium complex [UO2(TBP)2(NO3)2] is formed, then the organic layer bearing the uranium is brought into contact with a dilute nitric acid solution; the equilibrium is shifted away from the organic soluble uranium complex and towards the free TBP and uranyl nitrate in dilute nitric acid. The plutonium(IV) forms a similar complex to the uranium(VI), but it is possible to strip the plutonium in more than one way; a reducing agent that converts the plutonium to the trivalent oxidation state can be added. The general solid-liquid extraction procedure is applicable to a range of fields from environmental monitoring (shown in this video) to cosmetics and food processing. At a pH of 7.00 the extraction efficiency is just 3% . [35] In the modified Zincex process, zinc is separated from most divalent ions by solvent extraction. For this case, the extraction constant k is described by k = [HAorganic]2/[HAaqueous]. In a Polymerpolymer system, both phases are generated by a dissolved polymer. It has been shown that DNA fragments will partition into the light phase of a polymersalt separation system. The same calculation at a pH of 5.00 gives the extraction efficiency as 60%. Extraction is the dissolving process of a chemical component with a liquid out of a second non-gaseous phase. Lithium extraction is more popular due to the high demand of lithium-ion batteries. In a typical scenario, an industrial process will use an extraction step in which solutes are transferred from the aqueous phase to the organic phase; this is often followed by a scrubbing stage in which unwanted solutes are removed from the organic phase, then a stripping stage in which the wanted solutes are removed from the organic phase. In this case. At a pH of 1.00, we extract only 0.40% of the metal into the organic phase. \(P\) = Operating point. The ion reacts and then forms another ion, which is then transferred back to the aqueous phase. A novel settling device, Sudhin BioSettler, canseparate an oil-water emulsion continuously at a much faster rate than simple gravity settlers. Battery of mixer-settlers counter currently interconnected. It is important to investigate the rate at which the solute is transferred between the two phases, in some cases by an alteration of the contact time it is possible to alter the selectivity of the extraction. Use this composition to locate point \(M\) along the straight line connection points \(F\) and \(S\). Method 501.1 and Method 501.3 use a purge-and-trap to collect the trihalomethanes prior to a gas chromatographic analysis with a halide-specific detector (Method 501.1) or a mass spectrometer as the detector (Method 501.3). For the extraction of a product (white dots) out of the so called feed liquor (blue liquid with white dots) a suitable solvent (yellow liquid) has therefore to be found. For the design of a good process, the distribution ratio should be not too high (>100) or too low (<0.1) in the extraction portion of the process. The coating may be of such a concentration or characteristics that it would damage the instrumentation or interfere with the analysis. B has to be extracted into another liquid (C). Multistage countercurrent arrays have been used for the separation of lanthanides. and Example 7.7.2 CHE 418. In solvent extraction, two immiscible liquids are shaken together. (a) The solutes distribution ratio between water and toluene is, \[D=\frac{\left[S_{o r g}\right]}{\left[S_{a q}\right]}=\frac{0.889 \ \mathrm{g} \times \frac{1 \ \mathrm{mol}}{117.3 \ \mathrm{g}} \times \frac{1}{0.00500 \ \mathrm{L}}}{(1.235 \ \mathrm{g}-0.889 \ \mathrm{g}) \times \frac{1 \ \mathrm{mol}}{117.3 \ \mathrm{g}} \times \frac{1}{0.01000 \ \mathrm{L}}}=5.14 \nonumber\], (b) The fraction of solute remaining in the aqueous phase after one extraction is, \[\left(q_{a q}\right)_{1}=\frac{V_{a q}}{D V_{org}+V_{a q}}=\frac{20.00 \ \mathrm{mL}}{(5.14)(10.00 \ \mathrm{mL})+20.00 \ \mathrm{mL}}=0.280 \nonumber\]. Biotechnology 9:254. \[K_{\mathrm{a}}=\frac{\left[\mathrm{H}_{3} \mathrm{O}_{\mathrm{aq}}^{+}\right]\left[\mathrm{A}_{\mathrm{aq}}^{-}\right]}{\left[\mathrm{HA}_{\mathrm{aq}}\right]} \label{7.10}\], Solving Equation \ref{7.10} for the concentration of A in the aqueous phase, \[\left[\mathrm{A}_{a q}^{-}\right]=\frac{K_{\mathrm{a}} \times\left[\mathrm{HA}_{a q}\right]}{\left[\mathrm{H}_{3} \mathrm{O}_{a q}^{+}\right]} \nonumber\], and substituting into Equation \ref{7.9} gives, \[D = \frac {[\text{HA}_{org}]} {[\text{HA}_{aq}] + \frac {K_a \times [\text{HA}_{aq}]}{[\text{H}_3\text{O}_{aq}^+]}} \nonumber\]. There are two basic types of . In order to calculate the phase equilibrium, it is necessary to use a thermodynamic model such as NRTL, UNIQUAC, etc. \[\left(\operatorname{mol} \ S_{a q}\right)_{0}=\left(\operatorname{mol} \ S_{a q}\right)_{1}+\left(\operatorname{mol} \ S_{org}\right)_{1} \label{7.2}\], where the subscripts indicate the extraction number with 0 representing the system before the extraction and 1 the system following the first extraction. (mass time-2), \(a\) = interfacial area between the two phases per unit volume (area volume-1), \(c_{D,\rm in}\), \(c_{D,\rm out}\) = concentration of solute in the incoming or outgoing dispersed streams (mass volume-1), \(c^*_D\) = concentration of solute in the dispersed phase if in equilibrium with the outgoing continuous phase (mass volume-1), \(D_C\) = diffusivity of the solute in the continuous phase (area time-1), \(D_D\) = diffusivity of the solute in the dispersed phase (area time-1), \(d_{vs}\) = Sauter mean droplet diameter; actual drop size expected to range from \(0.3d_{vs}-3.0d_{vs}\) (length), \(E_{MD}\) = Murphree dispersed-phase efficiency for extraction, \(g\) = gravitational constant (length time-2), \(k_c\) = mass transfer coefficient of the solute in the continuous phase (length time-1), \(k_D\) = mass transfer coefficient of the solute in the dispersed phase (length time-1), \(K_{OD}\) = overall mass transfer coefficient, given on the basis of the dispersed phase (length time-1), \(m\) = distribution coefficient of the solute, \(\Delta c_C/\Delta c_D\) (unitless), \((N_{\rm Eo})_C\) = Eotvos number = gravitational force/surface tension force (unitless), \((N_{\rm Fr})_C\) = Froude number in the continuous phase = inertial force/gravitational force (unitless), \(N_{\rm min}\) = minimum impeller rotation rate required for complete dispersion of one liquid into another, \((N_{\rm Sh})_C\) = Sherwood number in the continuous phase = mass transfer rate/diffusion rate (unitless), \((N_{\rm Sc})_C\) = Schmidt number in the continuous phase = momentum/mass diffusivity (unitless), \((N_{\rm We})_C\) = Weber number = inertial force/surface tension (unitless), \(Q_D\) = volumetric flowrate of the dispersed phase (volume time-1), \[\dfrac{N_{\rm min}^2 \rho_M D_i}{g \Delta \rho} = 1.03 \left(\dfrac{D_T}{D_i}\right)^{2.76} (\phi_D)^{0.106} \left(\dfrac{\mu_M^2 \sigma}{D_i^5 \rho_M g^2 (\Delta \rho)^2} \right)^{0.084} \tag{6.1}\], \[{\rho}_M={\rho}_C{\phi}_C+{\rho}_D{\phi}_D \tag{6.2}\], \[{\mu}_M=\frac{{\mu}_C}{{\phi}_C}\left(1+\frac{1.5{\mu}_D{\phi}_D}{{\mu}_C+{\mu}_D}\right) \tag{6.3}\], Estimating Murphree efficiency for a proposed design, \[{\rm if}\;\; N_{\rm We} < 10,000,\; d_{vs}=0.052D_i(N_{\rm We})^{-0.6}\exp({4{\phi}_D}) \tag{6.4}\], \[{\rm if}\;\; N_{\rm We} >10,000,\; d_{vs}=0.39D_i(N_{\rm We})^{-0.6} \tag{6.5}\], \[N_{\rm We}=\frac{D_i^3N^2{\rho}_C}{\sigma} \tag{6.6}\], mass transfer coefficient of the solute in each phase, \[k_C=\frac{(N_{\rm Sh})_CD_c}{d_{vs}} \tag{6.8}\], \[(N_{\rm Sh})_C = 1.237 \times 10^{-5} (N_{\rm Sc})_C^{1/3} (N_{\rm Re})_C^{2/3} (\phi_D)^{-1/2} \tag{6.9}\], \[(N_{\rm Fr})_C^{5/12} \left( \dfrac{D_i}{d_{vs}} \right)^2 \left( \dfrac{d_{vs}}{D_T} \right)^{1/2} (N_{Eo})_C^{5/4} \tag{6.9} \], \[(N_{\rm Sc})_C=\frac{{\mu}_C}{{\rho}_CD_C} \tag{6.10}\], \[(N_{\rm Re})_C=\frac{D_i^2N{\rho}_C}{{\mu}_C} \tag{6.11}\], \[(N_{\rm Fr})_C = \dfrac{D_i N^2}{g} \tag{6.12}\], \[(N_{Eo})_C = \dfrac{\rho_D d_{vs}^2 g}{\sigma} \tag{6.13}\], Overall mass transfer coefficient for the solute, \[\frac{1}{K_{OD}}=\frac{1}{k_D}+\frac{1}{mk_C} \tag{6.14}\], \[E_{MD}=\frac{K_{OD}aV}{Q_D}\left(1+{\frac{K_{OD}aV}{Q_D}}\right)^{-1} \tag{6.15}\], \[E_{MD}=\frac{c_{D,\rm in}-c_{D,\rm out}}{c_{D,\rm in}-c^*_D} \tag{6.17}\]. 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