Prediction of Solubility of Racemic (R/S) (±)-Ibuprofen in n-heptane, Toluene, Benzene and Ethanol

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1 Predcton o Soubty o Racec (R/S) (±)-Iburoen n n-hetane, ouene, Benzene and Ethano Bagher H 1,, Ghader S 1* and Hata N 1 1 Deartent o Checa Engneerng, Coege o Engneerng, Shahd Bahonar Unversty o Keran, Johoor Bvd., Keran, Iran Young Researchers Socety, Shahd Bahonar Unversty o Keran, Keran, Iran * Corresondng author: Ghader S, Deartent o Checa Engneerng, Coege o Engneerng, Shahd Bahonar Unversty o Keran, Johoor Bvd., Keran, Iran, e and Fax: ; E-a: sattarghader@yahoo.co; ghader@uk.ac.r Receved: Ar 19, 017; Acceted: May 1, 017; Pubshed: June 8, 017 Abstract he soubty o racec (R/S) (±)-buroen n ure sovents: n-hetane, touene, benzene and ethano at range 15 C to 60 C usng the reguar-souton theory, the UNIFAC ode and the UNIQUAC ode s redcted and coared wth the corresondng exerenta vaues reorted n revous study. he resuts o the dea soubty show that s neggbe n coarson to the oar enthay o on. here s a good agreeent between the exerenta soubty data o racec (R/S) (±)-buroen and the resuts o UNIQUAC ode. Keywords: Racec (R/S) (±)-buroen; Soubty; Actvty coecent; UNIQUAC; UNIFAC; Reguar-souton theory Introducton A racec coound o seces s ndcated as a xture o two enantoers by 50:50 rato, and can exst as a racec congoerate, a racec coound, or a sod souton (seudoraceate) [1]. he denton n enantoers, a ane o oarzed ght s assed through any enantoer and the ght to the countercockwse as evorotatory or (-)-enantoer or R- or; on the contrary, the ght to the cockwse as dextrorotatory or (+)-enantoer or S-or []. Ooste enantoers have dentca hysca and checa roertes such as oecuar weght, soubty, etng ont, and they ony derence s ther three-densona sata arrangeent. Racec coound o buroen, (R/S) (±)-buroen -[4-sobutyheny] roonc acd, s a non-steroda ant-naatory drug. It s ost oten rescrbed to treat enstrua sytos, an, arthrts and ever. Racec buroen s a reatvey weak acd coound [3], and t s water nsoube coound. he checa orua o racec buroen s C 3 H 18 O and the structure o racec (R/S) (±)-buroen s shown n FIG. 1. Ctaton: Bagher H, Ghader S, Hata N. Predcton o Soubty o Racec (R/S) (±)-Iburoen n n-hetane, ouene, Benzene and Ethano. Che echno Ind J. 017;1(1): rade Scence Inc. 1

2 June-017 FIG. 1. Structure o racec (R/S) (±)-buroen [1]. Soubty s the ost basc noraton n a crystazaton rocess. Crystazaton rocess s a key unt oeraton n the roducton o haraceutca sods and ne checas, whch has a ajor eect on drug quaty n ters o crysta sze dstrbuton. It s evdent that the soubty redcton s necessary n sovent seecton and contro o crystazaton rocesses where the exerenta data are scarce. One o the ouar ethods to redct soubty s based on the actvty coecent evauaton. In the resent study, our assuton aed or the dea soubty o racec buroen are nvestgated; the soubty o racec (R/S) (±)-buroen n n-hetane, touene, benzene and ethano s redcted usng the derent odes (reguarsouton theory, the UNIFAC and the UNIQUAC ode) and then coared wth the corresondng exerenta data reorted n thess [1]. Exerenta heory At equbru [4]: s sat (1) s sat Where and are the ugactes o ure sod and o soute n the souton, resectvey. Usng the sub-cooed qud at teerature and sat as the standard state or actvty coecent ( ) and assung no soubty o sovent n sod sat can be wrtten: sat x () Where x s the soubty o sod n qud n oe racton and the sod. hus, 1 (3) s x s the ugacty o the ure sub-cooed qud state o he ugacty rato s ndeendent o the sovent roertes and can be reated to the oar Gbbs energy changes ( g ) o the sod.

3 June-017 g R n R n a (4) he rato o h ) and entroy ( ) changes. g h s s s 1 h s n (5) x R R s caed actvty ( a ) and the oar Gbbs energy changes can aso be reated to the oar enthay ( Where R s the unversa gas constant. Snce both enthay and entroy are state unctons (no ath unctons), they can be evauated ro any therodynac ath. Usng tre ont o sod, Prausntz et a. [4] aed a therodynac cyce to evauate the enthay and entroy changes [5]. h h c d t t c s st d t c c c s (6) where h t s the oar enthay o on at tre ont, tre ont teerature, whch can be consdered as the etng ont, and sod states. hus, s t s the oar entroy o on at tre ont t s the c and 1 h 1 1 s c n c d d (7) x R R R R s c are the heat caactes o soute n qud where the ndex shows a roertes at etng ont. he enthay o on s aso reated to entroy o on. h s thus: dea h c nx ( ) c d d 8 R R R he easured soubty s oten n ters o g o soute er 100 g o sovent (shown by S). o convert the soubty n ters o oe racton ( ) to ths unt, we have to use the oowng equatons: S xmw x soute x Mw sovent x Mw s the oecuar weght, g/oe. he dea and exerenta oe ractons are reated by: 3

4 June-017 x x dea (10) Predcton o the actua soubty requres the actua actvty coecent o the soute n the souton,, whch shoud be cacuated ro the therodynac odes. Idea soubty Assung dea souton, the actvty coecent o soute n the souton s equa to unty, and the genera equaton o dea soubty can be wrtten as [5]: dea h c n x ( ) cd d (11) R R R Eqn. (11) cacuates the dea oe racton o soute n an dea souton usng the thera roertes o the sod hase. Because ted data are avaabe n the terature to cacuate dea soubty. c, soe assutons are aed to eqn. (11) to estate the Case A: In ost checa engneerng acatons, the rst ter o the rght-hand sde o eqn. (11) s the donant one, and the next two ters wth two ooste sgns tend to cance each other. dea h 1 n x (1 ) (1) R r Where r s the rato o etng teerature to souton teerature ( ). Case B: Assuton c 0 s a good aroxaton to sove eqn. (11). dea h n x n r (13) R Eqn. (13) has been aed to haraceutcas [5] and has resuted n better aroxatons. Case C: o estate the dea soubty ore accuratey, eqn. (11) can be sed the derenta oar heat caacty s assued to be constant and estated at the etng ont. dea h c n x (1 r ) ( 1 n ) (14) r r R R Case D: I case o near changes c b c s not constant, eqn. (11) has to be ntegrated wth resect to derenta oar heat caacty changes. In c n teerature or buroen, eqn. (11) can be rewrtten as: 4

5 June-017 h b 1 n x (1 ) ( 1 n ) ( ) (15) dea r r r r R R R r Resuts and Dscusson herodynac odes (Hdebrand, the UNIFAC and the UNIQUAC odes) were used to redct the actvty coecent and soubty o racec buroen n derent ure sovents: n-hetane, touene, benzene and ethano. he actvty coecent s a uncton o any actors such as oecuar sze, oarty and nteracton orces between soute and sovent. herodynac odes to redct the actvty coecent can be categorzed n theoretca and se-erca odes. he theoretca odes have no adjustabe araeters and use the therodynac buk roertes (reguar-souton theory) or grou contrbuton o the soute and sovent (UNIFAC), and the se-erca odes (UNIQUAC) need exerenta data to estate adjustabe araeters to redct the actvty coecent. he otzaton rocedure was based on the nzaton o the error between the cacuated and exerenta vaues o the actvty coecents: Mn Error ( Ex. Cac. ) (16) Where Ex. and Cac. are the exerenta and cacuated actvty coecents o racec (R/S) (±)-buroen, resectvey. o redct the oe racton o soute n the sovent, an teratve rocedure was erored: 1. Cacuate the dea oe ractons ro eqns. (1-15) at teeratures that the soubty o sods s avaabe.. Cacuate the exerenta actvty coecent ro eqn. (10). 3. Cacuate the corresondng actvty coecent ro the therodynac odes (Hdebrand, the UNIFAC and the UNIQUAC odes). 4. Wrte a regresson rogra n Exce that rogra changes the adjustabe araeters o the UNIQUAC ode to nze the error n eqn. (16). In order to redct o actvty coecent, the thera roertes o racec (R/S) (±)-buroen are needed. A scannng caoreter ethod was used to easure the heat o on and etng teerature [1]. So, the vaues heat o on and etng teerature o racec buroen are 5.5 kj/o and 77 C, resectvey [6]. FIG. shows qud and sod oar heat caactes o racec coound o buroen [7]; accordng to the data, the derenta oar heat caacty s cacuated: c (17) 5

6 og (x ) og (x ) June-017 FIG.. he heat caactes o racec buroen [7]. (a) Exerenta Reguar-souton UNIQUAC UNIFAC -6 (b) eerature (K) Exerenta Reguar-souton UNIQUAC UNIFAC eerature (K) 6

7 og (x ) og (x ) June-017 (c) Exerenta Reguar-souton UNIQUAC UNIFAC eerature (K) (d) Exerenta Reguar-souton -3 UNIQUAC -4 UNIFAC eerature (K) FIG. 3. he coarson between exerenta soubty o racec (R/S) (±)-buroen and theoretca soubty by usng the reguar-souton theory, UNIQUAC and UNIFAC odes n (a) n-hetane (b) touene (c) benzene (d) ethano. Exerenta data o soubty o racec (R/S) (±)-buroen n derent sovents at the range o 15 C to 60 C are ustrated n ABLE 1 [1]. 7

8 June-017 ABLE 1. Exerenta data [1] o soubty (er g/) o racec (R/S) (±)-buroen n derent sovents: n- hetane, touene, benzene and ethano. Sovent eerature ( C) n-hetane ouene Benzene Ethano Idea soubty o racec (R/S) (±)-buroen Usng thera roertes o racec (R/S) (±)-buroen and eqns. (1-15), the dea soubty o racec (R/S) (±)-buroen at teerature range are obtaned n ABLE. ABLE. Idea soubty o racec (R/S) (±)-buroen. x dea ro cases ( C) A B C D Predcton o rea soubty o racec (R/S) (±)-buroen Reguar-Souton heory (Scatchard-Hdebrand theory) assues that the excess entroy and voue changes are zero durng the xng o coonents. he Reguar-souton equatons aways redct 1 ;.e., a reguar souton can exhbt ony ostve devatons ro Raout s aw. Reguar-souton theory shows that or a bnary souton o nonoar oecues, the soute actvty coecent can be exressed by: v * n ( 1) 1 (18) R Where * 1 s a voue racton o sovent, dened by: xv * x1v 1 x1v (19) 8

9 June-017 V and are the oar voue and soubty araeter o coonents, resectvey. Soubty araeter are uncton o teerature, but the derence between these soubty araeters, 1, s oten neary ndeendent o 3 1 teerature [4]. he oar voue o racec (R/S) (±) -buroen s c o, whch s cacuated ro V MW soute usng Mwsoute 06.8 / buroen, (J c -3 ) 0.5 [8]. g o and 1.11 g [1]. he soubty araeter o racec 3 c he UNIQUAC actvty coecent ode s se-erca ode based on two adjustabe araeters [4]: zq r n n n ( ) q n( ) q ( ) (0) where z ' ' ' ' ' ' ' ' ' x r z z 1 ( r1 q1 ) ( r1 1), ( r q) ( r 1) (1) a1 a1 1 ex( ), 1 ex( ) () where the coordnaton nuber Z s set to equa 10. Segent racton,, and area ractons,, and 1, are gven by r x r x, r1 x1 r x r1 x1 r x q x q x, (4) q1x 1 qx q1x 1 qx q x q x, 5 ' ' ' 1 1 ' 1 ' ' ' ' q1x 1 qx q1x 1 qx Paraeter r, q and areas. Bascay, ' q are ure-coonent oecuar-structure constants deendng on oecuar sze and externa surace ' q s equa to q, but or acohos t ders. a 1 and a 1 are the adjustabe araeters o UNIQUAC actvty coecent ode. he adjustabe araeters can be used n suaton sotware or redctng other roertes o the eoyed checas or or redctng the equbru n ut-coonent systes. he UNIFAC actvty coecent ode s searated nto two arts: one art rovdes the contrbuton due to derences n oecuar sze and shae (cobnatona art), and the other rovdes the contrbuton due to oecuar nteractons (resdua art) [9]: c R n n n (6) where 9

10 June-017 c z n n q n j x j j (7) x x R j j n q 1 n j j j j (8) k k kj For cases that the van der Waas area and voue are not avaabe, the unctona grou aroach s used. ( ) ( ) r k vk Rk, q k vk Qk (9) Where k s the nuber o unctona grous n the oecue, whch s 6 or racec buroen and v () k s the reeatng nuber o each unctona grou n the soute or sovent oecue. Rk and grous and grou voue and area o racec buroen are gven n ABLE 3. Qk are grou voue and area [9]. he unctona ABLE 3. Functona grous and the grou voue and area araeter o racec buroen. R Q Nuber o grous n the oecuar (ν) CH CH CH ACH AC COOH Usng ths tabe and eqn. (6), the nuerca vaues o r and q or racec (R/S) (±)-buroen were cacuated equa to 8.49 and 6.604, resectvey. n-hetane has two unctona grous, CH 3 and CH ; touene has three an unctona grous, CH 3, ACH and AC; benzene has ony one unctona grou, ACH; nay, an unctona grous o ethano are CH 3, CH and OH. he an grou and sub-grou nubers aong wth the roertes o seced unctona grous, together wth the vaues o grou nteracton araeters ( a ) were adated ro teratures [9]. n he resdua art o the actvty coecent, eqn. (8), s reaced by the souton-o-grous concet. n R ( ) n n ( ) k vk k k (30) Where k s the grou resdua actvty coecent and souton contanng ony oecues o tye. n k n k Q 1 n k (31) n n n s the resdua actvty coecent o grou k n a reerence () k 10

11 June-017 s the area racton o grou, and the sus are over a derent grous. s cacuated n a anner sar to that or : QX QX n n n (3) Where X s the oe racton o grou n the xture. he grou-nteracton araeter s gven by: n a n ex n (33) he grou nteracton araeters o kevns and a n a n. an ust be evauated ro exerenta hase equbru data. Note that n a has unts In order to choose the best redctve ode or dea soubty o racec (R/S) (±)-buroen n derent sovents, a odes are coared by the suaton o absoute errors between the exerenta and the cacuated soubty usng reguar-souton theory, UNIFAC and UNIQUAC odes (n oe racton) dened by: error x x,ex, ca (34) ABLE 4 s obtaned absoute errors or a actvty odes (Reguar-souton theory, UNIFAC and UNIQUAC odes) n derent ure sovents: n-hetane, touene, benzene and ethano at teerature range 15 C to 60 C. ABLE 4. Coarson o errors due to soubty redcton o reguar-souton theory, UNIQUAC and UNIFAC. Reguar-souton UNIQUAC UNIFAC Sovent Case A Case B Case C Case D Case A Case B Case C Case D Case A Case B Case C Case D n-hetane Benzene ouene Ethano It s aarent that n a actvty coecent odes, case A s better than other cases or racec buroen. So, dea soubty o racec buroen s cacuated by case A. ABLE 5 shows adjustabe araeters o UNIQUAC or case A that were cacuated ro nzaton the error n eqn. 16. he reorted errors n ths tabe are the absoute devaton between the cacuated soubty usng UNIQUAC and the exerenta data: 11

12 June-017 x x,ex, ca % error average ( ) 100 (35) x,ex ABLE 5. Adjustabe araeters o UNIQUAC; subscrt 1 reer to sovents and reer to racec (R/S) (±)- buroen. Sovent range ( C) r q q a 1 a 1 %error n-hetane ouene Benzene Ethano FIG. 3 dects the coarson between exerenta and cacuated soubty o racec (R/S) (±)-buroen n derent ure sovents: n-hetane, touene, benzene and ethano, resectvey. UNIQUAC ode have best redcton coared wth the reguar-souton theory and UNIFAC ode, n a sovents. Reguar-souton theory cannot be consdered as a sutabe redctve ode; n a sovents ths ode has a arge error excet Ethano souton. It s aarent that or non-oar bnary xtures, reguar-souton theory s good ode. However, reguar-souton theory usuay rovdes an easy way or aroxaton o soubty and actvty coecent by usng the buk roertes o soute. It was ound that as the oarty o sovent ncreases the soubty o racec coound o buroen aso ncreases: Soubty: n-hetane<touene<benzene<ethano Poarty: n-hetane<touene<benzene<ethano Concuson Idea soubty o the racec buroen was cacuated usng our cases. he resuts show that the c =0 assuton n case A s best assuton or estaton racec buroen soubty and actvty coecent. Assung near changes wth teerature (case D) n better estaton that cases B and C, because workng teerature range are near the etng ont. he UNIQUAC actvty coecent ode wth adjustabe araeters s a better redctve ode than the other odes (reguar-souton theory, UNIFAC). c 1

13 June-017 Sybos Bnary adjustabe araeters o UNIQUAC ode (k) [-----] Grou nteracton araeters o UNIFAC ode (k) [-----] a Actvty [-----] c Moar heat caacty [J o -1 K -1 ] Fugacty [bar] Moar gbbs energy [J o -1 ] h Moar enthay [J o -1 ] M w Moecuar weght [g o -1 ] Pressure [bar] R Unversa gas constant [J o -1 K -1 ] S Soubty [g soute/100 g sovent] Moar entroy [J o -1 K -1 ] eerature [K] r Rato o etng teerature to souton teerature [-----] Moar voue [c 3 o -1 ] Moe racton [-----] Coordnaton nuber [-----] Greek Letters Segent racton [-----] Voue racton [-----] Soubty araeter [J c -3 ] 0.5 Proerty changes [-----] Actvty coecent [-----] Grou resdua actvty coecent [-----] Area racton [-----] Area racton [-----] Reeatng nuber o unctona grou [-----] Densty [g c -3 ] ψ Grou nteracton araeters o UNIFAC ode [-----] 13

14 June-017 Subscrts a Soute Sovent Cacuated Exerenta Metng ont re ont Suerscrts dea sat Cobnatona Fuson Idea state Lqud Resdua Sod Saturaton REFERENCES 1. Chen YH, Lee. Inta sovent-screenng o racec (R/S) (±)-buroen and crystazaton knetcs o buroen sodu sats, Natona Centra Unversty Gohe MC. Overvew on chraty and acatons o stereo-seectve dssouton testng n the oruaton and deveoent work. Dssouton ech. 003;10: Potthast H, Dressan JB, Jungnger HE, et a. Bowaver onograhs or edate reease sod ora dosage ors: Iburoen. J Phar Sc. 005;94: Prausntz JM, Lchtenthaer RN, De Azevedo EG. Moecuar therodynacs o ud-hase equbra, 3 rd ed. Prentce Ha: New Jersey (1999). 5. Hojjat H, Rohan S. Measureent and redcton o soubty o aracetao n water-soroano souton. Org Process Res Dev. 006;10: Pacheco DP, Manrque YJ, Martnez F. herodynac study o the soubty o buroen and naroxen n soe ethano+ royene gyco xtures. Fud Phase Equbr. 007;6:3. 7. F Xu, L Sun, Z an, et a. Acta Phys Ch Sn. 005;1:1. 8. Jouyban. Handbook o soubty data or haraceutcas. CRC Press ayor & Francs Grou, USA Pong E, Prausntz JM, PO Conne J. he roertes o gases and quds, 5 th ed. McGraw-H, New York, USA