Conductance Studies of Aqueous Succinic Acid

Transcription

1 Cnductance Studies f queus Succinic cid lexander pelblat Department f Chemical Engineering, Ben Gurin University f the Negev, Beer Sheva, Israel Jsef Barthel Institut für Physikalische und Theretische Chemie, Universität Regensburg Z. Naturfrsch. 47a, (1992); received Nvember 2, 1991 Cnductance measurements f aqueus slutins f succinic acid and f di-sdium succinate were perfrmed frm t K and the limiting cnductances 0 (1/2 Succ 2- ) are reprted. The Waiden prduct is independent f temperature: 0 (1/2 Succ 2 ~) >/(T) = ± The salt cnductances clsely bey the Onsager limiting law. The evaluatin f the equilibrium cnstants fr the primary and secndary steps f dissciatin, K l and K 2, and the limiting cnductances f the hydrsuccinate in, (HSucc - ), are discussed using the Quint and Viallard cnductance equatin. 1. Intrductin 2. Experimental This wrk is a cntinuatin f ur studies n aqueus slutins f plybasic rganic acids [1], where it is difficult t btain a simple interpretatin f cnductance measurements due t the verlapping dissciatin equilibria. Frm many reprted cnductances f rganic acids nly in few cases the results fr dibasic acids are analysed [2-4], and even then the cntributin cming frm the secnd dissciatin step is usually cnsidered as a small crrectin t the measured cnductance. Succinic acid, a weak unsymmetrical 1:2 electrlyte is cnsidered here in a similar way as citric acid [1] by using the Quint and Viallard cnductance equatin. The cnductances f aqueus succinic acid slutins have already been measured in 1912 by Jnes [5]. Neutral and acidic succinates were cnsidered by Jeffery and Vgel [6], Davies [2] and Tpp and Davies [7]. Dissciatin cnstants f succinic acid at rm temperature were determined many times, mainly by Ptentimetrie methds [8, 9]. Pinching and Bates [10,11] perfrmed a systematic evaluatin f the dissciatin cnstants frm t K. The Fluka puriss. p.a. reagents anhydrus succinic acid (> 99.5%), and di-sdium succinate (> 98%), were used withut further purificatin. The slutins were prepared by weight, and cnversin frm mlalities t mlarities was perfrmed with the help f the density f pure water at given temperature fr dilute slutins (c < ml dm -3 ) f succinic acid and di-sdium succinate. Water with a specific cnductance f less than Scm~ 1 was used fr the slvent crrectins f the specific cnductances. detailed descriptin f the measuring system and applied prcedures is given in [1, 12, 13]. 3. Data nalysis The prperties f dilute aqueus slutins f succinic acid are usually interpreted in terms f the successive dissciatin steps: H2SUCC -> H HSucc - ; K t, (la) HSucc - H Succ 2- ; K 2. (lb) The equilibrium cnstants f these reactins are [H ] [HSucc - ] F 1 K x = [H2SUCC] (2 a) Reprint requests t Prf. Dr. J. Barthel, Institut für Physikalische und Theretische Chemie, Universität Regensburg, Pstfach , W-8400 Regensburg, FRG. K? = [H ] [Succ 2- ] F 2 [HSucc - ] (2 b) / 92 / $ 01.30/0. - Please rder a reprint rather than making yur wn cpy. Dieses Werk wurde im Jahr 2013 vm Verlag Zeitschrift für Naturfrschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.v. digitalisiert und unter flgender Lizenz veröffentlicht: Creative Cmmns Namensnennung 4.0 Lizenz. This wrk has been digitalized and published in 2013 by Verlag Zeitschrift für Naturfrschung in cperatin with the Max Planck Sciety fr the dvancement f Science under a Creative Cmmns ttributin 4.0 Internatinal License.

2 494. pelblat and J. Barthel Cnductance Studies f queus Succinic cid where dentes crrespnding qutients f the activity cefficients: / H /HSUCC" (3 a) /H2SUCC / H /SUCC2- (3 b) /» HSucc" In terms f the ttal degree f dissciatin a and the degrees assciated with the primary and secndary steps f dissciatin, a x and a 2, the cncentratins f species present in the slutin are [H ] (4 a) = c ( a : 2a 2 ), [H 2 Succ] = c(l a), (4b) [HSucc - ] = c a x, (4c) [Succ 2 (4d) = ca- where c is the ttal (analytical) cncentratin f succinic acid and a = ax a 2. (5) Use f (2) and (4) yields Ä i =. 7 = c(a12a2)a1 : 1 a c(ccl 2 a 2 ) a 2 > (6 a) r-,. (6 b) Fr given values f the equilibrium cnstants and activity cefficients it fllws at cncentratin c, that the degrees f dissciatin a t and a 2 can successively be evaluated by an iterative slutin f tw quadratic equatins: 1 «t-2 cf, " 2 = 4 a, 2aKx V, 4Kx(l-a2)' /, 8K2a, af cf 2 (7 a) 1ajB]//' = iqqq^ _ j= 1 c (9) c where L is the measured specific cnductance and Xj, Cj and Zj are the individual cnductances, cncentratins and valences f the ins. In the case under cnsideratin we have = a1[/(h) /l(hsuco] 2a 2 [(H ) -I- Succ 2 - )]. (10) The equatin fr Xj exact up t the linear term in the inic strength /, has the frm Xj = x -Sj]/l Ejl In I JXjl. (11) Fr unsymmetrical electrlytes, the cefficients Sj, Ej, and are available frm the Quint-Viallard thery [15,16], and with E- = 0 and J l 7 = 0 ( l l ) reduces t the Onsager limiting equatin [17]. t given temperature these cefficients depend n the limiting cnductances f the crrespnding ins, n the viscsity and the dielectric cnstant f water; the linear term in (11) depends als n the distance f clsest apprach a^. The cmplete expressins fr the cefficients are presented in [1, 15, 16]. When expressed in terms f the tw step dissciatin mdel, the experimental [, c) data require an adjustment r preselectin f six parameters. These are the equilibrium cnstants and K2, the limiting cnductances f the anins, 0 (HSucc - ) and Succ 2 - ), and the distances f clsest apprach a x and a 2. The values f a, are equal fr the activity cefficient and cnductance equatins, (8) and (11). (7 b) J In very dilute slutins, as cnsidered in this study, the activity cefficients f j f the different ins can be apprximated by the Debye-Hückel expressin ( j = H, HSucc" and Succ 2 - ) lg J5 = - where a} is the average catin-anin distance (distance f clsest apprach) and the inic strength is / = c(a 1 3a 2 ). t K the cnstants are [14] = m l - 1 / 2 d m 3 / 2 and B = m l - 1 / 2 dm 3 / 2 cm - 1. The activity cefficient f undissciated succinic acid is assumed t be unity. Mlecular cnductances are the sum f the inic cntributins: (8) 4. Results and Discussin The equivalent cnductances f di-sdium succinate and the mlecular cnductances f succinic acid are presented in Table 1 and in Figs. 1 and 2. The cnductances are pltted as functins f the square rt f the inic strength I, which fr a cmpletely dissciated

3 495. pelblat a n d J. Barthel C n d u c t a n c e Studies f q u e u s Succinic cid 140 Table 1. Experimental equivalent cnductances f di-sdium succinate and mlar cnductances f succinic acid in the investigated temperature range. T/K m 104 ml kg" cr 0) N yle(na2succ) 6 w 0.06 ml * d m Fig. 1. Equivalent cnductances f di-sdium succinate as functins f the square rt f inic strength I. 1: K ; 2: K ; 3: K ; 4: K ; 5: K ; 6: K ; 7: K (H 2 SUCC) * The equivalent cnductance f cmpletely dissciated electrlytes f the type 1:2, in the Onsager apprximatin [17] is given by e = L_ = (Na ) 0.60 I* 1 ml'' dm"* 1 Fig. 2. M l a r cnductances f succinic acid as a functin f the square rt f inic strength at K. : Jnes [5], : this wrk. 1:2 electrlyte is I = 3 c. s can be seen, di-sdium succinate is a cmpletely dissciated electrlyte and succinic acid is a partially dissciated weak electrlyte. In Fig. 2 the results f Jnes [5] are als presented, which cver mre cncentrated slutins f succinic acid. s many ld cnductances, they are systematically lwer than thse determined in mdern experiments; the differences are significant especially in dilute slutins. Taking this int accunt, bth sets f data are in reasnable agreement (Figure 2). The units f the equivalent and mlar cnductances are S cm 2 equiv~ 1 and S cm 2 ml - they will be mitted hereafter. -S]/l, 0 Succ2-), (12) S = c ß, where a = ß= q= (DT) 3/2 i l (13) rj(dt)1'2 ' 2 >l 0 (Na ) Succr.2 > 2 (Na ) Succ2-) and D and q dente the dielectric cnstant and viscsity f water. t a given temperature T, the measured equivalent cnductances e can be apprximated by a straight line (Fig. 1) and the slpes f these lines are very clse t the Onsager slpes (Table 2). The Onsager slpes are based n (Na ), D{T), rj(t) values frm [14,17], The intercepts f the straight lines serve as the limiting equivalent cnductances f di-sdium succinate.

4 496. pelblat and J. Barthel C n d u c t a n c e Studies f q u e u s Succinic cid Table 2. L i m i t i n g equivalent cnductances f succinate and sdium ins, the Waiden prducts and the ratis f the bserved t the Onsager slpes. 2 T/K / (±Succ ")i / (Na ) ^bs/^onsager and frm this investigatin yf e (Na 2 Succ) = j / c Frm the Khlrausch law the limiting cnductances were calculated (Table 2), and at K we have S u c c 2 - ) = This result is in a fair agreement with the Davies value [2], Succ 2 ") = 57.4; the Jeffery and Vgel limiting cnductance is much higher, Succ 2 ") = 60.9 [6], The Waiden prduct is practically independent f temperature, Succ 2 ") r](t) = ± The limiting cnductance f the hydrsuccinate in, x (HSucc"), cannt be determined directly frm cnductance measurements; its value must be prperly assigned. Frm an analysis f the ammnium hydrgen succinate and sdium hydrgen succinate cnductances, the values f 0 (HSucc") = 31.9 and 0 (HSucc") = 35.8 were adpted by Davies [2] and Tpp and Davies [7], The rati f limiting cnductances varies frm system t system and is usually fund between 0.5 and 1.2 [18]. Recently, Pethybridge [19] suggested t fix the rati at Evidently, with increasing succinic acid cncentratin, the cntributin due t the secnd dissciatin step is less and less imprtant and the prblem can be reduced t the case f a weak, mnbasic acid. In the Maclnnes and Shedlvsky prcedure [20], the degree f dissciatin f the primary step is given by (14) where * is the cnductance f the hypthetically cmpletely dissciated acid (t the primary dissciatin step nly) at the same cncentratin c as fr the measured cnductance. Values f * can be calculated frm * = /1(HC1) - /l(nacl) /l e (Na 2 Succ). (15) t K, the fllwing expressins fr the cnductances f HCl and NaCl were used [21]: zl(hcl) (17) Frm (14), (15), (16), and (17), fr the highest cncentratin in this wrk, c = ~ 3 m l d m " 3, we have * (Na 2 Succ) = and <xl = , and frm n /*, i.53 j / c 89.5 c(l ]/c) = K l1 = (16b) (NaCl) (16a) = ] / c c(l ]fc), = c(xjf1 (18) 1 cl the estimated value f the equilibrium cnstant is X n = ~ 5. This value may be cmpared with dissciatin cnstants f succinic acid reprted in the literature, which vary frm K 1 = t " 5 and frm K2 = 1.90 t " 6 [8, 9], The Pinching and Bates cnstants are K1= " 5 and K2 = " 6 [10,11]. The activity cefficient qutient F± was determined frm the individual activity cefficients (8). Using a t =0.2068, = 82.18, and 0 (H ) = , the Quint-Viallard equatins (11) fr * = l = (H )-f (HSucc") were slved simultaneusly with (14) t yield the limiting cnductance f (HSucc")=49.75, [ (HSucc")/ (f Succ 2 ") = 0.89], Evidently, this result is much higher than that adpted by Davies [2] and Tpp and Davies [7]. It fllws frm (10) that the measured cnductance f succinic acid as a functin f cncentratin c is = all 2a22, (19a) yl1 = a 1 [(H ) /l(hsucc")], (19b) 2= 2a 2 [(H ) (19c) Succ 2 ")], where and cc2 are given by (7) and the individual cnductances are calculated frm the Quint-Viallard equatins (11). The value f a(succ 2 ") = 8.0 Ä was selected, but the final results are nt sensitive t the chice f the distances f clsest apprach. Cnsidering (19), it is assumed that the cntributins cming frm the binary electrlyte cnstituents are additive. Frmally, in the limit at infinite dilutin (^ tends t zer and a 2 appraches unity) we have = 22, and this is the mlecular cnductance f a fully dissciated electrlyte f the type 1:2. Thus, (10) and (11) tend t the Onsager apprximatin (12). Since x, 2, a1, a 2, F x, F 2, and I = c((xl 3a 2 ) depend n the equilibrium cnstants Kt and K2, it fllws frm (19) that, since (c; K2), fr a knwn

5 497. pelblat a n d J. Barthel C n d u c t a n c e Studies f q u e u s Succinic cid set f (, c) values the dissciatin cnstants can be apprximated with the help f an apprpriate iteratin prcedure. If the equilibrium cnstants K t and K 2 are knwn at a given cncentratin c, then ix l, a 2, Fj and F2 can cnsecutively be evaluated frm (7), starting with initial values <x2=0 and a 1 calculated frm (18) with Fl = \. The calculatins are cntinued until repetitin des nt change the ccj and f j values. Few runs were sufficient in mst cases t cmplete the calculatins. and a 2 determined in this way permit the evaluatin f the inic strength I and finally f x and 2. The search fr the best agreement between the measured and calculated (19) values f will therefre prduce a set f the selfcnsistent equilibrium cnstants. The limiting cnductance at K can be used fr the evaluatin f 0 (HSucc") at ther temperatures frm the Waiden rule: Table 3. Experimental and calculated (19) mlar cnductances f succinic acid at K. 0 (HSucc -, T) satisfactry descriptin f the bserved cnductances with regard t a prper chice f 0 (HSucc"). Preselectin f the dissciatin cnstants gives results which are clearly incnsistent with the accuracy f ur experiments. The "best" set f parameters is practically equivalent t the case f a mnbasic weak acid with a very small crrectin due t the secnd dissciatin step. This disagrees with the accepted values f K i and K 2 fr succinic acid [8,9]. Cnsidering K 2, the selectin f the Davies limiting cnductance is smewhat better than that chsen by Tpp and Davies. Hwever, there is n clear distinctin between these tw cases, because the calculatins are rather insensitive t changes in 0 (HSucc"). The same picture is bserved at ther temperatures. t this stage f investigatin, withut knwledge f transference numbers, it is difficult t assign prperly the limiting cnductance f the in HSucc"; nly accurate 0 (HSucc 2 ") values as a functin f temperature are available. = 0 (HSucc -, K) 77( K) (20) The temperature dependence f (H ) and the cnstants and B (8) are knwn [14,17] and the distances f clsest apprach, a,-, can be assumed t be independent f temperature. t K, the determined "best" set f parameters is: 0 (HSucc - ) = 47.0, (HSucc - )/ (i Succ 2 ") = 0.84, = " 5 and K 2 = " 8, and the average standard deviatin is cr = 0.23 S c m 2 m l " 1. Since the equilibrium cnstants, especially K2, are significantly lwer than thse reprted in the literature, three additinal data sets were cnsidered. If the Davies value, 0 (HSucc") = 31.9, (HSucc - )/ ( Succ 2 - ) = 0.57, is selected, then we have frm (19): K j = and X 2 = " 6 with (7 = 0.28 S c m 2 m l - 1. The chice f the Tpp and Davies value, 0 (HSucc - ) = 35.8, (HSucc")/ ( Succ 2 ") = 0.64, gives K x = " 5 and X 2 = " 6 with cr = 0.26 S cm 2 m l " 1. Finally, if the Pinching and Bates dissciatin cnstants are intrduced we have: 0 (HSucc") = 22.9, 0 (HSucc")/ ( Succ 2 ") = 0.41, with cr=1.38 S cm 2 m l " 1. The measured and calculated values f fr these fur sets f parameters are presented in Table 3. s can be seen, in the framewrk f the Quint and Viallard thery there is n c104/ ml d m calc CXP calc B calc C calc d ( H S u c c - ) = 47.0, K, = and K2 = 5 10~ 8. 0 ( H S u c c - ) = 31.9 [2], X j = and K 2 = ~ 6. 0 (HSucc - ) = 35.8 [7], K, = and K2=09 10~6. ( H S u c c - ) = 22.9, X j = and K 2 = [10, 11]. cknwledgement The authrs are indebted t H. Hilbinger fr his kind interest and assistence thrughut the curse f this investigatin. One f us (..) is grateful t the staff f the Chemistry Department fr the warm hspitality ffered during his stay at the University f Regensburg.

6 498. pelblat and J. Barthel Cnductance Studies f queus Succinic cid [1]. pelblat and J. Barthel, Z. Naturfrsch. 46a, 131 (1991). [2] C. W. Davies, J. Chem. Sc. 1939, [3] L. S. Darken, J. mer. Chem., Sc. 63, 1007, (1941). [4] D. R. Cartwright and C. B. Mnk, J. Chem. Sc. 1955, [5] H. C. Jnes, The Electrical Cnductivity, Dissciatin and Temperature Cefficients f Cnductivity (frm zer t sixty-five degrees) f queus Slutins f a Number f Salts and Organic cids. Carnegie Institutin f Washingtn, Publicatin N. 170 (1912). [6] G. H. Jeffery and. I. Vgel, J. Chem. Sc. 1935, 21. [7] N. E. Tpp and C. W. Davies, J. Chem. Sc. 1940, 87. [8] G. Krtüm, W. Vgel, and K. ndrussw, Dissciatin Cnstants f Organic cids in queus Slutins, Butterwrth, Lndn [9] E. P. Serjeant and B. Dempsey, Inisatin Cnstants f Organic cids in queus Slutins, Pergamn Press, Oxfrd [10] G. D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand. 45, 322, (1950). [11] G. D. Pinching and R. G. Bates, J. Res. Nat. Bur. Stand. 45, 444 (1950). [12] R. Wächter and J. Barthel, Ber. Bunsenges. Phys. Chem. 83, 634 (1979). [13] J. Barthel, R. Wächter, and H.-J. Gres, in: Mdern spects f Electrchemistry, Vl. 13, pp (B. E. Cnway and J. O'M. Bckris, eds.), Penum Publ. Crp [14] R.. Rbinsn and R. H. Stkes, Electrlyte Slutins, 2nd rev. ed., Butterwrth, Lndn [15] J. Quint and. Viallard, J. Slutin Chem. 7, 137, 525, 533 (1978). [16] J. Quint, Thesis, Cntributin ä l'etude de la cnductibilite electrique des melanges d'electrlytes, University f Clermnt-Ferrand; pril [17] H. S. Harned and B. B. Owen, The Physical Chemistry f Electrlytic Slutins, Reinhld Publ. Crp., New Yrk 1958, 3rd ed. [18] C. B. Mnk, Electrlytic Dissciatin, cademic Press, New Yrk [19]. D. Pethybridge, Z. Phys. Chem. N.F. 133, 143 (1982). [20] D.. Maclnnes and T. Shedlvsky, J. mer. Chem. Sc. 54, 1429 (1932). [21] D.. Maclnnes and T. Shedlvsky, J. mer. Chem. Sc. 54, 1441 (1932).