HITOSHI OHTAKIAND NOBUOTANAKA
90
Ionic Equilibria in Mixed Solvents. VI. Dissociation Constants of Aliphatic Diamines in Water-Methanol Solutions by Hitoshi Ohtaki" and Nobuo Tanaka Laboratory of Analytical Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya, Japan (Received M a y 11, 1970) Publication costs borne completely by The Journal of Physical Chemistry
Dissociation constants of protonated l,Z-diaminoethane, 1,3-diaminopropane, and 1,Pdiaminobutane have been determined potentiometrically at 25" in various water-methanol mixtures containing 0.1 N sodium chloride as an ionic medium. Ion products, K,(s), in the mixtures have been calculated and used for calculations of pK's of the acids, equilibrium of hydronium ions with alkoxonium ions being taken into consideration. Since values of pKz - pK1 of the diamines have been independent of solvent compositions, it may be seen that interactions between charged sites in a molecule may scarcely be affected with the variation of the solvent composition.
Introduction In comparison with accumulation of data for dissociation constants of dicarboxylic acids, the number of pK values of diamines is limited. Moreover, theoretical considerations have been made only for dissociation of protons from dicarboxylic We have undertaken the present study to throw a little more light on dissociation equilibria of diprotic acids in mixed solvents. I n the present work we determined dissociation constants of protonated l,Zdiaminoethane, l,&diaminopropane, and 1,4-diaminobutane in various watermethanol mixtures containing 0.1 M sodium chloride as an ionic medium.
Experimental Section A. Reagents. 1,W-Diaminoethane Dihyclrochloride and 1 ,tI-Diaminopropane Dihydrochloride. Each base (reagent grade; Wako Pure Chemicals Co., Osaka) was dissolved in wator and then was treated with diluted hydrochloric acid. at low temperature. The solution was concentrated under a reduced pressure at 30-40". Diamine dihydrochlorides thus prepared were recrystallized three times from aqueous ethanol and crystals were dried in vacuo. 1,4-Diaminobutane Dihydrochloride. 1,4-Diaminobutane (Aidrich Cliemical Co., Inc., Milwaukee, Wis.) was distilled twice under a reduced pressure and dissolved in water, arid then was treated with dilute hydrochloric acid in a vessel cooled with ice. The solution was concentrated under a reduced pressure until crystals were formed. Temperature was kept lower than 40" in the course of evaporation. The crystals were dissolved in aqueous ethanol solution and recrystallized by addition of ethyl ether to the solution. They were dried in vacuo at room temperature. The Journal of I'hysiacal Chemistry, Vol. 76, No. 1, 1971
Sodium chloride (ultra pure) from E. JIerck Co. mas used after drying at 500". Sodium Hydroxide. A saturated solution of reagent grade sodium hydroxide was allowed .lo stand for several days in a polyethylene bottle. The solution was filtered through a G4 glass filter under nitrogen atmosphere and diluted with distilled water free from carbon dioxide. The solution was kept in a polyethylene bottle filled with nitrogen gas. Methanol. Reagent grade methanol was distilled once and was stored in a glass bottle. The concentration of water in the methanol was analyzed by means of Karl Fischer titrations. R. Apparatus. Beckman glass electrodes (No. 40498) were used. Silver-silver chloride electrodes were prepared according to Brownn6 The 'Wilhelm" type of half-cell described by Forsling, Hietanen, and SillBn' was used for emf measurements. A Beckman Research pH meter RiIodel 1019 or an Orion Digital pH meter IL'Iodel801was used. All titrations were performed in an ionic medium of 0.1 M sodium chloride at 25.00 f 0.01" in a paraffin oil thermostat, which was placed in a room thermostated at 25 i= 1'. Potentials at each point of measurements were determined within an accuracy of 0.1 mV. The
* Correspondence should be addressed to Department of Electrochemistry, Tokyo Institute of Technology, O-okayama, Meguro, Tokyo, Japan. (1) R. Gane and C. K. Ingold, J. Chem. SOC.,2153 (1931). (2) J. G. Kirkwood and F. J. Westheimer, .P. Chem. Phys., 6, 506 (1938). (3) H. M. Peek and T. L. Hill, J. Amer. Chem. Soc., 73, 5304 (1951). (4) C. Tanford, ibid., 79, 5348 (1957). (5) A: Ninomiya and K . Toei, J . Chem. SOC.Jap. ( N i p p o n Ragaku Z a s s h ) , 90, 655 (1969). (6) A . 8. Brown, J. Amer. Chem. SOC.,56, 646 (1934). (7) W. Forsling, 8. Hietanen, and L. G. Sillen, Acta Chem. Scand., 6, 901 (1952).
1 0 ~ E1 g~o r ~ ~ u XN ~ rMIXED a SOLVENTS
91
pH never excet3dcd 10.1 in the course of measurements in all svsttms,
Liquid ~~~~~~0~P0tc:ntials Activity coPKicients of species being assumed to be kept conslant i u a constant ionic medium with a given solvent composition an emf measured, E , is related with the concentration of hydrogen ion, [H+Is,through the equation
where [H+Isdenotek the concentration of the relevant species in a solation; Eo is a constant, which is determined experimenta1l.y by means of a Gran plot8 in each titration procedure; E , represents the liquid junction poteritial at the junction, 0.1 M NaCl in aqueous solutionl0.l M (??a9 H)Cl in water-methanol mixture. The liquid junction potential, E,, was determined in each solvent system. Values of E , in various watermethanol solutions of 0.1 114 sodium chloride are given in Table 1. Uncertainties of the results nere estimated t o be +50 mY [H+],-l. The decrease of liquid junction potential with increasing methanol concentration niay be due t o the decrease of mobility of protons in mixed solvents
%
-600 (-440," -550b in 0 . 1 M NaC104) -550 - 500 - 450 -400 -400 - 350 - 380 - 300
0 10 20 30 40
50 60 70 80
H+(ROH)
+ 1320
(4)
is given as
where x denotes a fraction of alkoxonium i o n produced from 1 mol of proton and y the mole fraction of methanol in a solvent, activities of the species being assumed to be equal to their mole fractions. Since both hydronium and alkoxonium ions are considered to be thermodynamic entities which determine the chemical potential of hydrogen ion, the activity of hydrogen ion, (€1 is given as9 (H+), = (€I+(H20))s"-". (W+(ROH)),"
(6)
A similar relationship with eq 6 for hydrogen ion i s obtained for (OH-),; thus
(OH-),
= (OH-),l-'*(OW-)s'
(7)
Since the ion product of a solvent, 1CTv(s), is defined as
Kw(s) = (H+L(OH:-), the ion product of a mixed solvent is given as =
K H z O 1 - ' . K ~ o ~(IX*O)8'-'* '. (ROH),'
(8)
(9)
Table 11: Values of -Log K,(s) Evaluated from Eq 9 Conon of methanel, % (w/w)
0 10
'
D. Dyrssen, So. Kent. Tidskr., 64,213 (1952). M. Tanaka, N. Nalrasulia, and H. Yamada, J. Inorg. A i d Chem.,in press. a
+ ROE
Under assumptions of K*lzo = 10 -14.0, -- 10-16*7,10 and x = 0.2311even in 0.1 M sodium chloride solutions, we calculated values of K,(s) in various water-meth-
Ej, mV/M [H*L
( W h )
H+(1120)
K,(s)
Table 1: Values of JAquid Junction Potential, E, Concn of methanol,
Here HzO and ROB in parentheses Irr eq 2 and 3 show molecules on which protons are distributed. The equilibrium coiivtant of the rcslction 4
20 30 40
50 60 70 80 90 100
of Solvents in Aqueous Methanol Solutions (9)
-Log Kw(s)
14.0 14. L 14.2 14.3 14.4 14 5 14.7 15.0 15.3 15'8 16.7
In an aqueous methanol solution the following equilibria hold for both water and methanol
a20
EI+(II,O) -t OH-,
K N ~ O (H +(H2O))s(oH->,/(H2o)s
(2)
and
+ OR-,
ROB :=M+rsKOH) =
(w:+(RoH)),(OR-),/(ROH),(3)
(8) G. Gran, Analyst, 77, 661 (1952). (9) H. Ohtaki, Bull. Chem. SOC.Jap., 42, 1573 (1969). (IO) N. Bjermm, A. Unmack, and L. Zechmeister, KgZ. Danslc. Vidensk. Selsk., Mat. Fys. Medd., 5 , 11 (1952); A. Unmack, Z. f h y s . Chem. (Leipzig,), 133, 45 (1928); G. Charlot and B. TrBmZon, Chemical Reactions in Solvents and Melts," Pergamon Press, Elmsford, N. Y., and Oxford, 1969, p 274. (11) B. E. Conway, J. O'M. Bockris, and 13. Linton, S.Chem. Phys., 24, 834 (1956).
The Journal of Physical Chemistry, Vol. 75, N o . 2 , 1971
HITOSHIOHTAKIAND Nosuo TANAKA
92
Table I11 : Dissociation Constants of 1,2-Diaminoethane (1,2-En), 1,3-Diaminopropaue (1,3-Pn), and 1,4-Diarninobutane ( 1,4-Bn) in Various Water-Methanol Mixtures Containing 0.1 M NaCl
0 10 20 30 40 50 60 70
80
7.12 7.04 6'.92 6.82 6.69 6.60 6.50 6.53 6.50
9.87 9.76 9.65 9.50 9.31 9.18 9.02 9.09 8.98
2.75 2.72 2.73 2.68 2.62 2.58 2.52 2.56 2.48
8.70 8.68 8.34 8.33 8.24 8.12 8.00 8.07 8.02
mol. mixtures, which are listed in Table 11. The values of K,(s) thus obtained were used for calculation of dissociation constants of diamines.
Results and Diseurasion Dissociation constants, K1 and K z , for each diamine were determined from the formation function, a, by means of a generalized least-squares method with the help of an electronic computer FACOM 230-60 in order to make the error square sum (U = E(% - %ca~cd)2)a minimum for the set of dissociation constants, K1 and K 2 . 'Yicalod denotes the value %onled = ([H+IsK1-' 2 [H'.],2K~-1K2-')/(1 [H+],Kl-l [H+]S2K1-'K2-*) for a particular set of the constants, K I and Kz. Dissociation constants thus obtained are summarized in Table 111. In all cases both pK1 and pK2 decreased with increasing methanol concentration up to 80% (W/W). Such variations of pK's of diamines are similar to those of monamines.9 Values of both ApKl (= pKl(in aqueous solution) pKl(in aqueous methanol solution)) and ApK2 (= pKz(in aqueous solution) - pK1(in aqueous methanol solution)) were slrongly dependent on the concentration of methanol. Moreover, it was found that ApK, and ApKz were very similar for 1,3-diaminopropane and 1,4-diaminobutarie. For 1,2-diaminoethane, however, the decrease of pK1 was less pronounced than that of pK2, although varirition of ApK2 for 1,a-diaminoethane with the methanol concentration was almost the same as those for other diamines. A thermodynamic comparison of dissociation constants of an acid in different solvents can be made through a comparison of free-energy differences of the acid existing in the different media. The difference of
+
+
The Journal of Phys
