Thermodynamics of ionization of trans-crotonic and adipic acids in water; the silver - silver adipate electrode

UPENDRA NATH DASH A ~ D UTTAM KUMAR NAYAK Department of Chemistry, Gangadhur Mrher College, Samhalpur (Oris~a), India

Received June 18, 1979

UPENDR.~ NATH DASH and UTTAM KUMAR NAYAK. Can. J. Chem. 58,323 ( 1980). The ionization constant, K, of trans-crotonic acid, and the first and second ionization constants, K, and Kz, of adipic acid

have becn determined in water at seven different temperatures ranging from 15 to 45°C with the help of the cells without liquid junction using silver - silver chloride and quinhydrone electrodes. The variations of pK, pK,, and pK2 with temperature have been expressed by the equations

and

pKZ = 4776.61/T - 27.98 + 6.01 x 10-'T

From the temperature coefficient of the ionization constants, the standard enthalpy, entropy, Gibbs energy, and heat capacity changes of the corresponding dissociation processes have been calculated. Using the values of ionization constants of adipic acid, the standard potential of the Ag(s)/Ag2Ad(s)/Ad2- electrode, and the related standard thermodynamic quantities for the electrode process

Ag,Ad(s) + 2e G 2Ag(s) + Adz-(solvated)

have been calculated in water at those temperatures.

UPENDRA NATH DASH et UTTAM KUMAR NAYAK. Can. J. Chem. 58, 323 (1980). On a determine la constante d'ionisation K de l'acide crotonique trans ainsi que les constantes de premikre et de deuxikme

ionisation K, et Kz de l'acide adipique en solution aqueuse et a 7 temperatures differentes allant de 15 45°C. On a fait ces determinations au moyen de cellules sans pont de jonction liquide et en utilisant des Clectrodes d'argent - chlorure d'argent et de quinhydrone. Les variations de pK, pK, et pK2 en fonction de la temperature sont representees par les equations suivantes:

A partir du coefficient de temperature et des constantes d'ionisation, on a calculC, l'enthalpie normale, l'entropie, I'energie de Gibbs et les variations de la capacite calol-ifique des reactions de dissociation correspondantes. En utilisant les valeurs des constantes d'ionisation de l'acide adipique, on a determine en solution dans I'eau et dans le mtme intervalle de temperature: le potentiel normal de I'electrode Ag(s)/Ag2Ad(s)/AdZ- et les quantites thermodynamiques relatives a la reaction de l'electrode

Ag2Ad(s) + 2e G 2Ag(s) + Ad2-(solvate) [Traduit par le journal]

Introduction [Al A~,A~C~(~)/KC~(~~),KA(~~),HA(~I),QHZ-Q~P~

Until quite recently, no work seems to have been [Bl A~,A~C~(S)/KC~(~~),KHA~(~Z),HZA~(~I),QH~-Q/P~ done on-the determination of ionization constants - - A

QllU

of trans-crotonic and adipic acids in aqueous medium over a range of tem~erature. A survev of [el A~,A~C~(~)/KC~(~~),KZA~(~Z),KHA~(~I),QI-~-Q/P~

the literature (1-3a,>), howevir, shows that the pK where A stands for trans-crotonate ion, and Ad for values of these acids have been reported in water at adipate ion, were made in water at seven temperatures 25"C, and the values of AN0 and AS0 are available ranging from 15 to 45°C for determining the ioniza- (2, 5 ) at this temperature. The Dresent work has been tion constant of trans-crotonic and the first and se- . . undertaken as a&part of our programme of deter- cond ionization constants of adipic acid, respectively. mining the ionization constants and the related ther- Although the electrodes of the type, Ag/Ag,X(s)/ rnodynamic quantities of organic acids in aqueous X2-, where X2- stands for oxalate, malonate, and mixed solvent media. succinate, or chromate ion, have been studied by the

Electromotive force measurements of cells of the authors (6-9) in aqueous, non-aqueous, and mixed type media, the behaviour of the silver - silver adipate

ooO8-4042/80/040323-05$01 .OO/O a1980 National Research Council of CanadaIConseil national de recherches du Canada

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324 C A N . J . CHEM. VOL. 5 8 . 1980

electrode has not yet been studied in aqueous medium. The present work, therefore, aims at deter- mining the standard potential of this electrode in water at different temperatures. The cell of the type

was used for this purpose.

Experimental trans-Crotonic acid (Fluka AG, Buchs SG 574253) was

crystallised from boiling conductivity water, dried at 603C for 2 h, and kept in a vacuum desiccator over anhydrous calcium chloride. Adipic acid (G.R., Proanalysis) was used without further purification. Potassium salts of trans-crotonic and adipic acids were prepared by the method similar to that described elsewhere (10, 11). The salts were dried at 110-120'C and stored in vacuum desiccator over anhydrous calcium chloride. Potassium chloride (BDH, AnalaR) was dried above 100°C and stored in uacuo. Quinhydrone and silver - silver chloride electrodes were prepared by the method similar to that described earlier (12, 13).

Silver adipate was prepared by adding silver nitrate (BDH, AnalaR) solution (0.2 mol dm-3) slowly to equal volume of potassium adipate solution (0.11 mol dm-3). The precipitate formed was carefully washed by decantation with conductivity water and stored in an amber-coloured glass-stoppered bottle for subsequent use.

Silver oxide was prepared by the method described else- where (14).

Silver - silver adipate electrode was prepared by the method similar to that of the silver - silver oxalate electrode (6). After preparation, the electrodes were stored in a 0.05 mol dm-3 aqueous solution of adipic acid for about 24 h and then rinsed with the cell solution containing adipic acid before use. Only those electrodes showing a potential difference of 0.1 mV or less when mutually compared with each other were used.

The cell vessels were of the type recommended by Harned and Wright (15).

Solutions for emf measurements were prepared in con- ductivity water. The cell measurements were carried out with electrodes set up as described earlier (6, 12, 16).

Results and Discussion

The method of calculation of the ionization con- stants of mono- and di-basic acids has been adequately described (6, 10, 11, 16).

The ionization constant, K, of trans-crotonic acid, or the first ionization constant, K,, of adipic acid, corresponding to the equilibrium

HxA + solvent ;lt H+(solvated) + Hx- ,A-(solvated)

where A is the trans-crotonate ion when x = 1, and adipate ion when x = 2, is defined as

where m and y are the molality and activity co- efficient, respectively.

The "apparent" hydrogen ion molality, mH+ ' is re-

lated to the emf E of the cell [A] or [B] through the relation (16),

[2] - log m,+' = (E - EO)F 2.302613 T + log m,,-

where I and do are the ionic strength of the solution and density of the solvent, respectively, and a0 is the ion-size parameter. As a first approximation I was taken to be equal to m, + m, but subsequently an accurate value was obtained by successive approx- imation and refinement to a constant value of I ( r r m, + n ~ , + m,+'). The "apparent" ionization constant K' (for trans-crotonic acid) or K,' (for the first ionization step of adipic acid) was calculated from the expression

[3] log K' or log K,' = - 2 ~ ( 1 d ~ ) ' ~ ~ I + a0~( ldo)112

mH+'(m2 + mH+') + log (m1 - ~ H + ' I

The true ionization constants, K and K,, were obtained from the intercepts of the log K' vs. I, and log K,' vs. I plots, respectively.

The second ionization constant, K,, of adipic acid corresponding to the equilibrium

HAd- + solvent g H+(solvated) + Ad2-(solvated)

is given by

and the "apparent9' second ionization constant, K2', was calculated from the expression

[5] - log K,' = (E - EO)F 2.302613 T

where m, is the molality of HAd-, m, is the molality of Ad2-, and m, is the molality of C1- used in the cell [C], E is the observed emf of the cell, and I is the ionic strength of the solution given by

The second ionization constant was obtained by linear extrapolation to zero ionic strength (I = 0) of the function, - log K,'.

The values of EO(Ag,AgCl), E0(QH2-Q), the Debye-Hiickel constants, and density, do, of the solvent needed for the calculation of log Kt9 log

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DASH A N D NAYAK

FIG. 1. Plot of - log K' versus ionic strength for trans- crotonic acid at different temperatures. FIG. 2. Plot of - log K,' versus ionic strength for the first

step ionization process of adipic acid at different temperatures.

K,', or log K2' at different temperatures were ob- tained from the literature (17, 18). The values of the ion-size parameter a0 were obtained by the method described earlier (16), and taken to be 0.6 and 0.55 nm for trans-crotonic and adipic acid, respectively.

The values of log Kt, log K,', and log K,' thus calculated were found to vary linearly with I (Figs. 1-3) for different temperatures and the linear extra- polation to I = 0 of values of log K', log K,', or log K,' yielded log K, log K,, or log K,, respectively, for trans-crotonic and adipic acids. These values are presented in Table 1. The standard deviations calculated by the least-squares method are also shown in Table 1.

The standard molal potential, Em0 of silver - silver

extrapolating (6, 8) the auxiliary function, EO: given by

[7] EO' = E + ( 2 . 3 0 T ) ( 1 + - 6A(Id0)'" a 0 ~ ( I d o ) 1 i 2 )

to ionic strength, I = 0, where E is the observed emf of cell [Dl, m is the molality of adipic acid solution, and a and p are the degrees of first and second ionization constants of adipic acid, respectively, defined by the expressions

adipate electrode was obtained by the method of and

{-(ma + K,) + [(ma + K,), + 4maK2]112} [91 P = 2ma

and the ionic strength I is given by

[lo] I = ma(1 + 2P)

Using the K, and K, values of adipic acid obtained at different temperatures from emf measurements just described, the degrees of ionization a and P of adipic acid at the corresponding temperature were computed following a reiteration procedure. The values of Em0 are also included in Table 1 along

with their standard deviations obtained by the least- squares method.

The variation of pK of trans-crotonic acid, pK, and pK, of adipic acid, and E,,' of the silver - silver adipate electrode with temperature has been ex- pressed by the equations

[11] pK = 105.54JT + 4.47 - 2.26 x 10-2T

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CAN. J . CHEM. VOL. 58. 1980

TABLE 1. Values of pK of trans-crotonic acid, pKl and pK2 of adipic acid, and E,,O of the silver - silver adipate electrode in water at different temperatures

T CC) PK PKI PKZ Em,"

TABLE 2. Values of AGO, AH0, AS0, and ACP0 for the ionization processes of trans-crotonic and adipic acid and the electrode process of the silver - silver adipate electrode in water at 25-C

Process

H A = H + + A- 10.90 40.43 172.23 257.77 HzAd e H i + HAd- 25.20 3.83 -71.72 17.34 HAd- = H + + Ad2- 34.03 -10.78 -150.36 -686.11 Ag,Ad(s) + 2e S 2Ag(s) + AdZ- 44.61 55.26 35.75 -

and

[14] E,' = 0.4626 - 1.92 x 1 0 - ~ ( t - 25) - 1.42

x 1 0 - ~ ( t - 2512

respectively, where T and t are the temperatures in K and "C, respectively.

The values obtained for the standard thermo-

6 0 g:

FIG. 3 . Plot of - log Kz' versus ionic strength for the second step ionization process of adipic acid at different temperatures.

dynamic quantities, AGO, AH0, AS', and ACpO associated with the reactions investigated are listed in Table 2.

Since this work constitutes the first attempt to measure thermodynamic ionization constants for trans-crotonic and adipic acids in aqueous medium over a range of temperature using galvanic cells, a direct comparison with the results of other works is not possible. However, different values of dissocia- tion constants for trans-crotonic and adipic acids are reported by various workers at 25'C. The values that have been reported earlier for trans-crotonic acid, pK = 4.698(1) and 4.686(4), and adipic acid, pK, = 4.418(5), 4.43(5), and 4.42(4), and pK2 = 5.412(5), 5.42(5), and 5.277(3) at 25°C were deter- mined from the studies of calorimetric and conducto- metric measurements. The different values of pK for trans-crotonic acid and pK, for adipic acid are in reasonably good agreement with each other, but the value pK, = 5.277 for adipic acid is found to be widely discrepant from the other values. The con- stants reported in Table 1 are somewhat higher than the constants reported earlier at 25°C excepting the pK, value for adipic acid. This discrepancy might be due to the use of ion-size parameter, a', in the calculation of pK values in the present work which was not considered in the previously reported values of pK of the investigated acids, since according to eq. [3] the pK is dependent on the ion-size parameter, and the pK values are expected to be higher than that calculated without considering the ion-size para- meter (3b). Since the cells of the type [A], [B], and [C] have been employed satisfactorily for determina- tion of pK values of a number of weak acids (19) and

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DASH A N D NAYAK 327

the ion-size parameter was ascertained by following the method of Roy, Robinson, and Bates (20), it is believed that the present set of data is more trust- worthy.

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