Calculation of Alkoxide and Ion Activity Ratios in the Water— System i E. KARÁSKOVA and U MOLLIN

Department of Inorganic and Physical Chemistry, Faculty of Natural Sciences, Palacký University, CS-771 46 Olomouc

Received 19 August 1991

The dissociation constants and ionic products of water and ethanol, equilibrium constants of the OH" + ROH ^ H20 + RO" reaction, and alkoxide and hydroxide ion activity ratios were determined in the water—ethanol system using various Gibbs energies of ions transfer + AGt°(H ). Validity of the Rochester equation is discussed on the basis of various literature data.

In the alkaline region in water— mixtures, where Ks is ionic product of a given mixture S, KR0H equilibrium establishes between the alkoxide and is the dissociation constant of alcohol in pure water, hydroxide ions according to the equation a* are activities of particles related to water as the

standard state, Кн2о is the dissociation constant of OH" + ROH г H20 + RO" {A) water in water, yH+ is the activity coefficient of Equilibrium reaction (A) is characterized by the hydrogen ions transfer from water to the certain mix­ equilibrium constant ture, % is the average activity coefficient of the trans­

ан2 ар>0 fer of halide ions from water to the given mixture, К = ° ~ (í) for which it holds ЗлонЗон- AG? (H+) = RT In 7H* (5) where a, are activities of particles. К can be ex­ r 1/3(AG? (Cľ) + AG? (Br) + AG?(|-)) = RT In pressed by dissociation constants of water and al­ r r r 7h

cohol in mixtures S (/(н2о> К%ои ) in this way Eqn (4) fits the experimental results for all alcohol Kh» concentration regions in the water— sys­ K = {2) tem [7]. In other systems water—alcohol the appli­ KH O 2 cability of eqn (4) is limited. It fits only up to a cer­ In rich alcohol mixtures К can be determined by 1H tain content of alcohol [5]. Nevertheless, the appli­ NMR spectroscopy [1] or by means of indicator cation of eqn (4) seems to be the most convenient colour changes [2]. In diluted alcohol mixtures К can to determine alkoxide and hydroxide ion activity ratios be derived from the absorbance of the alkoxide ions [5, 8, 9]. [3]. An empirical equation suggested [4] for the Pavelek [8] was interested in the influence of vari­ + water—methanol system is inapplicable in some other ous AG?r(H ) on the calculation of K (eqn (7)) in the [5]. Murto [6] tried to derive К on the basis water—methanol system. This work pursues the of kinetic measurement. К can also be determined same problem, but in the water—ethanol system. by the method [7] based on the assumption of the Solving of eqn (4) not only with %, but also with

linear dependence of Gibbs energies of lyate 7cr> 7вг-. 7*. or with (7c,- + 7Br-)/2 also seemed to be ions transfer and average Gibbs energies of halide interesting. ions transfer In the region where eqn (4) cannot be used, eqn (6) [9] can be used to calculate К log Гон- - W log % (3) log 7RO- - KRO- log 7h Ар/Сил - W(APKHK)' (6)

s s where /c0H-, /rR0- are the proportionality constants, where Ap/CHA - pK HA - pK^A. pK HA and p/CSA are pK 7OH". 7RO_ are activity coefficients of hydroxide and of weak carboxylic in the mixture solvent S and

alkoxide ions transfer, % is average activity coeffi­ in water, respectively. ApKm = pK^K - pK^Kt where cient of halide ions transfer, i.e. chloride, bromide, р/Снк and р/Снк are pK of water in the mixture S and and iodide ions. On the basis of these assumptions in water, respectively. W and у are the empirical Rochester [7] derived the equation constants.

KsY a Inn W ^ROH TOHv-^o-_ METHOD 'og—w Zw Yh - Constants /c0H-, /cEt0- from eqn (4) were determined = -/cOH.log7h+logK^o (4) by the way described earlier [10]. All quantities (ex-

156 Chem. Papers 47 (3) 156-159 (1993) ALKOXIDE AND HYDROXIDE ION ACTIVITY

Table 1. The Proportionality Constants /c -, к - from Eqn cept %•, %) needed to the calculation were also used Et0 ои like those in [10]. Gibbs energies of hydrogen and (4) and Relative Errors e of These Constants halide ions transfer were taken from [11—18]. + Parameter ^EtO" ^OH" e/% Ref. AG?r(H ), AG?r(Cr), AG?r(Br), and AG?r(r) were com­ % 0.96 1.30 28.0 [11] plete only in [11, 14]. 7H+ and ycf were given in [12, + 0.80 1.23 3.22 [14] 13] and 7H only in [15—18]. To calculate ycr, rBr-, y- + 1.00 1.24 - [15] corresponding to yH from [15—18] the following -0.29 2.10 64.6 [16] equation was used 41.5 - 71.8 66.0 [17] 7cr 0.75 1.15 11.9 [11] + [12](TPTB) AG?r(HX) = AG?r(H ) + AG?r(X") (7) - 1.61 2.32 45.6 0.50 1.30 35.3 [12](TATB) where HX is hydrogen halide. We took the average 0.45 1.32 30.2 [13] Gibbs energies of hydrogen halide ions transfer 0.60 1.20 25.6 [14] 0.18 1.41 46.0 [16] AG?r(HX) from [11]. Rochester's equation (4) was used for the follow­ Гвг- 0.86 1.23 8.3 [14] -0.48 2.35 68.1 [16] ing combinations: y + with %, y , y -, and y-, re­ H cr Br ъ- 1.00 1.30 8.72 [14] spectively, and ft+ with (/с,- + %r-)/2. y0H-, fecr, К|юн. -0.16 1.75 71.0 [16]

/Сн2о, K|h, Kl, K, alkoxide and hydroxide ion activ­ (ľcr + №r-)/2 0.68 1.25 17.8 [11] ity ratios О = а -/а н- were derived from /c - and ЕЮ 0 0H TPTB - tetraphenylphosphonium tetraphenylborate, TATB - /cEt0- by the way described earlier [10]. Ionic prod­ tetraphenylarsonium tetraphenylborate. ucts of mixtures calculated by us were compared

with those determined experimentally (ApKs). On the basis of this comparison the best results were cho­ Table 2. Differences between Calculated Ionic Products of the

Mixtures and Those Determined Experimentally ApKs sen and used to calculate рКн2о according to eqn (6) in ethanol-rich mixtures. The dissociation con­ ApK stants of acetic acid were taken from the same lit­ s erature as in [10]. rdicuiieiei w(EtOH)/% 10 20 30 40 50 Ref.

% 0.03 -0.02 - 0.09 - 0.06 -- 0.03 [11] RESULTS AND DISCUSSION 0.00 0.00 0.02 -0.10 - [14] -0.01 -0.01 - - - [15] 0.00 -0.01 -0.02 [16] The proportionality constants /c0H-, /cEto- from eqn - - (4), the dissociation constants of water and ethanol, 0.01 -0.04 -0.01 - - [17] 7вг- 0.02 ionic products of water and ethanol, the equilibrium 0.02 0.07 - 0.01 0.09 [14] 0.01 -0.02 0.04 - - [16] constants K (eqn (2)), and alkoxide and hydroxide Гсг 0.01 0.00 -0.03 0.01 0.03 [11] ion activity ratios in the system water—ethanol 0.01 -0.04 0.18 - - [12] (10—90 mass % EtOH) were obtained as mentioned 0.02 0.01 -0.05 0.02 0.10 [12] above and the results are given in Tables 1—3. 0.01 - 0.01 0.10 0.04 0.10 [13] - 0.05 - 0.05 -0.09 - - [14] The proportionality constants /c0H- and /cEt0- ob­ + 0.00 0.00 -0.01 - - [16] tained on the basis of different yH are listed in й- 0.02 0.01 - 0.05 - 0.01 0.05 [14] Table 1. The criterion of the use of Rochester's equa­ 0.00 0.00 0.02 - - - [16] + tion to solve the equilibrium (A) are always the dif­ (ľcr )V)/2 0.02 0.01 - 0.02 - 0.04 - [11] ferences between the calculated ionic products of the mixtures and those determined experimentally. centration region by the author, Rochester's equa­ These differences are listed in Table 2. tion was applicable: with yh and yc,- up to 50 mass From Table 1 it is obvious that /c - and /c - val­ 0H Et0 % EtOH, with yBr- and yr eqn (4) was not solvable, ues obtained from Jakuszewski's literature data [17] and with (yc,- + 7Br-)/2 this equation was solvable up differ most from the others. This is true both abso­ to 40 mass % EtOH. lutely and relatively. The values of /cEt0- are bigger The dissociation constants of water and ethanol than /c0H-. This relation is opposite according to other in the mixture were also calculated from all /c0H- and literature data, /cEto- is smaller than /c0H-. /cEt0-. These dissociation constants did not differ too From Tables 1 and 2 it is obvious where much (even the values obtained from Jakuszewski's Rochester's equation was applicable with different values [17]). That is why we averaged the dissocia­ + + literature values of AG?r(H ). I.e., with AG?r(H ) tion constants. These averaging values were further determined by Wells [11] on the basis of measu­ used for calculations according to eqn (6). The rement of the equilibrium constant of the reaction dependence of negative logarithms of these aver­ + + H (H20)x+ + ROH ^ H (H20)x-i(ROH) + H20, aging dissociation constants of water and ethanol which is considered constant over the whole con- on reciprocal relative permittivity of the mixture is

Chem. Papers 47 (3) 156-159 (1993) 157 E. KARÁSKOVA, J. MOLLIN

Table 3. Dissociation Constants of Water рКн2о and Ethanol Pavelek [8] obtained values for equilibrium con­ pKitoH» Ionic Products of Water pK% and stant К in the system water—methanol, which were Ethanol pKl , the Equilibrium Constants K (eqn (2)), th dependent a little on the extrathermodynamic way and Alkoxide and Hydroxide Ion Activity Ratios Q in of obtaining of AG? (H+). Our results for the system the Water—Ethanol Mixture r water—ethanol are similar. It is probably so because w(EtOH) there is lyates ions activity ratio in eqn (4), which is s P*SH o P*w P^EtOH pK К Q % 2 Eth proportional to the difference of the corresponding Gibbs transfer energies. But this difference AG?(RO") a 0.02 r 10 15.94 14.21 15.88 15.56 1.15 - AG? (OH") is independent of AG? (H+). 20 16.16 14.46 15.84 15.25 2.09 0.20 r r 30 16.39 14.70 15.74 15.00 4.46 0.62 We were also interested which halide ions were 40 16.57 14.89 15.80 14.97 5.88 0.82 the best for the calculation. Eqn (4) was solvable 50 16.75 15.10 15.86 14.99 7.75 1.14 with activity coefficients of chloride ions transfer and b 60 16.96 15.32 16.14 15.23 . 6.62 1.24 with the average activity coefficients of halide ions 70 17.21 15.60 16.47 15.52 5.49 1.19 80 17.49 15.94 16.60 15.60 7.75 2.16 transfer for the most data. 90 17.84 16.44 17.88 16.82 0.91 0.41 The total Gibbs transfer energy can be divided into a contribution determined by electrostatic forces and a) Values obtained by averaging of values obtained from eqn a contribution determined by chemical forces, (4) with various literature data [11—17]. b) Values obtained from eqn (6). For the calculation the dissociation constants i.e. [19] of water (10—50 mass % EtOH) obtained from Rochester's equation (4), the dissociation constants of water in pure ethanol [10] and of acetic acid [10] in water—ethanol mix­ AG?r(i) = AG?r(i)elst + AG?r(i) (S) tures were used.

shown in Figs. 1 and 2. The dissociation constants The electrostatic contribution can be calculated from with the different combination of halide ions do not Born's equation [20] according to which it differs only differ very much. That is why these values were also in the radii for different ions. According to conclu­

averaged. These reaveraging values were used to sions of paper [10], AG?r(i) is determined mostly by the calculation of ionic products of water pKl and electrostatic forces in the medium with sufficiently

ethanol p/Cfthf the equilibrium constants K, and high relative permittivity. Consequently, it results in alkoxide and hydroxide ion activity ratios, which are the proportion of Gibbs energies of different ions

listed in Table 3. Eqn (4) with yH* from [18] is not transfer up to the certain content of alcohol and also solvable. Rochester's equation validity [10].

18.0

P*Et0H

16.0 -

0.04 0.01 0.02 0.03 0.04

Vrr

Fig. 1. Dependence of рКн о on 1/e, in the water—ethanol sys­ 2 Fig. 2. Dependence of рК1юн on 1/^ in the water—ethanol sys­ tem. Dissociation constants were calculated using О % tem. Dissociation constants were calculated using О % (7), Э /er (2), Ф Гвг" (3). ® К (4), б ( + )fe -)/2 (5). 7сг r (1), Э /er (2), (D Гвг- (3), ® и- (4), 0 (Гсг + *г)/2 (5).

158 Chem. Papers 47 (3) 156-159 (1993) ALKOXIDE AND HYDROXIDE ION ACTIVITY

Our work confirms conclusions of papers [8] and Chem. Commun. 52, 1115 (1987). [10] and is a contribution to the knowledge about 10. Mollin, J. and Karáskova, E., Collect. Czech. Chem. the equilibrium (A). Commun. 56, 269 (1991). 11. Wells, C, J. Chem. Soc, Faraday Trans. 1 80, 2445 (1984). 12. Popových, О., Gibofsky, A., and Berne, D., Anal. Chem. 44, 811 (1972).

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