DISSOCIATION OF AMMONIUM ION IN METHANOGWATER SOLVENTS
247
Dissociation of Ammonium Ion in Methanol-Water Solvents
by Maya Paabo,Roger G. Bates, and R. A. Robinson National Bureau of Standards, Washingtun,D. C. (Received August 19, 1966)
The acidic dissociation constant of ammonium ion in five methanol-water mixtures at 25” has been determined from measurements of the electromotive force of cells with hydrogen and silversilver chloride electrodes. The solvents studied contained 10, 20, 33.4, 50, and 70% methanol by weight. The pK, of ammonium ion follows the same general c o m e as that of other cation acids studied previously, decreasing initially as methanol is added to the aqueous solvent and passing through a minimum at a solvent composition in the vicinity of 70 wt. % methanol. The results are interpreted in terms of combined electrostatic effects and a solvent “basicity effect.” Values of pa=* for equimolal ammonia-ammonium chloride buffer solutions in the methanol-water solvents are given.
Introduction We have recently taken considerable interesW in the contrasting effect on the dissociation of acids of different charge types resulting from the addition of methanol to an aqueous solution of the acid. An acid of the uncharged type, dissociating to give a negatively charged base, is almost invariably weakened on addition of methanol; that is, its pK value increases. This effect is qualitatively consistent with the decreasing dielectric constant of the solvent. However, a charged acid, dissociating to a neutral base, usually becomes stronger (its pK value decreases) on addition of methanol, at least until the solvent contains about 70 wt. % methanol. On further addition of methanol, a minimum is observed in the pK value, followed by an increase to values which may exceed that in pure water. This is the course followed by the pK of 0-chloroanilinium ion,’ mnitroanilinium ion,’ the anilinium ion itself, the N-methyl- and N,N-dimethylanilinium ions, * and a number of alkylammonium ions.’ The ammonium ion has been studied6 at one methanol concentration (60 wt. %). Its dissociation results in one of the simplest bases, and consequently a study of its dissociation constant in other methanol-water solvents is of interest.
Aqueous solutions of ammonia, about 0.2 m, were prepared by bubbling nitrogen through a concentrated solution of ammonia in a gas-washing bottle and conducting the stream of gas into conductivity water. The stock solution was standardized by potentiometric weight titration with standard hydrochloric acid. Cell solutions were prepared by weight dilutions of a stock solution containing a 1:l mole ratio of ammonia to ammonium chloride. Additional water and methanol were added to yield the final concentration desired. All of the solvent compositions in this paper are given as weight percentages ( X ) of methanol. The preparation of the hydrogen and silver-silver chloride electrodes has been described previously.6 The recorded values of the e.m.f. (Table I) have been corrected to a partial pressure of 1 atm. of hydrogen. The corrections took account of the partial pressure of ammonia in equilibrium with the buffer solution in the methanol-water solvent. The partial pressure (p) of ammonia over 50% methanol 0.1 m in ammonia was measured by the gas-
Experimental Section Methanol of Spectro Grade was used. Ammonium chloride was recrystallized once from water; gravimetric analysis for chloride led to an assay of lOO.OO%, with an uncertainty of 0.04%.
J. @Q. C h a . , 20, 747 (1965). (4) C.L.deligny, R e . trav. cham., 79, 731 (1960). (5) D. H.Everett and W. F. K. Wynne-Jones, Tram. Faraday SOC.,
(1) E. E.Sager, R. A. Robinson, and R. G. Bates, J. Res. Natl. Bur. Std., A68, 305 (19f34).
(2) M. Woodhead, M. Paabo, R. A. Robinson, and R. G. Bates, M., A69, 263 (1965). (3) A. L. Bacarella, E. Grunwald, H. P. Marshall, and E. L. Purl%,
48, 531 (1962). (6) R. G. Batetes, “Determination of pH,” John Wiley and Sons, Inc., New York, N. Y., 1964,pp. 241, 282.
Volume 70, Number 1
Janzlary 1966
M. PAABO,R. G. BATES,AND R. A. ROBINSON
248
x-,
=
7
.o-l
-
x
m
E
m
0.01071 0.01980 0.02984 0.04804 0.05982 0.07773 0.09000 0.09761
0.87890 0.86548 0.8566 0.84627 0.84191 0.83639 0.83350 0.83178
0.01076 0,01764 0.03747 0.04898 0.06722 0.08024 0.09542
-
-x
-2
-
3
3
.
h
7
x
E
m
E
m
0.86709 0.85625 0.84015 0.83460 0.82822 0.82466 0.82141
0.009074 0.01050 0.01292 0.01989 0.02590 0.03279 0.03890 0.04536 0.05272 0.05835 0.06499 0.07807 0.08455 0.09753
0 * 85457 0.85162 0.84700 0.83772 0.83221 0.82735 0.82395 0.82075 0.81798 0.81583 0.81352 0.81010 0,80846 0.80590
0.01019 0.01498 0.02058 0.02810 0.03216 0.04126 0.04693 0.05186 0.06007 0.06588 0.07063 0.08494 0.09444 0.1061
transpiration method,? and the Henry's law constant, p,", was found to be 0.023 atm. kg. mole-' at 25". The value of this ratio is about 0.017 atm. kg. mole-' in aqueous solvents at 25°.s The contribution of ammonia to the equilibrium pressure is therefore so small that, the corrections could be estimated at X = 10, 20, 33.4, and 70 wt. % from the data for water and 50% methanol.
Calculations The acidic dissociation constant (aa) of ammonium ion in methanol-water solvents at 25" was calculated from the e.m.f. ( E ) of the cell P t ; Hz (g, 1 atm.), NHdm), NHdCl(m) in X wt. % methanol, AgCl; Ag
-
-x
-5
=-7
E
m
E
0.83108 0.82287 0.81626 0.81018 0.80762 0,80278 0.80031 0.79851 0.79561 0.79381 0.79280 0.78919 0.78717 0.78535
0.01410 0.01884 0.02323 0.02831 0.03314 0.03914 0.04254 0.04746 0.05689 0.06252 0.07123 0.07832 0.08869 0.09956
0.79801 0.79176 0.78822 0.78431 0.78171 0.77870 0.77717 0.77527 0.77221 0.77050 0.76833 0.76697 0.76479 0.76273
solubility product constant of silver chloride in 50% methanol,1° the stability constant was found to be 5.8 X lo7,and the corresponding correction to be added to the e.m.f. was only 0.03 mv. in 50% methanol. The correction for other methanolic solvents was estimated from the corrections in water and in 50% methanol. The hydrolysis of ammonia was also taken into account. The molality of hydroxide ion was calculated by the approximation log mOE-
log KS
+ ps(aHYCl)
(2)
The autoprotolysis constant Ks for methanol-water solvents has been measured by Koskikallio.l1 The activity coefficient term in eq. 1 was estimated by the DebyeHuckel equation. It was thus possible to define an "apparent" value of p(&) by
where m is molality and X is 10, 20, 33.4, 50, or 70 wt. %, by theformula
I n this equation, gEois the standard e.m.f. of the cell at the particular solvent comp~sition.~The subscript s here and elsewhere in this paper signifies that the quantity is based on the standard state in the methanolwater solvent rather than on the customary aqueous standard state. Since silver chloride is somewhat soluble in the buffer solutions, the correction for the increased chloride ion concentration was calculated from the stability constant of the silver-ammonia complex in methanol-water solvents as described earlier.? With the aid of the The Journal of Phyaical Chemistry
In eq. 3, A and B are the Debye-Huckel constants, do is the density of the solvent, and I is the ionic strength. Values of A&'/' and B&'/' are given in Table 11. The (7) R. G.Bates and G. D. Pinching, J . Res. Natl. Bur. Std., 42, 419 (1949). (8) F. E. C. Scheffer and H. J. DeWijs, Rec. trav. chim., 44, 655 (1925). (9) R.G.Bates and D. Rosenthal, J . Phys. C k . ,67, 1088 (1963); M. Paabo, R. A. Robinson, and R. G. Bates, J . C h m . Eng. Data, 9, 374 (1964); M.Paabo, R. G. Bates, and R. A. Robinson, Anal. Chem., 37, 462 (1985). (10) H. N. Parton, D. J. Davis, F. Hurst, and G. D. Gemmell, Trans. Faraday Soc., 41, 575 (1945). (11) J. Koskikallio, S u m e n Kemistileehti, B30, 111 (1957).
DISSOCIATION OF AMMONIUM ION IN METHANOL-WATER SOLVENTS
ion-size parameter d was taken to be zero because the p(JCa)' values found in this way fell on a straight line when plotted as a function of the ionic strength. The intercepts, p(&KJ, at I = 0 were found by the method of least squares; they are summarized in Table 111. The standard deviation of the intercept, ui, is given in the last column. The PUH*values for ammonia-ammonium chloride buffer solutions in methanol-water solvents were evaluated by the two relations Ps (UHyCl) =
(E - a0)F log mC1RT In 10
+
(4)
and
249
useful in the study of the dissociation of other acidbase systems in methanol-water solvents. Table IV: pa=* for Buffer Solutions of Ammonia and Ammonium Chloride (Each at Molality m ) in Methanol-Water Solvents at 25'
m
10
20
X 33.4
50
70
0.02 0.04 0.06 0.08 0.10
9.220 9.249 9.269 9.284 9.295
9.126 9.158 9.180 9.198 9.212
8.985 9.020 9.044 9.062 9.077
8.798 8.838 8.866 8.888 8.905
8.711 8.762 8.797 8.823 8.843
Discussion In an earlier communication12it was shown that the ~ ( 3 , value ) for protonated tris(hydroxymethy1)aminomethane in the 5001, methanol solvent at 25" is 7.818, as compared with 8.072 in water. Thus, we have for the two processes: in 5001, methanol
~~
Table 11: Values of the Debye-Hiickel Constants A&'/z and l3&ll2 for Methanol-Water Solvents a t 25'
X
Ada'/%, kg?/z mole-'/a
10 20 33.4 50 70
0.5489 0.5944 0,6721 0.8015 1.0215
Bdo'/z, kg.'/z mole-'/Z om.-%
RNH+(s) -+ H+(s)
+ RN(s); AGO
0.3347 0.3419 0 * 3535 0.3708 0.3954
=
44.62 kjoules mole-'
and in water RNH+(w) --j H+(w)
+ RN(w); AGO
=
46.07 kjoules mole-'
Hence, for the transfer reaction Table ID: Acidic Dissociation Constant of Ammonium Ion in Methanol-Water Solvents a t 25' X
P(&)
a
See ref. 7.
01
9.245" 9.146 9.044 8.893 8.687 8. 591b 8.571
0 10 20 33.4 50 60 70
RNH+(s)
... 0.001 0.001 0.001 0.001
...
0.002
' See ref. 5.
The single-ionic activity coefficient s y ~ was ~ - defined by a modification of the Bates-Guggenheim conventionI2
-1%
8'ycl-
=
1
+
A (dJ) 4.56B(d&'/'
(6)
The PUH*values for equimolal buffer solutions at X = 10, 20, 33.4, 50, and 70 wt. % are given in Table IV. These acidity functions may be regarded as reference data
+ H+(w) + RN(w) -+ RNH+(w) + H+(s) + RN(s)
(7)
the corresponding free energy change is AGO = - 1.45 kjoules mole-'. The solvents are distinguished by the letters w and s, representing water and 50% methanol, respectively. Of the three transfers involved, that of the uncharged base RN might be expected to involve the smallest change in free energy. The other two will be accompanied by changes in electrostatic energy, but these are not necessarily the only changes. We have endeavored to evaluate the electrostatic contribution (AG,l) by using the Hepler model,I3 in the following manner. A region of dielectric saturation (with dielectric constant east = 5 ) is assymed to exist around any ion, up to a distance of 1.5 A. from the center of the ion. At distances of 4 8. and beyond, the macroscopic (12) R. G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1, 163 (1960). (13) L. G. Hepler, Australian J. Chem., 17, 687 (1964).
Volume 70,Number 1 January 1966
M. PAABO, R. G. BATES, AND R. A. ROBINSON
250
dielectric constant (eo) of the solvent is assumed, while at intermediate distances a linear variation of dielectric constant with distance is predicated. This model was used by Hepler for aqueous solutions, and we have applied it to dissociation processes in 50% methanol. When a reasonable value of 4 8. ww taken for the radius, a value of AGel = -0.87 kjoule mole-’ was found for the transfer of the protonated tris(hydroxymethy1)aminomethane cation from 50% methanol to water. A radius of 2.8 A. was assigned to the proton on the ground that this ion is probably solvated with four water molecules. The transfer of an ion of this size from water to 50% methanol would be accompanied by a free energy change of AGel = 1.35 kjoules mole-’. The net electrostatic effect predicted for reaction 7 is therefore 0.48 kjoule mole-’. This is opposite in sign to the total observed effect (- 1.45 kjoules mole-’) and differs from it by about 2 kjoules mole-’. We have termed this difference, the part of AGO which cannot be accounted for by the modified Born electrostatic calculation, the “basicity effect” AGb AG”
- AGel = A%
X Y2
2 4 Y’
0.5~0
2x- Y
-
0.5~’
X’In (Y’y 2X’ - Y’ for the transfer of 1 mole of ammonium ions from a methanol-water solvent to water. In eq. 9, X = 0.4(e0 - esst) and Y = 1.5X - Esat. The unprimed quantities refer to values for the aqueous solvent, and the primed quantities, to corresponding values for the methanol-water solvent.
(8)
If the dissociation of ammonium ion in water is now compared with that in 50% methanol, we find that reaction 7 corresponds to AGO = -3.18 kjoules mole-’. Qualitatively, it is easy to see why this decrease should be greater than the value found for the protonated tris(hydroxymethy1)aminomethane cation. For the latter, the net electrostatic effect is positive because the RNHf cation is larger than the solvated hydrogen ion. The opposite is probably true for the dissociation of ammonium ion, a cation that is probably smaller than the solvated hydrogen ion. The electrostatic contribution to the dissociation of ammonium ion is therefore lower and, indeed, negative in value. Hence, if the basicity effect is characteristic of the solvent mixture and equal for the two acid-base systems, one would expect AGO for reaction 7 to be more negative for ammonia than for tris(hydroxymethy1)aminomethane. This is indeed the case, for there is a larger decrease in p($(,) for. the ammonium ion than for the protonated tris(hydroxymethy1)aminomethane cation in going from water to the solvent 50% methanol. A quantitative treatment of this situation is more difficult because it is necessary to assign a value to the radius of the ammonium ion. Wishaw and Stokes14 gave 3.75 A. for the mean ionic diameter of the ions in ammonium chloride, and hence 2 A. can be regarded as a reasonable approximation to the radius of the ammonium ion* with this value Of the radius’ the equ* tion developed by HepleP becomes The J o u r d of Physical C h & l y
A G e ~ = -Ne2 [ - ( - -1$ ) +1- l n
Wt
% METHANOL
Figure 1. Basicity effect A G for ~ methanol-water solvents &s derived from the dissociation of ammonium ion.
When appropriate data for water and for 50% methanol are inserted in eq. 9, AGe1 for the ammonium ion is found to be -2.49 kjoules mole-’. It has already been shown that the transfer of l mole of hydrogen ions (effective radius 2.8 A,) in the opposite direction (from water to 50% methanol) is accompanied by a change in electrostatic free energy (AG,,) of 1.35 kjoules mole-’. The total electrostatic effect for reaction 7 is therefore - 1.14kjoules mole-l, but the total observed effect is -3.18 kjoules mole-’. Again the residual “basicity effect” amounts to about -2 kjoules mole-’. Table V gives the results of similar calculations for six different methanol-water solvents. Both this table and Figure 1 show that the “basicity effect” increases linearly with the percentage of methanol in the solvent in the region where the mole fraction of methanol is less than 0.5. When the medium is rich in methanol, the treatment outlined here is doubtless (14) B. E’. Wishaw and R. H. Stokas, Trans. Faraday SOC.,49, 27 (1963).
DISSOCIATION OF AMMONITJM ION IN METFLOTOGWATER SOLVENTS
Table V:
251
“Basicity Effect” in Methanol-Water Solvents Derived from Measurements of the Dissociation of Ammonium Ion” X
c
AGe1 ( N E + ) AGel(H+) Total, electrostatic
Total,observed (AGO) Basicity effect (AGb)
10
20
33.4
so
60
70
-0.36 0.19 -0.17 -0.57 -0.40
-0.76
-1.44 0.79 -0.65 -2.01 -1.36
-2.49 1.35 -1.14 -3.19 -2.06
-3.25 1.81 -1.44 -3.74 -2.30
-4.15 2.31 -1.84 -3.85 -2.01
0.42 -0.34 -1.16 -0.81
Data are in kjoules mole-’.
inadequate. For example, the presumption that the saturation value of the dielectric constant is 5 in the vicinity of the ion would be in error if solvation of the ions by both methanol and water (or by methanol alone) were to occur. Stokes16has treated the effect of dielectric saturation in a manner not unlike that of Hepler.’* To a univalent cation is ascribed a radius which is greater by r, (= 2.8 8.) than its crystal radius (rJ so that allowance is made for a primary hydration layer of water molecules. For this region, an effective dielectric constant is delined by
The electrostatic energy is then found to be
With = 5 as before and r. = 1.48 A., Gelfor the ammonium ion in water is 36.34 kjoula mole-‘ and in 50% methanol is 34.75 kjoules mole-l. The electrostatic term for the transfer of ammonium ion from 50% methanol to water is therefore -1.59 kjoules mole-l. The treatment suggested by Hepler gives 9.48 kjoules mole-’ in 50% methanol and 6.99 kjoules mole-’ in water, a difference of -2.49 kjoules mole-’. The discrepancy between the calculated electrostatic effects arises from the way in which the effective dielectric constant in the hydration layer is calculated.
Stokes uses a value of about 9 for Eeff in water; the Hepler equation allows E to vary in the hydration shell, but the same result would be obtained if a constant value of Gff = 36 were used for water. The Stokes treatment was devised for cations of the noble gas type rather than for the ammonium ion, while the Hepler treatment relates to the transfer of ions between two not very dissimilar solvents, HzO and DzO,rather than from 5001, methanol to water. It is not surprising, therefore, that our calculations can yield only approximations; what is important, however, is the large (and negative) value of the “basicity effect’’ calculated by either route, The causes of this basicity effect must remain in doubt. It has been suggested, however,l8 that the addition of alcohol to solutions rich in water promotes, inter alia, a breakdown of the water structure. The basic oxygen centers of the water molecules thus become increasingly available for participation in protolytic reactions with the solutes present. The destructive process is presumably complete before the maximum evident in Figure 1 is reached, and thereafter the gross basicity decreases as the solvent becomes rich in methanol. Thia explanation appears to be qualitatively consistent with the solvent effect of methanol on the dissociation of ammonium ion as reported here. (15) R. H. Stokes, J . Ana. Chem. SOC.,86, 979 (1984). (16) E.A. Braude and E. 8.Stern, J . Chem. Soc., 1976 (1948).
Vdums 70, Nu&
2
Jan-
1888
