IONISATION OF TWO ELECTROLYTES I N ALCOHOL-WATER MIXTURES; INFLUEICCE OF ENVIRONMENT OX IONISATION BY F. BRADLEY AND W. C . M . LEWIS
Part I While it is now fairly certain that strong electrolytes are almost completely ionised, the classical concept of degree of ionisation of an electrolyte can still be applied with advantage to weak or moderately strong electrolytes and the further classical assumption-that the degree of ionisation of an electxolyte at a given dilution is given by the ratio of the equivalent conductivity at that dilution to the equivalent conductivity a t infinite dilution-may also be employed. These concepts are more particularly applicable to the interpretation of certain experimental data referring to the influence of environment upon the ionisation of weak and moderately strong electrolytes. The ionisation of salicylic acid, cyanacetic acid and bromacetic acid has been investigated by Godlewskil, and although this author's results are not too accurate they do show roughly the enormous influence that the solvent has upon the ionisation of these acids. According to Godlewski the ionisation constant of salicylic acid at 18' in alcohol is only one ten-thousandth of that in water. Neale2 found much the same state of affairs for picric acid in acetonewater mixtures-the addition of acetone to an aqueous solution of picric acid diminishes the ionisation constant many times. Recently Pring3 has shown the same to be true for weak bases in acetone-water mixtures. Up to the present, however, the only relation which attempts to express, in a semi-quantitative manner, the influence of the solvent upon the ionisation of an electrolyte is the following: Ki = Di3 -Kz Dz3 where K1 and Kz are the ionisation constants of an electrolyte in two media of dielectric constants D1 and Dz respectively. I n various forms this relation has been deduced by Baur', by Kruger5and by Walden6,and it is really only a simple quantitative expression of the Nernst-Thomson rule. For electrolytes obeying the law of mass action, however, this relation is quite incapable of expressing the great changes in the ionisation constant K which occur while the dielectric constant D undergoes only relatively small change, and it was therefore obvious that a really satisfactory explanation of the behaviour of such J. Chim. phys. 3, 393 (1905). *Trans. Faraday Sac., 17, 505 (1921) Trans. Faraday Soc., 19 7 0 j (1924). 2. Elektrochemie, 11, 936 (1905). Z.Elektrochemie, 17, 453 (1911). e 2. phys. Chem. 94, 263 (1920). 1
783
IOKISATIOh7 I N ALCOHOL-WATER MIXTURES
electrolytes in different solvents would have to be based on different physical concepts. The first step was the obtaining of reliable experimental data, and to this end the conductances of solutions of salicylic acid and of cyanacetic acid were measured over a complete range of alcohol-water mixtures at both 2 j' and 35'. In the course of this investigation it was found that a considerable number of the existing data on the subject were based upon erroneous values of the equivalent conductivity at infinite dilution, a fact which of course vitiates to a large extent their utility'. The usual method was used for determining the conductances of the solutions, employing a metre wire bridge which was carefully calibrated. The cells used were of the Arrhenius closed type, made of borosilicate glass, with rigidly supported vertical electrodes. The electrodes were either lightly platinised or simply of smooth platinum, since only with such electrodes was it found possible to obtain accurate values. The experimental error in measuring the resistance of a solution did not exceed 0.1per cent. Conductivity water having a specific conductance of 0.7 X I O + to 1.0 x IO-^ mhos at 25' was employed throughout; the specific conductivity of the alcohol varied between 6.0 x IO-* and 1.0 x 1.0-7 mhos a t 2 jo.The alcohol used was the product of thorough drying with highly active quicklime (prepared by roasting mal ble at Boo' to 1000' for some hours2) followed by several distillations in a special apparatus. The thermostats were maintained a t 25' and 35' to within 0.02'. All the conductivities were corrected for the conductivity of the solvent by subtracting this quantity from the observed conductivity. Special attention was paid to the obtaining of accurate values of the equivalent conductivity a t infinite dilution. It was concluded that the most reliable method of estimating these values was to determine the mobilities of the separate ions and to apply Kohlrausch's law of the independent mobility of ions. Consequently the conductances of dilute solutions of hydrochloric acid, of sodium chloride and of the sodium salts of the acids concerned were examined over the whole range
TABLE I Equivalent Conductivity at Infinite Dilution Per cent 3.lcOhol 0.0
Salicylic acid 2j"
Cyanacetic acid
30" 439.0 299.0
3 92.0 255.7
307 ' 5
202.0
165.3
209.0 141.7 87.4
2 j"
35" 449.0
33.2
382.5 248.6 160.0
52.0
105.8
135.8
I 10.6
73.5 85.7
66.0 52.0
84.4 66.1
68.5 54.0
95.0
46.0 86.0
57.0
48.0
68.0 59.5
107.0
87.0
108.0
16.2
100.0
Cf. Godlewski's results: loc. cit.
* J. Am. Chem. Soc., 30,353
(1908).
F. BRADLEY AND W. C . &I. LEWIS
784
of alcohol-water mixtures. The numerical values of the equivalent conductivity at infinite dilution for salicylic acid and cyanacetic acid are recorded in Table I. Throughout this paper the term "per cent alcohol" means per cent by weight, i.e., grams alcohol per IOO grams of alcohol-water mixture. I n all the alcohol-water mixtures the ionisation constants of salicylic acid were found to he nearly independent of the dilution. The same slight trend with dilution of the ionisation constant was observed in all cases, in the sense that the ionisation constant decreases as the dilution increases, hut over thF8 range of dilution studied, usually 8 to 1 0 2 4 ~litres, the variations never exceeded 5% of a mean value and were often considerably less. Cyanacetic acid showed the same behaviour, although the variation with dilution of the ionisation constant was slightly greater. Table I1 gives the experimental values of the ionisation constants for salicylic acid and cyanacetic acid in alcoholwater mixtures. TABLE I1 Ti
Per cent alcohol
Kx105
x105a
Salicylic acid 25O
Cyanacetic acid 35"
0.0
100.0
16.2 33.2
66.0
103.0 65.3
26.0
25.0
52.0
73.5 85.7 89.0 93.3 97.8 100.0
9.0 1.8 0.45 0.25
8.8 1.7 0.40 0.23
0.08
0.07
0.01
0.01
0.00024
0.00026
2j"
320.0 190.0 94.0 36.0 8.4 1.7 I
.o
0.37 0.05 0.0032
35"
304.0 180.0 88.0 33.9 7.4 1.4 0.9 0.33 0.045 0.0030
Theoretical Let AB he an unionised melecule about to undergo ionisation into ions A+ and B- in a solvent of dielectric capacity D. Assuming that the molecule AB requires on the average a critical amount of energy E, which it must absorb before it can ionise, the rate of ionisation will be kl , e -E/RT x CAB where kl is a reaction velocity constant independent of temperature, and CAR is the concentration of the unionised molecules. If we now identify the critical increment E with the electrostatic work expended in separating the charged ions A+ and B- (constituting the unionised molecule) to a distance beyond their sphere of mutual attraction we can write E = E,/D where E, is the critical increment in a medium of dielectric capacity unity, Le., in vacuo, or in the gaseous state. 1
2
Measurements were taken at dilutions of 8 , 16, 3 2 , 64, 128, 256, and 1024 litres. Rounded values, measured at a dilution of 1024 litre?.
785
IONIf?ATION IN ALCOHOL-WATER MIXTURES
bpplying similar ideas to the recombination of the ions t o form the unionized molecule we obtain the rate of union k 2 .e -E,’/DRT x CA x C R where the sum of the critical increments of the ions E’, is identified with the work necessary to remove the solvent molecules with which the ions are hydrated. Equating the expressions for the rate of ionisation and for the rate of recombination of ions me have at equilibrium
x B‘ - -kl e (E,’-E,)/DRT CAB k2 and the left hand side of this equation is obviously the ordinary ionisation constant. This relation embodies in simple form the purely physical influences operative in the ionisation of an electrolyte, and as will be seen from the comparison of calculated with observed ionisation constants which is contained in the following table, it represents the observed results much better than does the relation K D3. It is, however, by no means satisfactory. Nevertheless the physical picture which the above formula conveys is much more illuminating than that afforded by the old relation. ‘A
TABLE I11 Salicylic acid, 25’ Percent alcohol 0.0
16.2 33.2 52.0
73.5 85.7 89.0 93.3 97.8 100.0
Dielectric constant
K obs. X 1 d
78.5 66.5 55.9 45.5 35.0
100.0
29.7
0.45
I< calc
I)
K calc. X 1 6 6 ( K a D3)
(100.0)
(100.0)
X
105
(Equation
1.7 45) 0.29
60.8 36. I 19.5 8.9 5.4 4.7
0.19 0.09 0.08
4.1 3.3 3.2
66.0
55.2
26.0
26.4
9.0
9.2
I
.8
28.3
0.25
27.0
0.08
25.3
0.01
24.9
0.0002
(0 ’
Although not reproduced here the data for cyanacetic acid show precisely the same behaviour as those for salicylic acid in the above table. To obtain the values of the constants kl/kz and (Eo’ - E,) in the expression (equation I ) for the ionisation constant two of the observed ionisation constants are substituted in the formula and the required terms are evaluated from the two simultaneous equations so obtained. In the case exemplified in the preceding table the data for 0.0 and 85.7 per cent alcohol have been used for this purpose, and the value of the composite critical increment term (Eo’- E,) is calculated to be - 153,700 calories. It will be seen that the agreement between the calculated and the observed ionisation constants is quite
786
F. BRADLEY AND W. C . M. LEWIS
good up to about 90 per cent alcohol, and this is a considerable range of solvent. The discrepancies in solvents of higher alcohol content are sufficiently serious to indicate the necessity of further investigation of the particular mechanism concerned, and as will be shown later they lead to considerations of a chemical kind as distinct from the purely physical concepts employed in the present instance. These chemical considerations prove to be only of first importance, so far as numerical values are concerned, over the range of alcoholwater mixtures containing very little mater, the values already calculated over the remaining range being comparatively little affected.
Part I1 We now proceed to the ((chemical”considerations, the object of which is an extension of the theory already developed so as to include, in what is believed to be a more satisfactory manner, the behaviour of these same electrolytes in alcohol-water mixtures containing very little water. The principal feature to be noticed in these solvents is that the influence of slight variations in the water content of the solution is inordinately great, and indeed in the solvent region extending from 90 to 100 per cent alcohol the decrease in the strengths of the acids studied (salicylic acid and cyanacetic acid) as the amount of water grows less and less is much too rapid to be accounted for by the exponential formula already deduced (equation I ) . In the absence of any purely physical influence likely to be capable of explaining the exaggerated effect of small amounts of water recourse was had to the chemical concept of hydration. For the sake of brevity the full evidence for and the plausibility of the hypothesis will not be entered into since they have been treated at length by J. Kendal1,l whose ionisation hypothesis is employed here. The basic idea is that “ionisation is a consequence of compound formation.” In the present case it is assumed that the ionisation of weak acids in alcohol-water mixtures is preceded by hydrate formation according to the following scheme:HA n HSO = HA. n H,O (2) HA. n H 2 0 = H+ (A-. n H 2 0 ) (31 H, 0 2 = 2 H,O (4) Assumang that the concentration of the complex HA.nHzO i s very small compared with that of the ions and of the unhydrated undissociated molecules12 it follows that K, the observed ionisation constant is given by:-.
+
+
where K1 is the equilibrium constant of reaction [HA.nHzO] K - [HA] [H,O]”
(2),
i.e.
J. Am. Chem. Soc., 39, 2303 2323 (1917). *According to Faurholt (Soc. Chim. phys. June 1924) in the case of dissolved carbonic acid approximately 99.6y0 exists in the unhydrated form.
787
IOXISATION IX ALCOHOL-WATER 31IXTURES
and K2 the equilibrium constant of reaction (3). Nz is the equilibrium constant of the true ionisation process, and may be replaced by the theoretical expression previously found for the ionisation constant of an electrolyte, (equation I ) , thereby yielding the expression :-
The result of applying this expression to the experimental data for the acids is shown in tables ITTand V. I n equation (5) n represents the number of molecules of monohydrol with which one molecule of the acid becomes hydrated, and must clearly be some small integer. The value found by trial was z2. The values of the constants
(3
K1 2
and (E,' - E,) were found by using the experimentally determined
ionisation constants for two solvent mixtures in two siinultaneous equations which were solved for the desired quantities. The values of the term (Eo' - E,), which are independent of the units eniployed in the equation ( 5 ) , are as follows Salicylic acid. . . . . . . . . . . . . . . . . . - I 13,900 calories per mole. 'I " Cyanacetic acid. . . . . . . . . . . . . . . . . -112,600 these values being found from the ionisation constants enclosed in brackets in Tables IV-V. I'
TABLE IV Salicylic acid, 25' Per cent alcohol
Dielectric constant
0.0
78.j
16.2
66.5
33.2 52.0
73.5 85.7 89.0 93.3 95.0 97.8
* These
.4c t ivit y of water
K obs.
23 7 21.4
100.0 66.0 26.0
'
x
I G ~
55.9 45.3 35.0 29.7 28.3
19.5 18. I
27.0
7.0 5.3
0.08*
26.0 25.3
2.
j
O.OI*
9.0
.8
15.5
I
12.0
0.45 0.25"
10.1
0.04
K calc.
x
106
(100.0)
56.0 27.0 IO.
7
2.2
(0.50) 0.26 0.09 0.04 0.007
ionisation constants are due to Goldschmidt: Z. phys. Chem., 91, 46 (1916).
[HzO]denotes the activity of water and is measured by the partial vapour pressure of water over the solution. I t may be seen from equation (5) that over a small range of alcohol-water mixtures Km (H2O)n. Sow when the concentration of the water in the mixture is small it nearly all exists as monohydrol, and therefore KO: (total water concentration)n. For salicylic acid in 90 to 98 per cent alcohol inspection shows that K a (total water concentration)2 roughly.
F. BRADLEY AND W. C. RI. L E W I S
788
TABLE V Cyanacetic acid, Per cent alcohol
Dielectrir constant
0.0
78.5 66.5 55.9 45.5 35.0 29.7 27.3 26.8 26.3 26.0 25.8 25.4
16.2 33.2 52.0
73 5 85.7 91 . o 92.7 94.4 95.0 96.2 98.1 '
Activity of water
23.7 21.4 19.5 18.1 15.5 12.0
8.8
7.7 6.5 5.3 4.8 3.0
2 jo
K obs. X io5 391 to 318 231 to 188 116 to 94 46 to 36 9 . 5 to 8 . 4
1 . 8 to 1 . 7 0.73 0.45 0.26 0.14
K calc. X 1c5
(362) 191 92 ' 5 36.8 7.8 1.8 0.55
0.36 0.22
(0.14)
0.12
0.11
0.05
0.04
As may be seen from Table 11,the observed ionisation constants for these acids a t 35' differ relatively little from those a t 2 5 O , and in fact these differences are somewhat less than those exhibited in Tables IV and V between the calculated and the observed values at 25'. In these circumstances, and in the absence of reliable direct data for the activities of water in alcohol-water mixtures a t 3.5' it was considered unnecessary to attempt, a test of equation ( 5 ) by reference to the experimental data obtained at 35'. It should be noticed that the observed ionisation constants, particularly for cyanacetic acid, are not wholly independent of dilution. The agreement shown between the calculated values of the ionisation constants is satisfactory, especially in the region 90 to 98 per cent alcohol, where physical influences alone fail to account for the behaviour. The ionisation due to the alcohol has been neglected in the above theory and to be able to account for the ionisation in a solvent which contains 98 per cent alcohol is rather remarkable. The ionisation of both salicylic acid and cyanacetic acid in IOO per cent alcohol is very small; the ionisation constants at 25' are 2 . 2 X 10-9 and 3.2 X IO-^ respectively. The term (Eo' - E,) in equation (5) deserves some consideration. Both E,' and E, represent work terms, but it seems probable that they are of quite different magnitude. E, is the energy expended in separating two oppositely charged ions while E,' is supposed to be the sum of the energies required to remove from the hydrated ions the water molecules that have been attracted t o the ions or to overcome electrostriction. The attractive forces in hydration must be considerably less than those involved in the structure of a stable compound, and therefore it is conjectured that -E, itself (the critical increment of the undissociated molecule with sign reversed) is of sensibly the same magnitude as the whole term (E,' - Eo). If this is so, E, for the cases studied here has a value of about IOO,OOO calories. It is to be remembered that E,
IONISATIOS I N ALCOHOL-WATER MIXTURES
789
does not indicate the actual critical increment of ionisation of the molecule in a solution, but in a medium of unit dielectric constant, Le., in the gaseous state. Considering the case of water it would follow that the critical increment of ionisation of salicylic acid in this solvent is of the order 1000to 2000 calories. As regards E, it may be pointed out that quantities of the same order have already been found for the critical increments of substances in the gaseous state. The ionisation potentials met with in gases correspond to this order of magnitude, and the calculated heat of ionisation of one-gram molecule of crystal lattice is much the same. Attention may be directed to the fact that the assumption that the critical increment of ionisation may be identified with a work term involving dielectric constant necessitates the drawing of a distinction between the influence of environment upon the breaking of a co-valent bond and its effect upon that of an electro-valent bond. The critical increment of an electro-valent bond would be expected to vary with the nature of the solvent, (in terms of the dielectric constant), while the critical increment of a co-valent bond might well be independent of the dielectric properties of the solvent. We have an illustration of this in the well known case of triethylsulphonium bromide, which can decompose in two distinct ways according to the nature of the solvent. In a large number of organic solvents it decomposes into ethyl bromide and diethylsulphide, evidently through the breaking of a co-valent bond. I t is observed that the critical increment is sensibly the same in all these solvents, although the dielectric capacities of the solvents are different1. In mater on the other hand the t r iethylsulphonium bromide splits up into bromine ion and the triethylsulphonium ion, an electrovalence being involved. Finally it is of interest to see what is the order of magnitude of the heat of ionisation to be anticipated on the basis of equation (5). On taking logarithms of both sides and differentiating with respect to temperature we obtain d log K - d log K, dT dT
+ - logK dT
+
d log _[HzO] _ dT
2_
~
Since kl and k, are independent of temperature, and the activity of water does not vary with T, equation (6) becomes d log K - d-__ log K1 + __ d E,,’ - E, (7) ._____ - d T d T dT( D R T ) On comparing with the van’t Hoff isochore it follows that the heat of ionisation, Q, is given by R T2.d log K1 _ _E”’_ _ -Eo T. d log D ( E o ’ Eo) (8) ‘= dT D d T R T 2 .dlog K1 In equation (8) the term is equivalent to the net heat effect, Qi, d T of the hydration of the undissociated molecule HA. Hence
;
Cf. Taylor and Lewis: J. Chem. Soc., 121, 665 (1921).
F. BRADLEY AND W. C. 11. LEWIS
i 90
log D E, - T.d -(9) & = & I 14 d T (Eo’ Q1 is the only unknown term on the right side of equation ( 9 ) , but assuming that it remains constant in all alcohol-water mixtures it may be evaluated by using the experimental Q for one case, when it becomes possible to calculate Q for the other solvent mixtures and to compare these calculated values with the experimentally observed ones. For the case of salicylic acid in water at 30’ the observed Q is 500 calories, and on inserting the appropriate numerical values for the other terms in equation (9) we find that &I = 1300 calories’. Using the equation Eo’ - E, - T.d log D( (E,’; Eo) (10) Q = 1300 D d T the values of Q for the other alcohol-water mixtures may be obtained. They are compared with the observed values in table VI.
E,’
-
iE0)
+
+
TABLE VI Heat of ionisation of salicylic acid a t 30’ Per cent alcohol 0.0
16.2 33.2 52.0
73 ’ 5 85.7
95.0 100.0
Observed heat
+-
2 00
-
300
500
Calculated heat
cals.
(+ 5 0 0 ) cals.
+-
200 200
- 400 - I200 - 2200
-
2100
-
3100
- 1700
- 4000
800
- 4300
+
900
The agreement between calculated a,nd observed values in Table VI is evidently not satisfactory. The electrolytes studied in the present work, however, are not suitable for a rigorous examination of the heat effect of ionisation, owing to the fact that this quantity happens to be very small in these cases and consequently liable to error. The trend of the calculated heats of ionisation agrees with that observed up to about 80 to 90 per cent alcohol, but the minimum in heat effect is not reproduced. It may be pointed out that d log D (E,’; Eo) has quite a large value compared with the the term T ___ d T ot,her terms in equation ( I O ) , and especially in the alcohol-water mixtures of higher alcohol content has a preponderating influence its effect being to make the net heat of ionisation heat evolved. 1 It will be observed that this quantity is positive, i.e. heat absorbed. At first sight it might have been thought that, the effect should be heat evolved. I t is to be remembered, however, that Ql is actually the sum of the true heat of the reaction HA z H20+HA 2 HzO, and also of the heat of depolymerisation of a molecule of dihydrol, which depolymensation I F a consequence of the removal of two molecules of monohydrol by the reaction (water being assumed to be practically all dihydrol). Hence 1300 cals is quit,e a possible value for the term Q1.
+
+
IONISATION I N ALCOHOL-WATER MIXTURES
79=
Summary ( I ) The ionisation of salicylic acid and of cyanacetic acid has been investigated in alcohol-water mixtures ranging from pure water to pure alcohol, at 25' and 35'. ( 2 ) A quantitative relation between the ionisation constant and the dielectric capacity of the medium has been developed, and the concept of the existence of critical increments of ionisation of an undissociated molecule and of recombination of ions has been given concrete expression. In addition to purely physical considerations a chemicil hypothesis as to the mechanism of the ionisation process has been used. The ionisation of salicylic and cyanacetic acids has been satisfactorily accounted for in all solvents up to 98 per cent alcohol. (3) It is pointed out that the order of the critical increment of ionisation deduced in the present work for a medium of unit dielectric constant is in agreement with that of the ionisation of other compounds in the gaseous state. (4) The preceding treatment demands a distinction between electro- and co-valency, according to which the critical increment of a co-valent bond should be independent of the dielectric capacity of the solvent while that of an electro-valent bond will vary inversely as the dielectric capacity of the solvent. ( 5 ) It has not been found possible satisfactorily to account for the variation of the heat effect of ionisation with changes of solvent, but the electrolytes studied do not afford very favourable instances for this purpose. Acknowledgment is hereby made on behalf of one of the authors, (F.B.) for a grant from the Department of Scientific and Industrial Research of the British Government. Department of Physacal Chernastry, Unzcersatu of Lmervool. England." " Jan. 67, 1926.
