GENERAL, PHYSICAL AND INORGANIC.
IO10
The ionization decreases in all cases steadily with rising temperature, the decrease being more rapid the higher the temperature and the greater the valence-product of the ion\ ot the wlt The freezing point lowerings cau>ed most of the same salts were also detcrmiiied. a i d from each of these lomerings the mol number 2 (that is, the number of mols resulting from 011e formula weight of salt) u as calculated and compated n ith tlie mol number derived from the conductixity by Llie nell-knomi eupression, z = I -t (72 -- I)(,I 'A,). Uetweeri the tm o 1 \ d u e s considerdk differences, far exceeding the esperiniental ciror (often of 5-10 per cent. in 0 . 0 5 - 0 . 2 normal solution), were found to exist, of frhich we Lire able to offer no evplanation Bo43 O Y , J u l y , 1909
[CONTRIBUTIONS FRO11
THE RESEARCH LABORATORY OF PHYSICAL CHEMISTRY ~IASSACHUSETTS INSTITUTE OF TECHNOLOGY. No. 441.
OP THE
THE CHANGE OF THE EQUIVALENT CONDUCTANCE OF IONS WITH THE TEMPERATURE. BY J O H N J O H N S T O N .
Received July r4. 1409,
In connectioii with a research 011 the electrical conductivity of salts of higher ionic type,' i t was necessary to determine the value of the equivalent conductance (.lo) a t infinite dilution a t eight temperatures ranging from o o to 156'. The conductance values obtained by actual measurement in extremely dilute solutions are not reliable, unless they are made with great care in a specially constructed apparatus, by means of which access of air or other impurity to tlie solution is prevented. Even in the case of 0.002 normal solutions it is often difficult to obtain completely concordant results. Recourse was therefore had to extrapolation from higher concentrations, using the function which has been previously employed in this laboratory, . , r!:l == 1 / A 0 i- E: (CA).-', where A is the equivalent conductance ai the concentration C, and IC' is a constant. A value of rz was chosen so that the graph obtained by plotting the values of I / i l against those of (C.Ll)'b-' was nearly a straight line, and two other graphs corresponding to neighboring x-alues of ~1 on opposite sides of the first line were also dra\vn. The value of 1,'&I0is obtained by determining the most probable point a t which these three graphs cut the I f -4 axis. For the salts of simpler type it had been found that lines very nearly straight were obtained with values of n. not far different from 1.45;b u t for the salts of higher types it appears to be impossible to obtain a straight line between the concentrations 0 . I id 0 . 0 0 2 normal, no matter what 1
THISJOURNAL,
31, 987 (1909).
CONDUCTANCE O F IONS WITH T H E TEMPERATURE.
IO1I
value is assigned to n. As an example the curves for potassium ferrocyanide a t 25' are reproduced in Fig. I.'
Fig.
I.
It is evident from this figure that values of n of 1.5 or 1.6 give curves convex to the horizontal axis; that when n is 1.3, the graph is mainly concave, while for the intermediate values of n there is double curvature. It is evident, too, that the point of inflexion lies a t greater concentrations for the lower values of TZ, which makes i t probable that double curvature exists even when n is 1.5 or 1.6, though in that case the point of inflexion would be near the vertical axis and the A, value would not be affected thereby to a great extent, It is also probable that this double curvature is present in the graphs of salts of simple ionic type: but there again it would exert only a small influence, since the ionization is greater and consequently the amount of extrapolation necessary is smaller. A comparison of the A, values at 18' obtained by this graphical method with those of Kohlrausch, which are based on unusually accurate measurements extending to 0.0001normal, shows that the former are uniformly higher than the latter,2 which is what we should expect if double curvature for the highest l In order to make the various curves comparable, the value of concentration (o.100 N)was made equal to IOO for each value of n and the other values were proportionally varied by multiplying by the appropriate factor. For the sake of clearness, the adjoining points are connected by straight lines. The following values illustrate this: Kohlrausch..
. . .. . . . . . . . . . . . .
Johnston ....................
KC1.
130.I 130.5
KzSOa.
132.8 134.6
Ba(NO3h.
116.9
118.3
GENERAL, PHYSICAL .\ND INORGANIC.
IO12
existed and had not been taken into account in producing the graphs. The values given in Table z are therefore doubtless somewhat too large, especially for the salts of higher ionic types; so finally, by assuming that the temperature coefficieiits tieri-\-ed from 'Fable 3 were correct, they were brought into agreement with thc values comnionly accepted. First of all, however, in order to seciire uniformity, I redetermined by graphical extrapolation .lo \ d u e s for all the salts whose conductivities haye been measured a t a series of temperatures i n this Laboratory,' excluding those in which the -1, could he obtained by combining other .I, d u e s , arid also the acids and bases HCI, 13N03! S a O H and Ra(OH),, which are for the prcsent purpose less important. These values, though derived independently, differ little, if at all, from those previously published. Table I contains these newly determined values of -I5,together with the values giT-en for the bases and acids2 in the prex-ious publication. **
1. I B I S I .---T-.\l.[:ES
OF
Salt.
A lDERIVED ~ I)IKGCTLY 0'.
KC1. . . . . . . . . . . . . . . .
81.9 . . . . . . . . . . 81
NaCl.. . . . . . . . . . . . . . . . . . NH,Cl.. . . . . . . . . . . . . . . . . . AgXO,.. . . . . . . . . . . . . . . . . . NaC,H,O ?. . . . . . . . . . . . . . . .
................ . . . . 80.6 . . . . . . .
$Ca(KO,), . . . . . . . . . . . . . 7 1 . 1 +K,C,H,O,. . . . . . . . . . . ..,i.j +I.a(NO,),.. . . . . . . . . . . . 77.8 $KsFe(CK)6... . . . . . . IOO HCl . . . . . . . . . . . . . . . . . . . . . HKO;. . . . . . . . . . . . . . . . NaOH.. . . . . . . . . . . . . . +B:i(gH),. . . . . . . . . . . . . . .
iX3.
25O.
PKODI THE CONDUCTIVITY soo.
:so,
128~.
156~.
414
... 480 ...
62j j76 555 628 570 450
130.5 126.4 109.1 130.6 116.1
. . . . . . . . . I4j 220 299
. . . . . . . . .
$85 362 415 36j
78.1
. . . . . . .
285
134.6 128.3 118.3 113.8
. . . . . . . . . 149 232 324
447 424 384 374 429
127 125
163 379 377 216 _".
.,-
. . . . . . . . . . . . . . . . . .
. . . . . . . . . 205 286 147 230 329 147 229 320 189 294 417 132
. . . . . . . . . 421 570 706 . . . . . . . . . 256
389
...
DATA.
IOOO,
... ... ...
". 537
... 475
715 6j3 600 j78
.......
42j
555
540
.......
850 826 594 645
945
. ...
685 1085 1047 835 847
Since the . I , values obtained by the graphical method are much affected by esperimental errors, it was sought to improve the individual values for each salt by plotting them against some function of the temperature. After sex-era1 functions had been tried, it n-as found that, when the logarithms of the A, values were plotted against the logarithms of the fluidity of water corresponding to each temperature, the resulting graph was a straight line, and hence could be used advantageously for interpolation. It was found that the corresponding graphs for the logarithms See THISJOURNAL, 30, 33.i, ct seg. (1908). C ' c ~ ~ x e gP7rblicatZon, ie 10. 6 3 , pp. 137, 1 7 4 , 2 G 2 (1907)
CONDUCTANCE
OF IONS WITH THE
TEMPERATURE.
1013
of the conductances of the separate ions (AK, etc.) are also straight lines; and, as i t is much more convenient to use these values than the A, values for the salts, such graphs were employed. To obtain such values, the conductances of K T and C1- were first derived for potassium chloride from the data of Table I with the help of the transference numbers for this salt. The best values of the latter are probably those of Jahn' and Bogdane2 For the transference number of the cation a t 18' a t a dilution of 1 2 0 liters (which for this purpose is equivalent to infinite dilution), a value of 0.497 was found. From this follows Further, the experiments of Jahn Ax = 64.8 and A,, = 65.7 a t 18'. at the three temperatures 0'. 18' and 30' show that with increasing temperature the transference numbers always approach 0.5 ; so in default of exact knowledge of the transference number a t IOO', the probable assumption is made that it is 0.5, when AK = A, = 207 a t I O O ' . ~ In equalizing the experimental errors and studying the effect of temperature on the conductance, the relation of the latter to fluidity was found most helpful, as stated above. The results on the viscosity ( q ) of water a t temperatures up to 100' given by Thorpe and Rodger4 were used, the values being calculated from the formula given by them,
which may also be written in the form log 9 = 1.5423 log (43.252 -k t ) - 0.7771, where y is the fluidity (equal to I/'). On calculating by means of this formula the viscosity of water a t 128', the value 0.00215 is obtained, which is identical with the value interpolated from the results of de H a a ~ . ~ At 156' the formula gives 0.00170, while extrapolation from the data of de Haas gives 0.00178. The mean of these two results was adopted.6 With values of log A, as ordinates and of log y as abscissae, the points for potassium-ion a t 18' and a t 100' were laid down on a large scale, and were joined by a straight line which was produced in both directions. 2. physik. Chem., 58, 645 (1907). Ibid., 37, 673 (1901). Bein ( Z . physzk. Chem., 2 7 , I (1898) has made transference experiments a t temperatures up to about 7 5 O ; his results a t the lower temperatures do not agree very well with those of Jahn, while a t the higher temperatures there is some uncertainty in the corrections to be applied. At the highest temperature, 76O, Bein obtained the values 0.490, 0.489, 0.482, 0.492 as the transference number of potassium ion On account of this uncertainty the procedure given above was preferred. The values of the fluidity a t the temperatures in question are: 00.
is0.
250.
50".
750.
1000.
128~.
150~.
56.24 95.35 112.2 182.5 263.1 353.3 465.4 575 See Landolt-Bomsteilz-Meyerhoffer Tabellen, pp. 76-77, This was done because the value 0.00178 seemed to be somewhat high, since, when it was used, all the graphs curved a little downwards beyond 1 2 8 ~ .
1014
GENERAL. PHYSICAL AND INORGANIC.
From this plot the values of log A, corresponding to each of the other temperatures in question were taken off. Then, taking as a n example the case of KNO,, these values of ilKwere subtracted from the original A, values for R N O , given in Table I ; the logarithms of the resulting rough values of ANo; were plotted xs before against log y and the best straight line drawn through all the points. The conductance values for chloride-ion and for the other ions \yere ohtairied in a similar manner, except that the graphs for hydrogen-ion and for hydroxide-ion are curves, in consequence of which the accuracy of the interpolation is not so great. Their graphs were the only ones that exhibited noticeable deviation from linearity. In what follows, unless the contrary is expressly stated, these two exceptional ions are not included in the discussion. The results for all the ions are brought together in Table 2 . I ABLE ~.---T.IAcT~I.:T OF THE EQ~:IVALENT CONDUCTANCES OF THE SEPARATE IONS.
.\
Ion.
ire,
XH,. . . . . . . . . . . 40.4 Ag.. . * 32.7 gI3a.. . . . . . . . . . . . . 33.4 +Ca..
. . . . . . . . . . 30.6
IOOO.
I,iho.
74.S 50.8
I59
207
319
I 16
15.5
248
74.9 63.1 66. I 61 .4
I Go
208
320
142 153 I45
187
297 330
75.4
IS1
205 195 246
29.
7 50
319
gL,. . . . . . . . . . . .
:i;
jLj 6
I 60
20s
319
so, . . . . . . . . . . . . .....
40.5
;o.o
141
I i?
2 64
20.3
.....
42.3
40.8 SI.: 74.3 72.6 117
I81 164 166 25.3
130 240 216
380 340
333
...
350 192
565 ,360
644 439
777 592
~
. . . . . . . . . . . 39
)C,H,O,. . . . . . . . . 37 +Fe(CS),. . . . . . . . 60.4
II. . . . . . . . . . . . . . .240'
96.3
221
406
21 I
'..
That this method of interpolation is justified as an empirical one by the results is shown by the fact that, if Ire compare the values of A, in Table I for all the salts for which '1, was determined a t each temperature with those obtained by adding together the appropriate values of the ionic conductances, the differences are irregular, and. with one or two exceptions, are within much less than I per cent. of the A. value. The equivalent ionic conductances a t 18' as tabulated above do not differ much from those given by Kohlrausch,? whose values are probably the most reliable a t present, because, since his measurements were extended to solutions of very small concentration, relatively less extrapolation was necessary, with a proportionately increased accuracy of the A, 2
Relatively inexact values Kohlrausch, 2. Elektrochem., 13, 333 (1907).
1015
CONDUCTANCE OF IONS WITH THE TEMPERATURE.
values. On this account, in giving a table of definitive values, i t seemed better so to amend Table 2 as to bring the values at 18' in accord with those of Kohlrausch. For several of the ions considered here, however, no data are given by Kohlrausch; in these cases, the values adopted were such as seemed most probable from a comparative study of the values of A, at 1 8 O . l The values a t 18' served as a basis from which those at the other temperatures were calculated with the aid of the temperature coefficients deduced from the values of Table 2 and given in Table 4. TABLE $-THE Ion.
K ..................
.................
Na NH, ................
Ag .................
3Ba. ...............
+Ca................ +La. ...............
................. ................ .............. +so,............... JJc,o,'....... ....... )C,H,O,. ........... aFe(CM),. .......... c1.
NOa C,H,O,
EQUIVALENT CONDUCTANCE 00.
180.
75'.
128~.
1560.
115
I59 116 I59 I43 I49 142 I73
263 203 264 245 262
317 249 319
252
312
312
388
160 140 96 I77 163 161 244
264
318 263
64.6' 43.9 64.5 54.3a 5s2 51,
74.5 50.9 74.5 63.5 65 60
61
72
41.1 40.4
65.9 61.7' 34.6 68, 632 60 95
75.5 70.6 40.8 79 73 io
20.3
H .................. 240 O H ................ 105
314 172
SEPARATE IONS.
50'.
40.4 26 40.2 32.9 33 30 35
41 39 36 58
OF THE
250.
82 115 IO1
104 98 119 116 104 67 125
115
I11
113 173
350 192
465 284
222
299 322
171
211
303 275
370 336
......
......
565
722
777
360
525
592
From the method of drawing the graphs, it is obvious that the relation between ionic conductance (A) and fluidity (Y)is given by the equation log A = m log (p log K,; or A = kl'pm,. (1) where m and k, are constants for each ion. The values of m and log k , for the various ions are given in the second and third columns of Table 4. The relation between the fluidity and the temperature function e (which is equivalent to 43.25 t, 1 being the temperature above zero centigrade), as obtained from the expression given by Thorpe and Rodger for the change of viscosity of water with the temperature, has the form p = k, 0%. (2) K, and 12 being constants ( f i having the value 1.542). Hence the relation between A and 0 has the form A = e@/& or log A = p log e - log &. (3)
+
.........
+
.....................
..........
The question of the choice of AO values at 1 8 will ~ be fully discussed in a later publication from this laboratory. Cf. also THISJOURNAL, 31, 746. * Kohlrausch, loc. cit.
1016
GENERAL. PHYSICAL AND INORGrlNIC
.
The values of p and of log k for each ion are given in the fourth and fifth columns of Table 4 . With their aid the value of A at any temperature can be readily derived . TABLE4.-VALUES
OF
THE CONST.4NTS IN THE EQUATIONS (I) (0 -- 43.25 t ; It = 1.542.)
+
--.log k,kl.. . logA=m logyllog
Ion .
logA=p loge-log . . * _ c _
m
E;. . . . . . . . . . . . . . . . . . . .
n.+
0.63j 1.034 0.647
-0.1;4 -0.04; -0.168 -0.079
S a . . . . . . . . . . . . . . . . . . . 0.97
-0.281
S H , . . . . . . . . . . . . . . . . . . 0.891 Ag . . . . . . . . . . . . . . . . . . . 0.949 $Ba . . . . . . . . . . . . . . . . . . 0 . 986 $Ca. . . . . . . . . . . . . . . . . . I .008 3La . . . . . . . . . . . . . . . . . . I .03
+0.045 -0.143
1.495 1.374 1.463 I . 521 1 . 554 I . j8S
C1....................
+0.0j4
0.88
NO, . . . . . . . . . . . . . . . . . . 0 . 8 0 ;
C,H, 0 *. . . . . . . . . . . . . . 1.008 $SO, . . . . . . . . . . . . . . . . . 0.944 . . . . . . . . . . . . . . . . 0.931 $C,H,O, . . . . . . . . . . . . . . 0.972 tFe(CN) . . . . . . . . . . . . . 0.929
.fc,o,.
-0.286 -0.2 j3 +0.194 --0.45j -0.037
-0.043 -0.146 +O.Ij9
.
P.
. 368
I
-0.212
.
log k .
+O.Oj4
0.887
k
( 3 ).
AND
0.88
1.357 1.245 1.554 1 . 456 1.436 1.499 1.433
0.978 1.069 1.053
w . 0 2 1
0.609 0.432 I . 238
--o .185
0.768
-0.086 -0.106 -0 . 043 -0.109
0.766 0.901 0.58~
+o.o12 +0.046
-
. 297
+0.012
From the above equations it follows that (4) Now. if the assumption is made that change of fluidity directly causes a proportional change in the conductance. the magnitude of the factor p - n (or of m - I ) is a measure of the influence of secondary specific factors characteristic of the separate ions-an influence which may well be due in part to changes in hydration . A consideration of the last column TABLE5.-vALUES
.
IO00
.
.
.
1000
128O
156O
678 456 677 569 578 535 640
665 454 665 565 575 536 640
630 449 630 551 573 539 650
603 442 605 543 569 540 660
584 440 586 533 568 54 1 665
565 435 567 527 562 541 670
553 433 554 519 561 544 675
C1............... 41.1
729 717 361 734 685 640
686 648 363 714 661 630
672 628 364
587 504 367 662 608 605 9 10
553 456 367 644 583
1000
606 534 366 671 616 615 930
568 476 367 651 592
1030
633 572 365 685 633 620 950
..
..
,
NO p . . . . . . . . . . . . . 40.4
........... +so,. . . . . . . . . . . . C,H,O,
20.3 41 39 36
+C,O, . . . . . . . . . . . . QC,H,0 58 tFe(CN),
,.........
......... H ............... 240 OH
............. 105
.
A/p X
718 463 715 584 580 533 620
A a t oo
.
OF
I;. . . . . . . . . . . . . . . 40.4 Na . . . . . . . . . . . . . . 26 N H . . . . . . . . . . . . . 40.2 Ag . . . . . . . . . . . . . . 32.9 3Ba . . . . . . . . . . . . . 33 3Ca . . . . . . . . . . . . . 30 +La. . . . . . . . . . . . . 35
Ion .
00
1 8. ~
250
.
soo.
75O
4270 3300 1870 1800
707
654 625 990 3120 1710
2550 2150 1560 1370
.
..
1820 1550 I?+O
1130
..
1350 1030
CONDUCTANCE OF IONS WITH THE TEMPERATURE.
1017
of Table 4, in which the values of p - n are tabulated, shows that the influence of these secondary factors is in most cases comparatively small. This is also shown by Table 5 , which contains the values of A l y for the various ions a t a series of temperatures; besides which, for purposes of comparison, the values of A a t o o are given in the second column. A consideration of the results in Table 5 suggests that with increasing temperature there is a normal decrease (arising from physical causes) which is a function of the conductance of the ion.' Thus this decrease is large and nearly constant for the four ions K+, NH,+, C1-, and C,O,--. having an approximately equal and fairly high conductance a t 0'; it is less for Ag+ ion, and still less for Naf ion in correspondence with their smaller conductances, and it has disappeared altogether in the case of C,H,O; ion, which has the least conductance; the decrease is, moreover, exceptionally large in the case of the highly conducting H+ and OHions, and larger in the case of the former. The fact that some ions (Ba++, Ca++, La+++, SO,=, Fe(CN,==) form exceptions to this principle in the respect that their conductance does not undergo the normal decrease may be explained by a decrease in their hydration with increasing temperature.2 (The NO; alone forms an exception in the opposite direction, exhibiting, as i t does, am abcormally large decrease.) This suggestion is, of course, only of the nature of a hypothesis; but it is one which can be further tested with the aid of additional experimental data. The relation expressed by equation ( I ) above appears to be applicable also to solutions in other solvents. Dutoit and Duperthuis3 published recently some results on the conductance a t zero concentration of sodium iodide in a number of solvents a t a series of temperatures lying between oo and 80'; these A, values they obtained from their conductivity data by applying the Ostwald dilution law, which holds a t high dilutions for the solutions in question. In addition the authors give data (in part from the work of Thorpe and Rodger) on the viscosities of the pure solvents a t the temperatures in question. The various values are reproduced in Table 6, in which, however, fluidities, instead of viscosities, are giren. On plotting, as b e f ~ r e the , ~ values of log A, against those of log G , That the temperature coefficient of the conductance of ions is in general closely related to the value of the conductance itself has been clearly established by Kohlrausch (see Sitzungsber, konigl. preuss. Acad., 26, 5 7 2 - j 8 0 ( ~ g o z ) , and also 2. Elektrochem., 14,129 (1908)). That these multivalent ions are largely hydrated a t low temperatures is indicated by the abnormally small values of their equivalent conductance. See No yes, Carnegic Institution Publacation, No. 63, p. 336 (1907). J . chim. phys., 6, 726 (1908). ' I n these solvents, however, it was necessary to use the A. value for the salt sodium iodide instead of that for either of the ions, since the transference numbers are unknown. Although, considered from a n exact mathematical standpoint, the functions for these two cases can not both be of this same form, yet they seem to be
1018
GENERAL, PHYSICAL AND INORGANIC.
TABLE 6.-vALUES
OF
A0
FOR S O D I U M I O D I D E I N \TARIOUS SOLVENTS, AND OF THE P U R E SOLVENTS.
Propyl Alcohol.
Ethyl Alcohol.
p
FOR
Isobutvl Alcohol.
c -
to.
0 IO 20
30 40 50 60 io
so
A,.
9.
27.95 33.83 40.52 47.87 56.13 66.24 77.25
56.5 68.96 84.03
.....
.....
IOI
120.8
143.3 168.9
...... ......
Ao
......
Isoamyl Alcohol.
20
4.49 5.95 7.8
30
10.06
40
12.7 15.i9 19.24
0 IO
50 60 io 80
22.7j
28.3
12.03 17. I 3 23.64 31.95 42.55 S j . 55 71.43 89.28 111.1
‘p.
.I..
26.15 34”5
5.48
4j.02
10.81
57.12 72.36 90.02 110.5 133.7
14.87
I
11.85 15.63 20.28 25.73 j2.42 40.33 48.93 58.26
......
127.5 142.7 159 I 76 192.9
2j3.8 280.9 309.6 341.2 373.2
......
...... ......
......
......
......
......
19.54 25.6 32.02 38.73 45.33
So.72 102.8 128.4
Pyridine.
Acetone.
......
e , ‘ I-13
9. 12.44 1S.03 2j.6 34.92 47.15 62.16
42.1 50.4 59.15 68.1 77.86 88.23 98.76 109.65 120.9
73.53 88. j 104.4 120.6 138.1 156.5 175.8 196.8 216.5
the graphs proved again to be straight lines. The deviations from linearity are small and irregular, except a t the two highest temperatures in the case of isobutyl alcohol; this di\-ergence is probably due to some experimental error, since the concordance is otherwise so good. For each of the solvents, therefore, the relation between A, and (5 has as before the form log A, = m log - log h. The values of m and of log L are brought together in Table 7 . TABLE7.-vALUES O F THE COEFFICIENTS I N THE EQUATION log A0
nt log
Solvent.
Ethyl alcohol.. ............... Propyl alcohol.. .............. Isobutyl alcohol, . . . . . . . . . . . . . Isoamyl alcohol.. ............. Acetone.. .................... Pyridine. ....................
- log k.
0.935 0.974 0.955 0.806 1.086
log k. 0.192 0.303 0.308 0.213 0.507
0.99
0.228
712.
This table shows that, notwithstanding the diversity of character of the solvents, the coefficient m does not differ greatly from unity (except jpl the case of isoamyl alcohol) ; in other words, for any one solvent, under varying conditions of temperature, the conductance a t zero concentration approximately so in practice, as shown by the results obtained in aqueous solutions, owing no doubt to the fact that t h e exponent m is nearly unity and vanes little with the nature of the ion.
CONDUCTANCE OF IONS WITH THE TEMPERATURE.
1019
is very nearly proportional to the fluidity of the solvent. This is shown perhaps more clearly by Table 8, containing the values of A, /p. TABLEVALUES
OF
Ethyl alcohol.
Propyl alcohol.
Isobutyl alcohol.
Isoamyl alcohol.
Acetone.
Pyridine.
0
495
IO
491
453 45 I
440 43 1
20
482 474 465 462 457
451
422
450 448 448 443 436
426 414 412 397 377 353
373 347 330 315
502 508 5x4 5x6
299
517
572 570 567 565 564 564 562 557 558
10.
30 40 50 60 io 80
... ...
...
2 84
269 255 255
... ... ...
...
Summary. I n this article are presented (in Table I ) newly derived values of the equivalent conductance (Ao) a t zero concentration between o o and 156' for the salts previously investigated in this laboratory up to the latter temperature. On the assumption, which is doubtless nearly correct, that a t the higher temperatures the equivalent conductance of potassiumion and chloride-ion are equal, values for the equivalent condlsctances of the separate ions were calculated for eight different temperatures between o o and 156'. These values are presented in Table 3 above. A consideration of the results has shown that the equivalent conductance (A) in aqueous solutions of each of these ions (except hydrogen-ion and hydroxide-ion) through the range of temperature in question, is a function d the fluidity (9) of water of the form A = kpm where m is a constant for each ion, varying between 0.81 and 1.03 for the different ions (see Table 4). The graph is therefore linear when the values of log A for any one ion are plotted against those of log 9 ; and such a plot can be used to advantage as a method of obtaining by interpolation the value of A for a given ion a t any temperature. I t has been further shown by combination of this result with the known functional relation between the fluidity of water and the temperature that the relation between A and the temperature t may be expressed by the equation A = ( I / k ) ( t i43.z5)fi. Values of the constants p and of log k have been given in Table 4, thus enabling one to calculate the conductance for any ion a t any temperature. Values of the ratio Alp have also been given (in Table 5) for the various ions a t the various temperatures. Consideration of these values seems to show: ( I ) that with increasing temperature there is a decrease in this ratio arising from physical causes which is a function of the conductance of the ion, the decrease being greater when the conductance is greater; l
Cf. Dutoit and Duperthuis, Zoc. cit., p. 729.
I020
GENEK4L, PHYSICAL AND INORGANIC.
and (2) that the exceptional behavior of some ions, especially those of higher valence, is to be attributed to a change in their state of hydration with the temperature. Finally, making use of the data of Dutoit and Duperthuis, it is shown that analogous relations hold for solutions of sodium iodide in six organic solvents of diverse character I n conclusion, I desire to express my thanks to Prof. A. A. Noyes for valuable suggestions in connection with the preparation of this paper.
ON THE NATURE OF PRECIPITATED COLLOIDS. [SECOND PAPER.] BY H. W. FOOTE, S R. SCHOLES, A N D R . W. LANGLEY. Received June 2 0 , 1909.
In a previous article’ by one of us, evidence has been given to show that precipitated iron or aluminium hydroxides may be regarded as solid solutions of water in the oxide or in some lower hydrate. In that article, a method was described for determining the composition of the so-called saturated solution of water in the oxide. Briefly the method consisted in s1owLy drying the moist precipitated hydroxides in the air, a t intervals placing them over pure water in a closed vessel immersed in a thermostat for twenty-four hours or more. In the drying process, a point was reached where the material began to gain in weight when placed over water and the composition a t the point where gain in weight first occurred, was that of the saturated solution. The water removed up to this point was considered mechanical water and the water remaining in the oxide was regarded as dissolved. The reasons for this conclusion will be found in the first paper. The results obtained showed that the composition of the “saturated solutions” was practically independent of the method of preparation but varied with the temperature as is the case in general with saturated solutions. It was found that the point where the residues began to take up water, or in other words, the point where mechanical water was removed, could be determined approximately by the mechanical condition of the residues which were moist and somewhat waxy or pasty up to this point and were dry and powdery when more water was removed. This fact was of the greatest assistance in carrying out determinations, for the precipitates could be dried till nearly all the mechanical water was removed before testing them over water in the thermostat for loss or gain in weight. The errors in the results obtained were considerable. This was partly because the tests for gain or loss in weight showed only the limits bel
THISJOURNAL, 30, 13811.
