FLUIDITY OF ELECTROLYTES
885
FLUIDITY OF ELECTROLYTES' EUGENE C. BINGHAM Gayley Chemical Laboratory, Lafayette College, Easton, Pennsylvania Received August 24, 1959
When the theory of electrolytic dissociation waa proposed, members of the Ostwald school examined a wide range of properties in search of evidence for the theory. Viscosity waa by no means overlooked. The Ostwald viscometer was invented, and a series of papers appeared containing data but little evidence for the theory advanced. In the light of our present knowledge this failure was due to a lack of understanding that fluidities and not viscosities are additive, for if the former are additive, the latter cannot be (1). It has long been known that the conductance of electrolytes, whether in aqueous solution or as molten salts, is dependent upon the fluidity, but no simple analogy of Kohlrausch's law of conductivity has been proposed, 9 =
*w
+ + @a
*e
(1)
where 9 is the fluidity of the solution, aWis the fluidity of water, @a is the fluidity derived from the anions, and is the fluidity derived from the cations. The conductance of water does not need to be introduced into the conductivity formula, but the fluidity of water is so important that in dilute solutions it far exceeds the fluidities of the ions, so the latter may conveniently be regarded as corrections to the fluidity of water. The above formula then becomes Am
=
As
f Ac
where A,,, = 9 - QW, A, is the elevation produced in the fluidity of water by the presence of one equivalent weight of the cations in normal solution a t 25"C., and A, is the corresponding elevation of the anions. A depression of the fluidity is of course a negative elevation. A, and A, may therefore be called equivalent ionic elevations, and A, similarly the molecular elevation, when the solution is normal. Assuming the approximate equality of the fluidity of the potassium and chloride ions as indicated by their conductances, the ionic elevations have been calculated as given in table 1. In table 2 there are given both the 1 The data are from the International Critical Tables except where otherwise noted. The fluidities are based on water a t 20°C. as having a fluidity of 99.5 rhes. Since different workers use as standard a value varying by about 0 4 per cent, i t is hardly to be expected that observed and calculated values will agree with each other t o much better than 0.4 per cent.
886
EUQENE C. BINGHAM TABLE 1
Ionic elevations, A, at 86°C.
II
Amoas
CAnONa
Inorganio
I-. ...............
7.58 7.4 3.09 3.09
C104-. . . . . . . . . . . . Br- . . . . . . . . . . . . . . CNS-. . . . . . . . . . . . NOZ-. . . . . . . . . . . . . ClOa-. . . . . . . . . . . . c1- . . . . . . . . . . . . . . . BrOa-. . . . . . . . . . . . -0.8 Na- . . . . . . . . . . . . . . CN- . . . . . . . . . . . . . CrrO - . . . . . . . . . -9.0 OH-, . . . . . . . . . . . . -12.18
,-
Cs+.............. Pb++............. Rb+.. ............ NHa+. . . . . . . . . . . .
Na+ . . . . . . . . . . . . . .
2.59 2.6 1.86 0.44
-9.60
Ba++. . . . . . . . . . . . . -25.3 Sr++... . . . . . . . . . . -28.4
A
(CHa)NHa+. . . . . (CH:):NHi+. .... -10.4 (CH,):NH+. . . . . (CH:)dN+. . . . . . . -14.0 (CxHs)NH:+. .... -16.2 (CsHs)rNH*+.... ' -25.7 (CaH,):NH+. .... -33.1 (CiH&)cN+.. . . . . . -34.3 (C:H1)4N+.. . . . . -74.3 (CaHs)NHa+.. . . . -25.6
F- . . . . . . . . . . . . . . . HiPO4 (acid), . . . . . -17.9 ClO4-- . . . . . . . . . . -17.9 CrO4-- . . . . . . . . . . -19.6
so4- - . . . . . . . . . . .
-20.4
Fe(CN)a---. . . . . . -21.1 C:HsOx-. . . . . . . . . . -21.4 HiASOk-. . . . . . . . . .
Cr+++ (green). . . . Zn++. . . . . . . . . . . . . Mg++. . . . . . . . . . . . Cd++. . . . . . . Ni++. . . . . . . Be++. . . . . . . . . . . . .
-35.4 -35.6 -36.5
-45.0
c0:- - . . . . . . . . . . . H,PO4- (salts) , . ,
SiOI-- . . . . . . . . . . . HP04- - . . . . . . . . . Fe(CN)a---- . . , . PO4--- . . . . . . . . . .
observed and the calculated fluidities2 for a number of strong electrolytes in normal solution at 25°C. One compound is required in obtaining each constant, but in spite of this the table is large enough to show the utility of the formula. It is not to be supposed that a law of this sort can be 2 Data from Simon (Compt. rend. 178, 1076, 1606 (1924); 179, 822 (1924)), when converted to fluidities, demonstrate this type of system for KOH-KClOa, NaOHHClOa, and NaOH-HxCr04. Sam Re and the author have worked i t out for the system KOH-HBr a t 20', 30°, and 30°C. in three-normal solution. Heil with the author has studied similarly KOH-HNOa. Russell and the author studied KOHHC104 in tenth-normal solution a t 20" and 30°C. In the more dilute solution tho curves were linear; in the more concentrated solution they are perceptibly aagged. Since the fluidities of the solutions of the pure acid, base, and salt are all calculable, and the fluidities of the mixtures are linear between the three, it is evident that the fluidities of the mixtures are calculable.
887
FLUIDITY OF ELECTROLYTES
applied to concentrated solutions. But if the formula applies to normal solutions of strong electrolytes, it seems logical to infer, as our first approximation, that for more dilute solutions, the actual elevation will be C(A, An), where C is the molal concentration. Table 3 gives the observed and calculated values of the fluidity for a number of half-normal solutions. The constants are one-half of those for a normal solution but the agreement is of the same order as before. There has been much discussion as to why mixtures of seemingly inert liquids do not behave as expected. Solutions of both polar and non-polar
+
TABLE 2 The fluidities of normal solutions of electrolytes at 96°C. The fluidity of water at 25°C. = 111.91 rhes ANIONS
I-
Rb+ +l 86
' 1 Obsd Calcd.
NH4+
11 Obsd.
+O 44
Calcd
K+ +0.28
Obsd 1 Calcd.
'1
11 Calcd
Na+ -9 60
I ' Obsd.
LI+
Obsd.
,
i iii 1 ~
~1
H+ -6 41
-13 99
+7.58
Br-
+3.w
116.9
120 1 119 9
115 4 115 4
119 6 119 8
' 115.5 115 3
-__ 114.7 99.2 115.2 i 113.1 112.5 100.0
'112.51 I
-1-1
~
l-
I I 108 5 I 113 1 108.6 ~
1 94.4 i (85.1)'
I
I
~
I [ Calcd
I
109 9 105 4
1 Obsd l l Calcd
I
105 5
105 4
1012 I 101.0 ( 101.0 1 I
103 2 102.6
90.1 1
9 8 1 1 9 8 0 ~9 1 0 ~ 6 7 2 98 8 I 98 2 (85.7)1(63 5)
* Parentheses call attention to the widest variations
liquids in mater have seemed to be quite abnormal, but particularly the former. We are not attempting here to add any theory to what we already have concerning the fluidity of an electrolyte at varying concentrations. We are first of all concerned with proving that at one concentration the knowledge of the fluidities of a few electrolytes will enable us to calculate the fluidities of many others in a manner quite analogous to that employed in calculating the conductivities of electrolytes from the conductivities of the ions. The question of applying this conception to solutions at other concentrations and temperatures is considered here, but it is an entirely different matter and the solution is only proximate. Since the fluidity of the solution a t zero concentration is that of water
888
EUGENE C. BINGHAM
itself and since the fluidity of the inorganic salts a t 25°C. even in the undercooled condition may be considered to be zero, the fluidity, 9, of a solution may as a first approximation be considered to be directly proportional to the volume concentration (91)of the water present, i.e., 9 = acpl. Assuming the electrolyte to be completely dissociated, if an ion lowers the fluidity, doubling its concentration should have double the effect, in accordance with the above equation. TABLE 3 The fluidities of half-normal solutions of eleciroEytes at 86°C. The fluidity of water a t 25°C. = 111.91 rhes
I --
CATIONS
ANIONS
I
A/2 AI2..
I. . . , . . , .,I +3.79 -I
Bt-
+1.M
NOr
+LE3
c10,+0.44
c1-
+O.lC
OH-
-8.08
HSOi -0.3
--
sor-10.2
Obsd., . . . . 116.9 114.3 Calcd.. , . . 116.6 114.4
113.0 106.8 111.4 113.3 113.0 106.8
NH,+ +o .22
Obsd.. . . . . 116.2 113.6 Calcd.. . . . 115.9 113.7
112.6 110.8 113.5 113.7 112.6 112.3 :106.0
-
-
101.7 101.5
K+
Obsd., . . , . 116.1 113.7
114.0
112.2 105.2
100.9
113.6
113.6 112.5 112.2 1063.0
101.3
__
- ~- __110.4 109.2 108.4 110.2 109.2 108.8
Rb+ +0.93
___--
+0.14
H+
Obsd. Calcd.
103.6 103.6
I _
110.2 110.3 __ (83.6) 108.6
102.6 102.6 __ - _- __ 109.2. 107.5 107.0 100.8 100.4 91.2 Sa+ Obsd. -4.80 Calcd. 108.6 107.6 107.2 101 .o 100.9 92.1 -_ __ 104.7 99.9 Li+ Obsd. l06.2t 106.2 57.0 108.7 106.5 106.4 105.4 105.1 (98.8 87.7 -6.99 Calcd. __ __ __ __ * On going to Reyher's original paper, this value was corrected t o 108.6,which is identical with the calculated. The value for lithium hydroxide seems questionable. t Obtained by Yanak a t Lafayette College in 1939. -3.20
_____
112.5 __ 110.4 110.9
I _
But there are other effects, which we shall regard as corrections. (1) If the ion is highly hydrated, the lowering for a given weight of electrolyte will be greatest in the most dilute solution. ( 2 ) On the other hand, the ion or ions may have a strong depolymerizing action on the water, which will almost certainly raise the fluidity of the water. (3) The interionic attraction is well recognized as a third factor to be taken into consideration, and therefore the subject is complex. This method for calculating the fluidity of solutions a t varying concen-
FLUIDITY OF ELECTROLYTES
889
trations is frankly a first approximation, which should lead to further knowledge of the corrections. But neither the correction for concentration nor the temperature is the feature upon which emphasis is laid in this paper. THE SALTS OF STRONQ ACIDS AND BASES
There are several observations which may be of interest a t this point. We note that, although the hydrogen and hydroxyl ions are known to have a high mobility, they both lower the fluidity of water. This at first may seem strange, since there are numerous ions, both cations and anions,
FIG.1. Hypothetical titration curves for sodium and potassium hydroxidtx with nitric and hydrochloric acids in molal aolution at 25°C.
which have $positive elevation of the fluidity. This is a proof, if proof were needed, that hydrogen ion and hydroxyl ion, to an even greater extent, are hydrated. Or, putting it in another way, the fluidity of water would be lowered to the extent of 12.2 6.4rhes by the presence of a gram-equivalent of hydrogen and hydroxyl ions. Conversely, when a strong acid and a strong base are brought together in solution, the union of hydrogen and hydroxyl ions should result in the elevation of the fluidity by 18.6 rhes for each equivalent weight over the expected value were all of the ions to remain. This seems to be true irrespective of the nature of the strong acid or strong base in dilute solution at 25OC. As demonstrated by figure 1, it does not matter whether the base forms a salt that is more fluid than
+
890
EUGENE C. BINGHAM
water or not. In either case there is a well-marked singular point a t the neutral point of the solution.2 The bases used are sodium hydroxide and potassium hydroxide and the acids are hydrochloric acid and nitric acid. In titration, the neutral salt would be one-half molal, starting from the normal monoacid and monobase, but for our theoretical consideration, it seems clearer to consider neutralization which takes place without dilution. This can be done (3, 5), for example, by having one component much more concentrated than the other, or by having the solvent removed, as by vaporization. 114
II3 Ilt
p 7 111
uo -
109
108
i
7 Nac I lot
I
?5% Ot __ FIG.2. Hypothetical fluidity-volume concentration curves of sodium and potassium salts of nitric and hydrochloric acids in molal solution a t 25°C.
Since the left half of this figure may be considered as a mixture of solutions of potassium hydroxide and potassium chloride or sf solutions of sodium hydroxide and sodium chloride, a further conclusion is reached. In each mixture the metallic ion is common to both components and, if the anions vary, the fluidity will vary directly as their number. This is another example of the law of additive fluidities. The anions are of different fluidity but the fluidity of their mixture must be determined solely by the number of each, since they do not react with each other. We reach the conclusion that these curves in dilute solution must be linear. If we mix the normal solutions of the four salts containing the four ions Naf, K+, C1-, and NO,-, we could obtain six mixture curves, four of which are illustrated in figure 2. The other two would be obtained by mixing sodium
TABLE 4 The fluidities o j sulfate solutions The calculated values are obtained from ionic elevations: SO,-HSOI- = -12.6
1
CONCENTBITION
I
I
TllLwadTvaE
1
OBBEBYED FLUIDITY
= -20.4 and
FLUIDITY ESTIMATED B Y EQUATION3 €'OB 26'C.
c
~
~
AT
25'c'
(a) Normal salts '0.
CS+.. . . . . . . . . . . . . . .
0.5 1.o
25 25
104.2 96.7
104.3 96.7
Rb+. . . . . . . . . . . . . . .
0.5 1.0
25 25
103.6 95.6
103.6 95.2
.............
0.5 1.0
25 25
101.7 92.6
101.5 92.0
K+. . . . . . . . . . . . . . . .
0.5
25
100.9
101.4
Na+. . . . . . . . . . . . . . .
0.5
25
91.2
92 1
Li+. . . . . . . . . . . . . . . .
0.5 1.o
25 25
87.0 67.2
cu++. . . . . . . . . . . . . .
0.5 1.0
25 25
82.5 59.7
Mn++.. . . . . . . . . . . . .
0.5 1.0
25 25
81.9 58.0
84.3 56.7
Zn++.. . . . . . . . . . . . . .
0.5 1.0
25 25
81.9 59.1
83.9 (55.9)
Mg++.. . . . . . . . . . . . . .
0.5 1.0
25 25
81.9 58.9
83.5 (55.0)
Xi++.. . . . . . . . . . . . . .
0.5
25
82.2
82.2
0.25
25 25
96.4 82.5
"I+.
Be++.. . . . . . . . . . . . . .
0.50
I
87.7 (63.5)
i
84 4 (56.8)
I
95.6 79.2
1
(b) Acid salts
j
,
Xa+.. . . . . . . . . . . . . .
0.5 1.o
18
K+. . . . . . . . . . . . . . . .
0.5
18 18
H+. . . . . . . . . . . . . . . .
0.5
25 25
I
1.0
l8
I
1
,
I
891
85 0 76 1
100.4 91.7
1,
88 4 82 8
104.8 98.4
I
104.8 99.6
1
102.4 92.9
102 6 94 4
1
i
100.8 89.7
~
~
~
892
EUQENE C. BINOHAM
TABLE 5 Fluidities of additional ilormal and acid Yalt solidiona
97.6
I
1.0
Na+. . . . . . . . . . . . . . .
0.5
I
70.7
84.3
1
75.6
100.1 91.0
87.8 80.7
103.2 94.3
Normal chromates (cc 0.5
I
I I
~
84.0
1 j
100.7 89.4
____
18 18
NHd+
102.4 92.9
104.2 97.1
102.6 93.2
Na+
K+
97.9
74.3
Nat. . . . . . . . . . . .
K + . . ...........
1
92.5 73.1
I
NHd+.. . . . . . . . . . . .
Acid chromates (CrrO,--, A 0.125
1
25
1
111.2
1
-9.0)
1
110.9 109.9 107.8
893
FLUIDITY OF ELECTROLYTES
TABLE 5-Concluded CATZON
I
I
CONgoF-
1
rrlPEaATnaE
1
OBBERYED FLUIDITY
Secondary phosphate (HPOi--, A
K-. . . . . . . . . . . . . . .. I
I ~
1
=
'C.
86.6 78.7 62.5
18
0.25 0.5 1.0
1
FLUlDlTT ESTIMATED BY
EQUATION8
FOR 25'C.
-35.9)
I ~
I
103.0 94.3 76.5
1 'zu%? "25'c*
'!
103.1 94.2 76.6
Tertiary phosphate (POI--, A = -47.5)
K+
...I 1
0.25 0.3
1
18 18
1
83.7 73.2
Primriry arsenate (H*AsO,-, A
__
Na+.. . . . . . . . . . . . . . .
=
i
1
100.1 88.8
1I
100.2 88.6
1
93.7
-26.9)
25 --______.__
___-_ H+. . . . . . . . . . . . . . . .
Phosphoric acid (HsPOd-, A = -17.9) 0.25 ~
1 ~
18 25 25 18 25
I 1 1
1 1
89.0 105.4 99.0 73.2 87.9
1
'j
105.8
1
87.8
1
99.5
I
1 ~
105.8 105.8 99.7 99.7
:;'!
chloride with sodium nitrate and potassium chloride with potassium nitrate. These curves must all btc linear in dilute solution. From table 1, summarizing the ionic constants of the elevations of fluidity, it is now easy to determine what compounds will raise the fluidity of water a t 25"C., by simply determining which cations and anions give a sum which is positive. Those electrolytes give every evidence of not forming hydrates, Le., they dissolve without contraction or heat evolution aud they do not crystallize out of solution with water of crystallization. On comparing the different sulfates (table 4 (a)), it appears that the normal sulfates agree among themselves with an ionic elevation of -20.4 for the SOa--. ion in a molar solution a t 25"C., hut the acid salts (table 4 (b)) and sulfuric acid require the assignment to the HS04- ion of a much higher elevation of -12.4. This behavior is quite general, so far ae we have been able to observe. The acid carbonates, chromates, and phosphates appear to be more fluid in dilute solution than the normal salts at the same temperature. The tribasic PO,--- ion has a lower elevation than HP04--, and this in turn a lower elevation than &PO4-. Values for the observed and calculated fluidities of some normal and acid salt solutions are given in table 5.
894
EUGENE C. BINQHAM WEAK ACIDS AND BASES
The above remarks in regard to the acid salts bring us to a discussion of the weak acids and bases. As in other cases of neutralization of weak acids and bases, we cannot expect the same relations to hold as with strong acids and bases; e.g., ammonium hydroxide and acetic acid do not give a singular point, as is the case with strong acids and bases. The fluidity of
TABLE
6
The fluidities of normal acetates Ionic elevation of C1HsO2-= -21.4 at 25°C.
CATION
1
CONCENTRATION
IXPERATURE
OBSERVED FLmDITY
FLmDITP OITIMAWD BY EQUATION 3 FOR 25°C.
CUWLAWD FLUIDITY AT 25'c.
'C.
Ba++.. . . . . . . . . . . . .
0.5
15
61.5
Sr++.. . . . . . . . . . . . .
0.5 1.0
25 25
76.4 52.4
Lie. . . . . . . . . . .
0.5 1 .o
15 15
71.1 59.5
102.4 83.7
(94.2) (76.5)
............
0.5 1.0
15 15
78.4 70.8
102.3 92.7
101.4 90.9
K+. . . . . . . . . . . . . . .
0.5 1.0
18 18
84.2 75.9
101.7 91.5
101.4 90.8
Na+. . . . . . . . . . . . . .
0.5 1.0
25 25
95.1 81.5
Cat+.. . . . . . . . .
0.5 1 .o
15 15
59.9 41.1
H+. . . . . . . . . . . . . . .
1 .o
25
48.0
cu*. . . . . . . . . . . . .
0.2
18
81.9
"a+.
83.4
(77.8) 76.2 (40.7)
96.4 80.9 81.8 60.7
(74.8) (37.8) (84.1)
105.3
(96.4)
ammonium acetate, for example (table 6), is almost midway between that of ammonium hydroxide and of acetic acid. Acetic acid (A = 84.1; table 6) is known to be highly associated and undoubtedly the observed value is low on this account. The agreement between the observed and calculated fluidities of the acetates (table 6) is in general not good. It would naturally be expected that when a substance like phosphoric acid is neutralized by a base containing a metal with a positive ionic elevation, such as potassium, the introduction of suc-
895
FLUIDITY O F ELECTROLYTES
cessive potassium atoms would steadily raise the fluidity of the salts formed. This is very far from being the case, as is shown in figure 3, the primary potassium phosphate being elevated above the phosphoric acid, as would be expected by the substitution of hydrogen (with A = -9.6) by potassium (with its positive elevation), but on adding successive potassium atoms, the fluidity is sharply depressed. The question arises whether this is due to hydrolysis and the production of hydroxyl ions (A = - 12.2), or whether the increasing negative charges on the ions are increasing the hydration. After considerable investigation of the subject it appears that hydrolysis is not adequate to explain the phenomenon; e.g., in the neutralization of
50
Oil
25 X
50 %
75
P
FIG.3.
potassium hydroxide by means of sulfuric acid, the potassium sulfate has a fluidity of 88.4 in half-normal solution a t 18"C., but the acid salt has a fluidity much greater, viz., 100.9 rhes. These salts are not appreciably hydrolyzed; therefore we are forced to the conclusion that the ions with the higher number of charges are more highly hydrated and therefore generally more viscous. There setim to be a few exceptions to this rule which it will be necessary to explain at a later time; e.g., the ferricyanide ion (table 1) has a very much higher elevation than any trivalent ion in spite of its high molecular weight. The acetate ion has a lower value than the ferricyanide ion, but this is probably due to its association. In general, the ions in table 1 with the highest electric charge also have the lowest elevation, regardless of the sign.
896
EUGENE C. BINGHAM
When we come to investigate cases of neutralization, such as the reaction of ethyl alcohol with acetic acid, the fluidity curve shows no singular point, as has been shown by more than one investigator. This also is as we would expect, because the reaction does not go to completion. It is not apparent how the effect discussed here can be explained by the. interionic attraction of Debye and Huckel, because the effect is so highly specific for the different ions, being large for the hydroxyl, hydrogen, and sodium ions, but small for potassium ion even when the number of ions is the same. The lowering in fluidity due to interionic attraction is understood to take place in very dilute solutions. We must be able to explain the elevation of the fluidity caused by potassium ion and the depression of the fluidity caused by the sodium ion, the ionization being about the same. The evidence appears to be very strong that the ions which elevate the fluidity are derived from salts which show every cvidence of non-hydration. THE FLUIDITY OF MOLECULES
versus
THEIB IONS
Increasing the molecular weight of molecules decreases the fluidity ; therefore it would be expected that the ionization of a salt would increase the fluidity, since it apparently lowers the molecular weight. The contrary seems to be the case, which must be explained by the hydration of the ions. The most striking example of this is water itself. If water, the elevation of which is assumed to be zero, were to dissociate into itu ions to the extent of one gram-molecule per liter, it would lower the fluidity by 12.2 6.4 rhes. Mercuric chloride and mercuric cyanide are all that we have to give us a value for the elevation of Hg++, which we have placed in table 1. But that value is obviously high, owing to low ionization, since it is next to sodium. The value for lead, which is based on too scant data, is extremely high, being higher than that of potassium. Cadmium chloride also illustrates the same principle of high molecular fluidity. Ammonium hydroxide also has, a very high fluidity. This is probably due to the high fluidity of the molecules of unassociated ammonium hydroxide or ammonia or possibly both. It should be added here that mercuric chloride, mercuric cyanide, and cadmium chloride are all said to be slightly ionized compounds and this may sfford an explanation.
+
TEE EFFECT OF CONCENTRATION AND TEMPERATURE TJPON THE FLUIDITY OF SOLUTIONS
It has already been shown that equation 2 represents the effect of the concentration upon the fluidity within the approximation we are aiming at in this paper. We cannot expect our generalization to apply to solutions much more concentrated than normal, and it will be interesting to ascertain to just what extent they deviate in the more dilute solutions.
897
FLUIDITY OF ELECTROLYTES
TABLE 7 Observed and! calculated values of the fluidities of potussium chloride solutzons of iiarious co?rcentrutions at temperatures from 0" to &"C., culculated according to equation 8
,I
NORMALITY
FLCIDITlES
18°C.
1
25°C.
35'C.
45'C.
0.1
Obsd. Calcd
56 1 ' 56.4
67.9 88.0
94.9 94.9
I
112.0 112.0
13S.3 138.2
166.5 166.6
0.25
Obsd. Calcd.
56.9 57.2
88.5 88.4
95.2 95.2
112.1 112.0
137.9 138.0
165.6 166.1
0.50
Obsd, Csicd.
58.3 59.7
89.1 89.1
95.7 1 112.4 95.7 j 112.2
137.4 137.7
164.5 165.2
1.o
Obsd. Calcd
60.9 61.6
90.0 90.4
96.5 96.7
'I
112.5 112.5
136.4 136.9
161.9 163.4
2.0
Obsd . Calcd
62.4 67.4
90.6 93.1
96.4 98.7
111.7 113.1
133.7 134.4
156.8 1519.8
55.8 _--
87.7
138.4
167.0
-1.5
-3.6
-1
-_
-
Ohsd. 1.0
O'C.
I
I Calcd
15'C. ___
+5.8
I
I ~
'
~
f2.7
The molecular elevatiow at &b"C. and the temperature coeficients of these elevations of various electrolytes
I
ELECTROLYTE
Ammonium iodide . , . . . . . . , , , . , , . , , . , , i I Potassium iodide . , . . . . . . . . . . . . . . . . . I . Potassium bromide.. . . . . . . . . ., , . . . Potassium n i t r a t e . , . . . . , . , . . . . . . . .. 1 Potassium chloride . , . . . , . . . . . . . . . .i Hydrobromic acid . . . . . . . . . . . . . . . Nitric acid . . . . . . ., . . . . , . . . , , , , , . . , , Hydrochloric acid , . . . , . . . , . ,,, Sodium chloride.. . , . . . . . . . . .
Am
~
,
,
,
~
, ,
,
~
~__
._I........-.._._--
Cesium su!fttte.. . , . . . . . . . . . . . . Ammonium sulfate. . . . . . . . . ., . , . . . . ,
,
Ferric chloride
,
,
,
, , , , ,
....................
,
.
j ~
~
1
+7.8 +5.7 f3.4
1
+O.G
, , ,
,
f8.02
-3.3 -3.4 -6.1 -9.3 -16.4
-- 19.4 -51.4
-
I
I
1, 1
! ,I
-0 14 -0 23 -0.21
-0 24 -0.20 -0.18 -0.18 -0 23 -037 -0.67 -0.68 -0.99
898
EUGENE C. BINGHAM
TABLE 9 The fluidities of various compounds i n solution: observed values and values calculated from the ionic fluidity elevations BLmDITY
COXPOUNDS
TEMPERATUBE
CONCENTRATION
>STIMATEI BY EQUA-
OBBERVBI BLrnDITY
ION
3 PO€
26'C. ___
'C.
Inorganic compounds: A12(SOJa. . . . . . . . . . . . . . . . .
0.1
25
91.8
91.2
Ba (C2Ha02)*,. . . . . . . . . . .. . . .
0.5 1.o
15 15
61.5 43.4
77.9 43.8
BaCl2... . . . . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
99.4 87.1
99.5 87.2
Ba(NO8)I.. ..
0.25
25
107.3
107.1
Ba(CNS)2.. . . . . . . . . . . . . . .
0.5
25
101.2
102.4
BeCI2. . . . . . . . . . . . . . . . . . . .
0.25
25
100.8
100.8
BeSO,. . . . . . . . . . . . . . . . . . . . . .
0.25 0.5
25 25
96.4 82.5
96.4 79.2
CdClt.. . . . . . . . . . . . . .
0.25 0.5
25 25
105.3 98.9
(102.8) (93.6)
0.25 0.5
25 25
104.2 96.4
104.1 96.4
CdSO,. . . . . . . . . . . . . . . . . . .
0.25 0.5
25 25
96.6 83.3
97.5 83.1
CrCla (green).. . . . . . . .
0.5 1.0
25 25
91.7 77.2
(94.6) 77.4
CrCl3 (violet) . . .
0.5
25
85.1 62.9
87.5 63.1
CoC12. . . . . . . . . . . . . . . .
0.5 1 .o
93.1 78.1
95.0 78.1
Co(XO& . . . . . . . . . . . .
0.25 0.5
25
1
104.2
104.8 97.8
Co(CNS)2. . . . . . . . . . . . . .
0.5
25
1
96.3
CuCI2.. . . . . . . . . . . . . . . . . . .
0.5
25 25
1 1
92.6 I 78.0 I
......
l.o
i ~
25
25 25 I
1.0
I
98.8 94.2 77.8
899
FLUIDITY OF ELECTROLYTES
TABLE 9-Continued CONCENTRATION
COMPOUNDS
TEMPERATURE
>BBERVEI FLUIDITP
FLUIDITY EBTIMATED B Y EQUAlION 3 FOR
wc.
LLCULATED FLUIDITY AT
25°C.
'C.
Inorganic comvounds-Continued. C;(XOJ)Z., . . . . . . . . . . . . . . .
0.1 0.5
25 25
108.7 95.3
109.1 97.6
FeCls.. . . . . . . .. . . . . . . . . . . . . . . .
0.5 1.o
25 25
81.7 60.5
86.2 60.5
MgClz. . . . . . . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
93.3 76.2
94.0 76.0
...............
0.5 1.0
25 25
96.1 81.4
96.7 81.5
0.5 1.o
25 25
81.9 58.0
83.5 55.0
0.5 1.0
25 25
92.7 77.7
94.8 77.7
0.5 1.0
25 25
95.2 81.7
97.6 83.3
0.5 1.0
25 25
81.8 58.9
83.5 55.1
HgCl?. . . . . . . . . . . . . . . . . . . . .
0.25
25
108.4
109.0
Hg(CN)z.. . . . . . . . . . . . . . . . . . .
0.25 0.4
25 25
108.2 106.1
107.6 105.0
hfg(X0J)l . . .
MgSO,. . . . . . . . . . . .
MnCL . . . . . . .
. .
. . . . . . . . . . .
Mn(SOa)? . . . . . . . . . . . . . . . . MnSO,. . . . . . . .
..............
XiCl2 . . . . . .
..............
0.5
25
92.9
92.6
S i ( N O J ) z . .. .
..............
0.5
25
95.1
95.1
SiSO,. . . . . . . . . . . . . . . . . . . . . . .
0.5
25
82.2
81.4
..............
101.9
101.8
K4Fe(CN)s... . . . . . . . . . . . . . . . .
90.5
90.5
KF. . . . . . . . . . . . . . . . . . . . . . . . . . .
88.7 83.5
K N j . . . . . . . .. . . . . . . . . . . . . . . .
111.2
110.2
KCNS. . . . . . . .. . . . . . . . . . . . . . . . .
115.4 __
115.3
K,Fe(CN)s.. . .
105.1 99.0
105.2 98.6
TABLE 9-Conclwled COXPOUNDB
~
C0"-
RpUPnB-
TBATION
3BSBBmI T?.UIDIl!T
U.COUTID FLUIDITY AT
-_
~~~~~~
2(i'c.
'0.
Inorganic compounds-Concluded: NsN,. .........................
.
1.5
25
109.5
109.0
SrClr.. . . . . . . . . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
97.6 84.1
98.0 84.1
Sr (NO&)*. ......................
0.5
25
100.6
100.8
(CHa)aNHOH. . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
87.3 70.0
88.6 65.4
(CH8)cNOH....................
0.5 1 .o
25 25
98.2 87.0
98.5 85.1
CHtNHsCl.. . . . . . . . . . . . . . . . . . . .
0.5 1 .o
25 25
108.9 105.9
108.9 105.9
(CH&NH&I. . . . . . . . . . . . . . . . . .
0.5 1 .o
25 25
106.5 101.8
106.9 101.8
(CHa)INHCI, . . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
93.2 77.8
94.9 77.8
0.5 1 .o
25 25
104.3 97.6
104.7 97.6
(C2Hs)NHICI. . . . . . . . . . . . . .
0.5 1 .o
25 25
104.0 97 .O
104.4 97.0
(C*Hs)iNHnCl.. . . . . . . . . . . . . . . . .
0.5 1 .o
25 25
97.6 86.5
99.2 86.5
CsHsNHaCl. . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
97.3 86.6
99.2 86.6
(C2Hs)aNHCI.. . . . . . . . . . . . .
0.5
25 25
93.3 79.1
95.5
1 .o
(CzH,)4NCl.. . . . . . . . . . . . . . . . .
0.5 1 .o
25 25
Y4.0 77.9
94.9 77.9
(CaH1 ) 4N Cl . . . . . . . . . . . . . . . . . . . .
0.5
25
74.9
74.9
(C2HS),NBr.. . . . . . . . . . . . . . . . . . .
0.5 1.0
25 25
94.4 79.6
96.3 80.7
0.5
25
76.8
78.5
Organic compounds:
BOO
79.1
FLUIDITY OF ELECTROLYTES
901
The fluidity of solutions vuies rapidly with the temperature; therefore
it is important to be able to calculate from one temperature to another, since the change in the fluidity is principally due to the change in the fluidity of the solvent itself. It appears that the changes in the fluidity of the ions may be regarded m small corrections, since the ionic elevations are themselves regarded m corrections in equation 2. From the data at hand we find, in fact, that the molecular elevations invariably go down as the temperature is raised, and in a linear manner. Thus for potassium chloride the molecular elevation, A,, may be represrnted by the equation A, = 5.7
- 0.204 X
t
(3)
where t is the temperature Centigrade. This shows that Am is lowered by approximately 0.2 of a rhe for each degree of temperature. In table 7 the observed and calculated values are given for potassium chloride. The results are quite satisfactory as a first approximation. The values of the temperature coefficient da,/dt for several compounds are given in table 8. For the binary compounds most of the values lie around 0.23 but those of the ternary compounds are about double this value, while the value of the single quaternary compound (FeC18) is fully four times this value or 0.99. To calculate the fluidity of a binary electrolyte at some temperature other than 25°C. it is necessary to obtain first the fluidity of the concentration desired at 25°C. Subtract the temperature a t which the fluidity is desired from 25°C. and multiply the difference by 0.23. This is the elevation to be added to the fluidity of water at the supposed temperature. Thus the calculated molecular elevation of normal sodium chloride at 25°C. is, according to table 1, -9.6 0.28 = -9.32. At HOC. the elevation would be greater by 0.23 X 7 = 1.61. This, added to the above, gives A = -9.32 1.61 = -7.71. The fluidity of water at 18%. is 94.7. This value, less 7.7, gives 87.0 for the fluidity of the solution. The observed value is 87.4 rhes. The fluidity of a half-normal solution a t 18'C. would be 94.7 - 7.7/2 = 90.8 rhes, compared with the observed value of 91.0. We include herewith a table (table 9) of miscellaneous data of observed and calculated fluidities a t a variety of temperatures.
+
+
CONCLUSIONS
1. The fluidity of a dilute electrolyte is obtained a s the sum of the fluidities of the solvent, the ions, and the undissociated solute molecules. 2. Electrolytes whose molecular elevations are greater than zero are by definition all more fluid than water; hence characteristics of these substances can be predicted by means of table 1, e.g., they do not crystallize out.of water with water of crystallization. They have low or negative heat of solution and the ions are comparatively little hydrated. In every
902
EUGENE C. BINGHAM
known case, an acid salt has a higher fluidity than the corresponding normal salt, even when the cation of the latter has a positive ionic elevation tending to raise the fluidity. This can be only partly explained by hydrolysis. 3. The elevation of an ion may be calculated by the formula Am = @ - @w - A,, assuming A, to be known, and conversely for A,. We have assumed the equality of the values of A, and A. for potassium chloride with a molecular elevation of 0.56. 4. In general, the higher the valence of the ion the lower the ionic elevation (see table 1). 5. Molecules of undissociated electrolyte are more fluid than the ions derived from them. Examples: water, cadmium chloride, and mercuric chloride. 6. In the case of salts of polybasic acids the different radicals such as so4-- and HSO,, etc., have quite different values characteristic of entirely unrelated ions. There is a tendency for the elevation to be proportional to the valence, thus so,- = -20.4; HSO4- = -12.6; cos-- = -27.4; HC03- = -12.9; HPO4-- = -35.9, and HzP04- (in acid) = -17.9. 7. The higher the weight of an ion the lower the ionic elevation, provided the electrical charge is the same. Examples: dimethylammonium ion (A = -15.2) and diethylammonium ion (A = -25.7); tetramethylammonium ion (A = -14.0), tetraethylammonium ion (A = -34.3), and tetrapropylammonium ion (A = - 74.3) ; finally, methylammonium ion (A = -6.3) and phenylammonium ion (A = -25.6). 8. The strongest acids and bases are in general the most fluid. There is a large amount of evidence among inorganic compounds in favor of this conclusion and the evidence from organic compounds is shown in tetramethylammonium ion (A = -14.0), as compared with the trimethylammonium ion. The greater ionic weight of the tetramethylammonium ion would make the ionic elevation lower in value were it not stronger, but it is higher in elevation than trimethylammonium ion (A = - 34.4). There are apparent exceptions to this law, because in table 1 the values for Pb++ and S H 4 + ions are greater than for Na+. There are too few data for a reliable constant for lead, and ammonium hydroxide is anomalous, owing to the presence of ammonia dissolved in solution. 9. Nevertheless the elevation of trimethylammonium ion (A = -34.4) is less than that for tetramethylammonium ion, where A = -14.0, which seems to contradict the preceding conclusion (paragraph 7). The reason is perhaps that, according to our above conclusion (paragraph 8), the stronger the acid or base the less it is hydrated. We assume, therefore, that the tetramethylammonium hydroxide, being a very strong base, is very weakly hydrated. Trimethylammonium ion (A = -34.4) shows a slightly lower elevation than triethylammonium ion (A = -33.1); this is also explained by the hydration of the former compound.
CRITICAL TEMPERATURE FROM REFRACTIVE INDEX
903
10. The ionic elevation varies directly as the concentration in dilute A J , assuming Aa to be known for a solution, so that Am = C(A, normal solution at 2 5 O ( ’ . 11. The value of A,,, always decreases as the temperature is raised and in a linear manner which is not directly proportional to the absolute temperature. For a binary electrolyte the molecular elevation is lowered by 0.23 rhe for each degree Centigrade, for a ternary electrolyte the lowering is greater and approximately double that amount, and in the single instance of a quaternary electrolyte that we have available, namely, ferric chloride, there is ,t lowering of four times that amount per degree. 12. The decrease in ionic elevation with the temperature rise is very naturally explained by the lessening of the hydration. 13. Since a salt showing positive elevation, such as potassium chloride, raises the fluidity of water, it might seem tempting to regard such a salt in solution as itself a liquid, more fluid than water. This would be an incorrect view. Rabinowitch (4) and the author (2) have independently reached the conclusion that the rise in fluidity must be due to the breaking down of association in thc nater itself, caused by the presence of thc salt.
+
+
REFERENCES (1) HI\c;Hnhr, E c : F l u z d ~ t ya d Pluslicit?/, p 81 et S P ~ lIcGIau--Hi11 Book conipany, Inc , Sew York (1936) (2) Reference 1, p 179 et sep (3) KOLTHOFF, I. ILI : Konduktometrzsche Tztratzonen Steinkopff, Berlin (1923). (4) RABINOWITCH, A I.: J. .im. Chem. Sor. 44, 9.54 (1922). ( 5 ) TAYLOR, H. S : P h y s ~ c ~ C z lh e m s t r y , p 937 D Van Yostrand Company, New York (1932)
T H E DETERlITS-iTIOS OF CRITICAL TElIPERbTURE FROLZ IXDEX OF REFRACTIOS
s. w.W.4K Dcpnrtiwnt o j Chemzstry, Yale-zn-Chzna School of Science, Hua Chung College, Hszchow, Y u n i m n , Chznn
Recezved J a n u a r y 10, 1941
‘The llacleod constant ( 5 ) , C, in the following equation C = s / ( D - d)4‘ (1) where s, D,and d are, respectively, the surface tension of the liquid, the density of the liquid, and the density of the vapor a t the same temperature, is unaffected by temperature for normal liquids, but shows a slight and steady increase with increasing temperature for associated liquids.
