*IS ELECTRIONIC THEORY' B Y PHILIP BLhCKMXh
SEC I . 'fhe formation of a salt 1 1 s from the acid H S and the base M.OH mal- be represented ' electrolyticallv' bx- the equation' -
'H - XI
--
(11
OH1
-
X ) - I3 OH
(31
I).
'The initial and final electrical 5tate5 differ h\ the cuprei\ion -
H.OH
I1 - OH
-.),
hence n c ~ h o u l dekpect in the formation of the ialt the (115appearance of ' electrical conductivity ' equi~-alentt o that required 1 ) ~ -equation I 2 ) . This quantity of ' electrical conductivitv nil1 he dependent on ( I ) the temperature, ( 2 ) the inolecular concentration ( o r dilution), a n d ( 3 ) the nature of the acid H S Suppose theie three condition5 l x fixed, thvrc. ought t o be a con\tant cluantitj- for the electrical conductivit! corre5ponriinq t o equation I 2 1 . r,et PTHY
p".i\I, O H @ ; \ I .
011
pL.\l 1
@\l,Y>
represent respecti\-cl!- the inolecular conductir-itieb fall measured at the 5aine iiiolecular concentration 2 , and a t the smie temperature) of the acid H S , the h i e s M,.OH and 312OH, and the salts N l S , and N 2 S . Then according t o the argument just advanced, paHY
PZHX
- pvvI O H - PVM- O H
K.
= +M,X
-
=
-t E;.
p1\1 Y
(7).
(4),
Being a complete iumrnary, rei ised, and \ ery conciderably enlarged tabularly, of a series of papers by the author published in the PhzloJophzcal .Ilagazzize, London Chemical Society'\ Piorccdzrtgs, C IirnLical Sc;s, and J O W rial 07 P l z ~ s z c a l Clzemzsivj The tables on molecular conducti\ities of salts 'ire quite original, and a great number of the ionic conductiLities in the tables are also original Compare Phil Nag [6] 11, 416 (1906)
Philip Blackman
610
where K is a constant. pvnx PV
Therefore
+ pvM,,on p v ~ , x + on -
PVM,
- pv>i2x.
(5).
Table I is an illustration of the above; the data (as in all the other tables, unless otherwise mentioned) are taken from the ‘‘ Physikalisch-Chemische Tabellen” , von Landolt und Bornstein; numbers in brackets are from an early edition of that work, the others from the 1905 edition. SEC. 2 . Equation (5) on simplification becomes
which it will be at once evident furnishes a means for calculating the molecular conductivities of salts and bases, whether soluble or insoluble, or stable or unstable, in aqueous solution, whose molecular conductivities cannot be determined by direct tiieasurement.l Such results will be found under Table I1 and Table 111. Similarly it can be shown that
= pm1x2 - P.z’M2X, - ...... - ...... ...............................
(7).
Hence,
Equation (8) it will be seen is identical with the hitherto unexplained fact discovered by Kohlrausch and further extended by Ostwald, see “Lehrbuch der allgemeinen Chemie,” 11, i, 672. Cf. Jour. Phys. Chem., 13, 144 (1909).
A n Electrionic Theory
61 I
z
0 I
-
P
0 ~
.
8
612
Phil+ Blackman TABLEI1
(TO
SEC.2)
;2Iolecular conductivities at 18O
I0000
5000 2000 I000
500 2 00
I OC i0
,492 Electiionic Theoiy
613
TABLE111 Nolecular conductivities at 32
12s ~
94 103 10s
85 108
256
~~
I 16 I 2j
130 io6 128
83
92 I06
71
2j
I20 129 I33
109 I33
96
93
113
109 Ii h
119
140
144
96
122
I28
IO1
I26 111
131
I16
I22 I,32
93 90 9s
12s
I12
104 I23 111 I20
123 126 I I. i 126
127
126
131
I33
102 125
I06
I08 130
129
I28 I 16 I28
S8
92
93
IO1
i O j
107
'34
I35 116
I39 II S I22 I IO 117
II O IIj 106 107 1 0j
120
109 iIj II8
95 104
106 I 16
I23 I11 121
I09
121
I 26
86
99
109
120
IO1 1 2j
72
83
87
87
97
IO1
99
104
I08
IO0
98
I12 131 113
1x7 I37 I20
IO1
117
121
94
IO1
104
I20
Philip Blackman
614
V =
qBaSO, f BaSzOx +SrCl,
I I2
124 130 I I8 128 I33 I08 '34 94 I08
+Sr(C103)Z
+Sr~ClO,), ;tSrRr, +Sr(BrO,), @rI2 +Sr(
+SrF2
4BrhInO, $Sr (NO,)
11.5
,
124 I44
$Sr(NO,) 2
iSrSO, iSrCrO, +SrCr,O, $SrSO, +SrS,Ox $CaCl, +Ca(ClO,), tCa(C10,), gCaBr, $Ca(BrO,),
127
131 I11
119 131 127 IIj
125 130 104 131 91 104
+CaI, $Ca(103)2 +CaF, $CaXnO, 4C4N03)* +Ca(NO,), +CaSO, +CaCrO, $CaCr,O, +CaSO, +BaS,O,
I I2 I21
141 124 128 I08 I 16 128
+
-
ions (i. e . , H OH= not H.OH but H f OH), the value of E; would have been equal to zero; that is, K would represent the molecular conductivity of water at the stated concentration v and temperature. It has already been shown that K is a constant for each series only, as it varies with the nature of the acid. This can
A n Electrionic Theory
615
only be explained on the hypothesis that the variability is due to the fact that the stronger the acid is the greater does the value of the quantity K become, the maximum relative value (at any one concentration and temperature) being reached in the case of the strongest acid. Assuming for the moment that all acids were of equal strength it would be a necessary consequence that PVHX
= PVHX, = PVHX,
4-C/VM~.OH--
+
+
-
,UVM~.OH ,UVM,.OH
= K(Hx)
PW,X ~
~
"
=~ K1 (HX1)
1
- PVM,X~ ==
- .......................
K(Hx*)
- ......
= P v H X n $- P V M l . O H - P v M I X n = K(HXn) = constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(supposing that the terms be so arranged that PvHX > J*z'HX1 > PVHX, > . . . . . . > P v H X n ) . In practice, however, this constancy is not observed, as acids are not all of equal strength. The equations may nevertheless be rendered mathematically equal in several ways, the most useful of which, for our purpose, being that which will give quantitative, comparative results. By introducing the factors x,,x,,. . . . . . . . . . , and yl, y z , . . . . . . . . . respectively, such that PVHX = x l . P v H X , = xz.PVHX, = . . . . . . . . . ., and ' 3
PVMIX =
yl./-%T,Xl = y2.PvMI,X2 == .
,
.
,
' ,
.
,
.j
the above equations become mathematically equal. Bearing in mind that the greater the equalizing quantities x,,x, . . . . . . , are, the smaller must be the respective strengths of the acids, it is at once evident that the relative strengths of the acids HX, HX,, HX,, etc., are respectively
, or, expressed as percentages, IO0
100,
-,
xi
IO0
-,
x2
Philip Blacknza n
616
But therefore, the relative percentage strengths of the acids HX, HX,, HX,, etc., are respectively
1
100, I O O , U U H X ~ , ~ V H X ,I O O ~ J V H X ,
1, ~ V H X ,
etc. Table IT', of the relative strengths of some acids at IS', is especially interesting as it was largely employed in the calculations as explained in the next section.
TABLEITT (TO SEC. 3) Relative strengths of acids at 18'
1000
99.4 99.4 99. j 99. j 99.2 99.2 99.2 99.7 99.4 99.4 99.0
100 100 100 IO0
j00 2 00 IO0
50 33.33 20 IO
100 100 IOO 100
5 3.33
IOO 100
2 I
IOO IOO
100.0
95.9 93.4 86.5 80.5 77.9 74.7 70.3 64.1 6 2 .j 62. j 62.4 62.6
48.0 46.0 43.9 42.7 38.9 39.2 36.9 33.3 32.3
-
23.2 19.8
28.1 27.4 24.6 22.9 20.1
18.4
20.7 19.7
-
11.4
-
7.6 6.1 4.5
-
-
-
0.2
7.0
0.18
10.9 8.0
5.4 3.9 2.8 I .8 1.3 0.9
0.8
0.6 0.4
SEC. 4. The foregoing results show unmistakably that molecular conductivities are additive properties, the molecular conductivity of any substance in aqueous solution being equal to the sum of the atomic or ionic conductivities of its constituent ions. Xo such regularity apparently exists between the molecular conductivities of the acids, but if the assumption be made that the ionic conductivity of the H ion is a function of the relative strengths of acids, then it is possible to calculate its value, and consequently those of other i0ns.l According to the equations 13) and (4) with the _ _ _
~
' Cf. Phil. Mag.
[ 6 ] , 12, I j o (1906).
--I?, Electyionic Theoiy
617
argument thereon, together with the remarks just set forth , $.
the ionic conductivity from the equations
,UTI
Rv,,
of the H , ion may be determined
.,IJV;I
R d H X , . ,UT;
- ,pOH, = K,
+ ,uvOH, -- K,,
RvHXi:!.;m;,- poH, = IC?.
. . --
. . . ', R z I ~ /LZIH ~ , ~-t. ,pvoH, = K,
