July, 1942
LIMITINGIONIC MOBILITIESOF UNIVALENT IONS [CONTFSBUTION FROM TEE
1635
DEPARTMENT OF CHEMISTRY, THECATHOLIC UNIVERSITY 1
Conductivity Studies. IV. The Limiting Ionic Mobilities of Several Univalent Ions at Temperatures between 15 and 45' BY NORMAN C. C. LI AND WILHELMBROLL Conductance data on aqueous solutions of potassium chloride a t several temperatures are given in a paper preceding this one.' Allgood, LeRoy and Gordon2 describe the accurate determination by moving boundary method of the transference numbers of aqueous solutions of potassium chloride at 15, 25, 35 and 45'. With these data on conductances and transference numbers a t hand, we can calculate the equivalent conductances of ion constituents and the limiting ionic mobilities a t different temperatures, with an accuracy of a part in several thousand. Table I contains the assembled data on the equivalent conductances, A, of potassium chloride solutions and the corresponding transference numbers of the chloride ion, tc1, for 15, 25, 35 and 45'. The values of A are calculated from the equation A = Ad (1
- a@)
- /3fl
in which the theoretical coefficients a and P are calculated in the same way as described by Li and Fang' and A i is given by the equation
ad
=
a.
+ BC = 1 -+a sd-C lrc
TABLEI h a FOR POTASSIUM CHLORIDE SOLUTIONS OF DIFFERENT
CONCENTRATIONS C
AKC~
1c1
XCI
?.:
0.005 .Ol .02 .05 .10
116.07 114.29 111.97 108.08 104.73
15' 0.5074 ,5075 .5076 .5077 .5079
58.89 58.00 56.84 54.87 53.19
61.50 61.70 62.09 63.21 65.12
0.005 * 01 .02 .05 .10
143.67 141.38 138.41 133.36 128.98
25" 0.5097 .5098 .5099 .5100 .5100
73.23 72.08 70.62 68.02 65.78
76.58 76.82 77.33 78.71 81.06
0.005 .Ol .02 .05
171.74 168.89 165.17 158.83
35O 0.5113 ,5114 .5115 .5115
87.81 86.37 84.48 81.24
91.96 92.24 92.80 94.48
0.005 .Ol .02 .05
199.72 196.26 191.73 183.96
45 a 0.5131 .5132 .5132 .5131
102.48 100.72 98.40 94.37
107.48 107.81 108.44 110.33
This equation was first given by MacInnes, ShedThe constants A. and B are either given in or in- lovsky and Long~worth.~Fig. 1 shows values of terpolated from Table I11 of the preceding paper. X plotted against C< and hi against C. The The transference numbers as given by Allgood, \ [ deter[ 0 2 ,1 LeRoy and Gordon are either the directly mined values or calculated by the equation . e
where A is a disposable constant and /3 is the same theoretical coefficient as before, It is interesting to note that data on transference number and equivalent conductance can be treated in a similar way. Column 4 of Table I gives the conductance of the chloride ion constituent Xcl = Atcl, and column 5 gives the values of 1: obtained by means of the equation Xi
X
+ 1 / * / 3 a / 1 - a@C
= Aa
+ bC
(2)
in which & is the limiting equivalent conductance of the ion species and b is an empirical constant. (1) Li and Fang, THISJOURNAL, 64, 1644 (1942). (2) Allgood, LeRoy and Gordon, J . Chcm. Phrs., 8,421 (1940).
0.05
0.25
0.15
0.35
0.45
0.07
0.09
4;. 0.01
0.05
0.03 C.
Fig. 1.-Variation
of equivalent conductance with concentration.
(3) Maclnnes. Shedlovsky and Longsworth, THISJOURNAL, 64, 2760 (1932).
NORMAN C. C. LI AND WILHELM B R ~ L
1636
Vol. 64
From the values of A& and A& just given and the limiting conductances A, of sodium chloride and sodium acetate in water as given by Brescia, TABLEI1 LaMer and Nachod,4 the limiting ion conductLIMITINGMOBILITIES OF THE CHLORIDE IOK 1, o c . b Xa for CI ion ances of sodium and acetate ions a t different 15 40 61.30 temperatures can be calculated from Kohl25 48 76.34 rausch’s law of independent ion mobilities. The 35 56 91.68 results obtained are shown in Table IV and in 45 64 107.16 Fig. 2. The values for A& and A i c a t 25’ The values of A& can be calculated directly given by MacInnes, Shedlovsky and Longsworth3 from the product of i Z o K ~ land toC1. Table 111, are 50.10 and 40.87, respectively, and differ concolumns 4 and 5 list the values of A,, for potassium siderably from the corresponding values given in and chloride ions, respectively, for 15, 25, 35 and Table IV, owing to the differences in the values of 45’. The values of A,Kc1 are taken from Li and and h g a A c used. Fang’ and tTIcclfrom Allgood, LeRoy and Gordon. values of Xo and b in Eq. 2 are obtained graphically and are listed in Table 11.
AsaCl
TABLE IV
TABLE 111 LIMITINGIONIC MOBILITIES t.
‘c.
AoKCI
15 25 35 45
0.4928 .4906 ,4889
59.57 73.50
57.71
61.31 76.31 91.69
,4872
1i)l.Xl
107.15
The values of X& as seen agree very well with those listed in Table I1 and the very close agreements are somewhat surprising, since the transference numbers a t very low concentrations are not known accurately. The relationship between Xo and temperature is linear so that the following equations can he applied A,-, =
:ix.50
=
,
+ I.5lOt + 1.4OTt
. ..i
..
,-
- ~ --
,
- --
it-)
“5 :13 $7
-
,- --. .
. -7
10 20 30 40 Temperature, ‘ C . Fig 2.--Variation of limitirig ionic conductances with temDerature.
0
AN*
hilo
t + in NaCl
39.70 39.29
32.80
,%.ti7
51.65 61.36
0.3930 .3923 .3898 .3872
67 72
43.0;
0
f+
in NaAc
0.5476 .5395 .5314 ,5256
The values of l&,cl and RgaAc given by Hrescia, LaMer and ;“u’a~hod,~ however, are calculated from data in “International Critical Tables” and are not as accurate as the more recent values given by MacInnes, Shedlovsky and Longsworth. Using the equation
G
t;=------=-
A:
The value of A& a t 25‘ agrees with that given by Maclnnes, Shedlovsky and Longsworth.” .
t oc
LIMITINGTRANSFERNUMBERS
I O N CONDUCTANCES AND ENCE
E.,
XK
KC1
120.88 149.83 179.40 208.M
LIMITIYG
+ Xz
A:
AO
we have calculated the limiting transference numbers of aqueous solutions of sodium chloride and sodium acetate at the several temperatures and the results are shown in columns 3 and 4 of Table IV. The cation transference numbers in aqueous solutions of sodium acetate are seen to decrease with rising temperature. This decrease is in accord with the well-known generalization that if the transference numbers are less than 0.5 they increase, and if greater than 0.5 they decrease with rise in temperature. The cation transference numbers in aqueous solutions of potassium and sodium chlorides, which are all less than 0.5, are seen to decrease with rising temperature and this is apparently contrary to the above generalization. Allgood, LeRoy and Gordon2 have tentatively explained the anomaly of potassium chloride solutions as due to the hydration of the cation resulting in a different mechanism of transport for cation and anion. This difference may be(4) Hrescia. I.aMer a n d N a c h o d .
Tms JOURNAL, 63, 615 (1940).
July, 1942
X-RAYDIFFRACTION PATTERNS
come prominent because the anion and cation of potassium chloride have approximately the same mobility, but it is not sufficient to explain the case of sodium chloride, in which the mobilities of anion and cation are quite different. We believe that the apparent decrease in cation transference numbers in sodium chloride solutions with rise in temperature is due to the inaccurate conductivity data given in “International Critical Tables.” Thus if we use the more recent value, A, = 126.42, for sodium chloride a t 25’, the calculated value of t: for aqueous solution of sodium chloride at 25’ will be 0.3963 in agreement with the value found from direct transference data and in agreement with the above generalizations in that the limiting transference number a t 25’ is higher than a t 15’. However, since the recent accurate conductivity data have been determined for 25’ only, all the values given in Table IV for the four different temperatures are taken from the paper by Brescia, LaMer and Nachod which is based on the values given in “International Critical Tables.” The older value
OF
LEADOXIDE MIXTURES
1637
for doN ~ at C 25’ ~ is 125.63, which is only 0.79 unit different from the new value. This illustrates the immense importance and need of obtaining accurate conductivity data a t different temperatures, in order to obtain limiting ionic mobilities and limiting transference numbers with a high degree of accuracy.
Summary Tables are given of the limiting mobilities of potassium and chloride ions at 15,25,35 and 45’, based on conductance data given by Li and Fang and transference data given by Allgood, LeRoy and Gordon. Approximate values for the limiting ionic mobilities of sodium and acetate as well as the limiting transference numbers in aqueous solutions of sodium chloride and sodium acetate for these temperatures are also given. The transference numbers calculated for sodium chloride solutions illustrate the necessity of obtaining accurate conductivity data not at one temperature, 25’, only, but a t different temperatures. PEIPING,CHINA
[CONTRIBUTION FROM THE NOYESCHEMICAL LABORATORY OF THE UNIVERSITY
RECEIVED APRIL10. 1942
OF
ILLINOIS]
Studies of Lead Oxides.’ VI. The Effect of Grinding on the X-Ray Diffraction Patterns of Mixtures Containing Lead Oxides BY GEORGE L. CLARKAND STANLEY F. KERN Of all the variables which are known to affect it exhibits an abnormal chemical activity toward the nature of materials used in the lead storage hydrogen peroxide and an increased heat of solubattery, grinding, especially of mixtures, has been tion in perchloric acid over that of the normal studied the least. Leblanc and Eberius2 report, R-PbO. “A hard stroke with a spatula, leaving a brownIt has been observed previously in this Laborared trail in the yellow oxide, suffices for the con- tory that intense grinding of normal R-PbO version of Y -PbO (yellow, orthorhombic) into caused a slight broadening of some lines on the R-PbO (red, tetragonal), while the conversion of X-ray diffraction pattern. This non-uniform Pb304 (black) into Pb304 (red) proceeds only broadening is indicative of distortion. under the hardest grinding and crushing on the Brown, Cook and Warner4 have reported the roughest surfaces.” Clark and Rowana have effect of grinding upon the apparent density of shown that the R-PbO obtained on grinding Pb304 samples obtained by oxidation of three difY-PbO is different from the normal R-PbO in ferent lead oxides. that it gives an X-ray diffraction pattern identiProcedure cal with a distorted R-PbO formed by the vacuum Seven binary mixtures involving the lead oxides were decomposition of lead carbonate, basic carbonate investigated using six to eight different percentage comor white lead, or lead oxide hydrate, and in that positions of each. These mixtures were ground with a (1) For the fifth paper of this series, see Clark and Rowan, THIS rubbing or shearing action and in identical manner in an 1305 (1941). agate mortar and samples reserved after various times of (2) M.Leblanc and E. Eberius, Z.physik. Chcm., A160,69 (1932); see also M.Petersen, THISJOURNAL, 68, 2617 (1941). (4) 0.W. Brown, S. V. Cook and J. C. Warner, J . P h y s . Chcm., 1 6 , 477 (1922). (3) Clark and Rowan, ibid., 68, 1302 (1941). JOURNAL, 68,
