JEAN M. STOKES AND R. H. STOKES
2442
This is a semiempirical equation, the constants in which have been found to render the equation applicable for many polymer systems. In order to test the fit of the present data to eq. 6 the following procedure was adopted. From a plot of log K us. ( T - T g ) ,the K-value a t 7" was obtained by extrapolation. Making use of the equations
values of the viscosity and retardation time were obtained a t several temperatures using the value of 7 6 5 as determined from tJ(t)= t / y for the steady flow region, TABLE I Temp.,
K
OC.
7 10 15 19 21 23 25 27 29 30 35 40 55
2.98 2.52 1 2 7.15 3.97 1.8 7.52 5.0 3.14 6.3 3.0 7.46
q , poises
X lo2 X 10'
x x
10-1 10-2
X
x
10-2 X X loea X x 10-4 X loe6 x 10-7
8 x 6.76 X 2.68 X 5.36 X 1.98 x 1.06 X 4.82 X 2.01 x 1.34 X 8.42 x 1.65 X 8.0 x 2.0 x
7,
1014 1013 1012
10" 10" 1011 10lo
10'0 10lo 109 log
107 10h
see,
1.46 X 1.20 x 4.8 X 9.6 x 3.42 x 1.9 x 8.65 X 3.59 x 2.40 x 1.50 x 3.01 X 1.44 X 3.58 X
lo8 107 1Oj
104 104 104 loa 103 103 103 lo2 10' 10-'
Vol. 67
and 7 1 5 = 4.8 X 1oj sec. evaluated as described above. The values of K, v, and T are listed for the various temperatures in Table I. h plot of [-17.6(T - T g ) ] ' [51.6 ( T - T g ) ]us. ( T - T g )is shown as the dashed ) from line in Fig. 6. Values of q ( T ) ' ~ ( 7 ' ~calculated Table I are also plotted as a function of T - T , and the experimental points are seen to be in good agreement with the theoretical line. From the volume temperature study, the coefficients of expansion a1 and ag for the liquid and glassy states were calculated. Equation 6 may be written, from the free volume theory, as
+
j gbeing the fractional free volume at the glass transition so:4fg = 17.6 and fg = 0.023. temperature. Thus Experimentally a1 - a, = 3.3 X deg.-'. From the second constant in eq. 6, jgis determined as 0.017. Considering the relatirely poor precision with which a1 - ag can be measured, the agreement between the predicted and experimental values of fg can be considered as satisfactory. This investigation by transient rather than dynamic measurements reinforces and confirms the conclusions of previous investigations on low molecular weight glass-forming materials, s?amely, that a single retardation time is sufficient to represent the process. In this investigation, moreover, the W.L.F. equation is Sound to predict the temperature variation over the complete temperature range studied.
ACTIVITY COEFFICIENTS I N CALCIUM PERCHLBRLATE-HYDROCHLORIC ACID MIXTURES I N YATER AT 25' BY JEANbI. STOKES ASD R. H. STOKES Department o j Physical Chemistry, Lnaversity of S e w England, Armidale, A'.S.TV., Australia Receiced June 4, 1969 By measuring the change in potential of the hydrogen-silver, silver chloride cell as calcium perchlorate is added a t constant hydrochloric acid molality, the activity coefficient of calcium perchlorate a t vanishingly low concentration in hydrochloric acid solutions is evaluated. That of hydrochloric acid a t a low concentration in calcium perchlorate solutions is obtained from a separate experiment.
Tntroduction I n connection with other work in this Laboratory, the question arose: what is the activity coefficient of a 2 : 1 electrolyte a t vanishingly low concentration in a hydrochloric acid solution of 1 m or higher concentration? Two such systems, in which the 2 : 1 electrolytes were barium and strontium chlorides, have been studied by Harned and collaborators,l but the concentrations of the two electrolytes were not such as to make a reasonably accurate estimation of the required activity coefficient possible. A recent paper by Argersinger, Leifer, and Davidson2 deals with the system cadmium chloride-hydrochloric acid using both cadmium and hydrogen electrodes in combination with a silver-silver chloride electrode, but this system is not typical beS.Harned and T. R. Paxton, J .
Phgs. Chem., 67, 531 (1953); H. S. IIarned and R. Gary, J. Am. Chem. SOC.,76, 5924 (19641, 77, 1994 (1955). (2) W. J. Argers~nger.L. Leitpr, and A, W. Davldson, J . Phys. Chem., 66, 1321 (1962) (1) H.
cause of strong complex formation. KO divalent metal free from chloro-complexing difficulties appeared likely to operate as a reversible electrode toward its ions at high hydrochloric acid concentrations, so the method described below mas adopted. This method depends on a rather direct exploitation of the well known "cross-differentiation identity" b log Y1
b log Yz
bm2
(1)
The cell used is (Pt)Hzl HC1, mllAgC1-hg The 2 : l electroIyte is progressively added in such a way as to maintain a constasit hydrochloric acid molality. The initial rate of change of the e.m.f. gives the left-hand side of eq, 1 as m2 + 0; integration of the
Kov., 1963
,
HZ
ACTIVITYCOEFFICIENTS IN MIXEDELECTROLYTES
,mWEIGHT
2443
BURETTE
INSERTED HERE
t
4
THERMOSTATED JACKET
c
Fig. la.-The
cell vessel and electrodes.
right-hand side with respect to ml then gives log Y ( O ) Z , Fig. 1b.-Weight-buret. Presaturated hydrogen is passed the required activity coefficient of the 2:l electrolyte a t through the solution, while the buret is inverted, to remove disvanishing concentrat5on. solved oxygen. The three-way tap is connected to the hydrogen Experimental supply during delivery of solution; the position shown is for Hydrochloric acid was analytical reagent quality material, suitably diluted and analyzed conduetometrically with the help of the data of Stokes.3 Calcium perchlorate was prepared as a stock solution of known concentration as follows. Analytical reagent quality perchloric acid (chloride content less than 0.0001%) was diluted t o about 40% by weight and analyzed by weight titration against carbonate-free sodium hydroxide, prepared from amalgam and analyzed as in ref. 3. To a known weight of this perchloric acid a very small excess over the calculated amount of A.R. calcium carbonate was added, with precautions to avoid loss in spray. The solution was boiled free of carbon dioxide and weighed, ,and the composition calculated from the original perchloric acid content. The hydrogen electrodes were conventional and were supplied with electrolytic hydrogen presaturated a t 25" in a solution near the composition of that in the cell. The silver-silver chloride electrodes were of the thermalelectrolytic type. The cell is shown in Fig. l a ; it contained in practice two hydrogen electrodes, of which for clarity only one is shown. Agreement between these was within 0.02 mv. Since silver chloride is appreciably soluble in hydrochloric acid above a few tenths molal, it v a s necessary to isolate the silver-silver chloride electrode from the bulk of the solution to prevent contamination of the hydrogen electrodes by reduced silver, which was formed in a few minutes in 1 M hydrochloric acid when the silver-silver chloride electrode was in the bulk solution, and which resulted in a rapid drift of the e.m.f. The silver-silver chloride electrode was therefore placed inside a tube with a bent capillary tip and with provision for drawing off solution by the tap to replace the solution round the silver-silver chloride electrode by fresh cell solution. For each run, a solution was prepared by mixing suitable weights of the hydrochloric acid and calcium perchlorate stocks and diluting a8 required. This solution (solution A) contained hydrochloric acid at molality m,, and a known weight percentage of calcium perchlorate. A solution of hydrochloric acid alone (solution B) of the same molality ml was then prepared. (3) R. H. stokes, J . Phys. Chem., 66, 1242 (1961).
flushing out air from the hydrogen delivery tube. The electrodes were rinsed in solution B, and the guard tube containing the silver-silver chloride electrode was completely filled with solution B. The hydrogen pre-saturator (a vessel jacketed with thermostated water, similar to the cell vessel) was also filled with this solution. About 200 g. of solution B was then weighed into the clean dry cell vessel, and when the temperature had reached 25" the hydrogen flow and the stirrer were started. Complete removal of dissolved oxygen took about 1hr., but in most cases the cell was left overnght with a slow hydrogen flow. The potential of the cell, at this stage containing only hydrochloric acid of molality wl, was measured on a Tinsley vernier potentiometer. A few milliliters of the cell solution was then bled off via tap T through the silver-silver chloride electrode guard tube into a weighing bottle, to check that the solution round the electrode was still of the cell composition. If any small change in potential occurred, this operation was repeated until the potential was constant. Meanwhile, about 60 ml. of solution A had been freed from dissolved oxygen in a weight-buret of the design shown in Fig. lb. The flow of hydrogen into the cell was increased and the stopper S removed; a few grams of solution A was then introduced into the cell against the flow of emerging hydrogen. Stopper S was replaced and the solution thoroughly stirred; then a few grams of the cell solution was bled off through T, and as soon as the temperature was back to 25' the new potential was measured. The bleeding was repeated until the potential was constant within 0.01 mv.; usually no more than three bleedings sufficed. Equilibrium readings could be obtained within 20 min. of the addition of solution A, provided that oxygen was completely excluded from the solution in the weight-buret, but even a trace of oxygen would increase this time t o 1 hr. The additions of solution A and the bleeding operations were continued until the change from the original cell potential was a few millivolts. At this stage the stopper carrying the whole electrode assembly was removed from the cell, without disturbing
JEAK M. STOKESAND R. H. STOKES
2444
0.8 l.O
k
Vol. 67
and hence by eq. 1
3k
Omz (E) b log yz bml
=
-
bmz
(4)
ml
where yzis the mean activity coefficient of the 2 : 1 electrolyte 2. I n particular, as m2+ 0, we have
-0.2
c
-0.4
I-
-0.6
L
-0.8
I 0.5
0
Fig. 2.-Integration
I 1.6
I
1.0
4;.
of eq. 6 to give log ~ resents 1% in y.
2.0
( ~ 1Hatched ~ .
area rep-
the electrodes, and the cell and electrodes were rinsed with solution B and the cell refilled with it. The reading, after removal of dissolved oxygen and bleeding through T, provided a check on the constancy of the electrode behavior during the run; the drift after correcting for changes in barometer reading during the run did not exceed 0.02 mv. I n this a'ay, since the same electrodes were used throughout a run, the changes in cell e.m.f. with the addition of calcium perchlorate were, we believe, obtained with a higher order of accuracy than could be expected by setting up a new cell for each composition of the mixture. Bias potentials were certainly present in some of the silver-silver chloride electrodes, for the observed e.m.f. values in solution B often differed by a few tenths of a millivolt from the best literature values for the hydrochloric acid cell, but these bias potentials were proved to remain constant during the run. The molality of calrium perchlorate m2 in each solution is calculated a t each stage from the initial weight of solution B in the cell, the weights of solution A added, and the weights of cell solutions withdrawn via T. This rather laborious piece of bookkeeping is the most tedious feature of the experiment. As a check on the arithmetic, it is desirable to calculate both mi and m2 a t each stage; mi should of course remain constant. Runs were made with nine different hydrochloric acid molalities from ml = 0.01 to ml = 4. I n addition, one run was made with 0.01 M HC1 as solution B, in which the addition of calcium perchlorate was continued until the calcium perchlorate molality was 1.1. From this run, the activity coefficient of hydrochloric acid a t near-vanishing concentrations in calcium perchlorate was obtained. The results are assembled in Table I.
Theoretical Computation of the Activity Coefficient of Calcium Perchlorate at Trace Concentration in Hydrochloric Acid.-The potential of the cell ml ' AgCI-Ag (Pt) HP I HC1 l Ca(C104)z m2 I is, with the convention that E represents the excess positive potential of the right-hand electrode over the left-hand electrode
E = Eo - 2k log
(~~17)
(2)
where k = 2.303RT/F, and E o is the standard potential. Differentiation with respect t o m2 a t constant ml yields 2k
b log y1 bmz
(-)ml
=
-
(E) am2
ml
(3)
where y(o)zis the activity coefficient of 2 at vanishing coiicentration in 1. The right-hand side of ( 5 ) was evaluated in several ways from the data of Table I. It was thought undesirable to use any theoretical function as a guide t o obtaining the required initial slope; therefore, graphs were prepared of (AE/m2) or of (m2/ AE) us. either m2 or AE; in every case at least one of these graphs was sufficiently linear to permit an evaluation of Y from the intercept a t m2 = 0 (or A E = 0). We now integrate (5) at constant m2 = 0 with respect to ml (see Fig. 2 ) , obtaining
the second form being chosen since the integrand remains finite as m l + 0. The integrand a t the lower limit may be evaluated from the Debye-Hiickel limiting law log YZ = - 2 A d m l 3. 3m2 where A
=
0.5107
(7)
kg.'/I a t 25'.
lim ( Y G 1 ) ml + 0
=
3kA
Table Ia includes the values of Y and the integrand in eq. 6. The integrated values of log y(0)2a t round concentrations, obtained by a tabular integration of data read off a t close intervals from Fig. 3, are given in Table 11. The estimated precision of the y ( o ) 2values is about i1%. Table I11 gives the activity coefficient of hydrochloric acid a t vanishing concentration in calcium perchlorate solutions, y(ojl. These were obtained from a largescale graph of the data of Table I b ; in order to allow for the fact that the actual hydrochloric acid molality was not zero but 0.01075, the log y values read from the curve were lowered by the amount 0.01075 (log y1:o) - log y(lj)!'I = 0.0006, where I is the total ionic strength and log yl(o)is the activity coefficient of hydrochloric acid alone a t ionic strength I . The precision of these data is considerably higher than those for the calcium perchlorate, since they are much closer to the directly measured experimental quantity; it is estimated a t i=0.0005in log 7 1 . Discussion Figure 3 compares the trace-activity coefficients with those of the single electrolytes; the log y scale for
Nov., 1963
2445
,lCTlVlTY COEFFICIENTS IS MIXED ELECTROLYTES 0.2
I
1
0.1
k = 2.303 RT/F 2Y2/m7/3k
AE, my.
ma
m1
0.009754 .009754 .009754 .009754
0.000540 .001607 .002525 .004197
.04118 .04118 ,04118 ,04118 .04118
.00321 ,00538 .00939 ~01376 .02232
.I0323 .lo323 .lo323 .lo323 .lo323
.io0617 .ID1211 .02191 ,03605 .05542
2.51 3.33
.2532 ,2532 .2532
,01948 03316 05276
.79 1.06)
.5532 .5532
0244 0434
,7702 .7702 .7702
.0216 .0763 1948
-2.39
.9360 .9360 ,9360
0130 0464 ,0787
-1.00
2.214 2.214 2.214
.0289 0664 1268
-0.72 -1.61 -3.12
4.372 4 I372 4.372
.0367 " 0762 .1285
-2.58 -4.19
~
a
y
0.0 $ M
1.14
.537
-0.1
.331
-0.2
2.44 3.53 J
0.545 1.03
J
.10
~
0.75
1.39 1.92 J
.16g
-0.3 0
-
.oo2
-
,103
)
,140
-
,412
-
,848
I
I
1.0
1.5
... 2.0
1/17 Fig. 3a.-Activity coefficients of calcium perchlorate at vanishing concentrations in hydrochloric acid ( with those of calcium perchlorate in water a t the same ionic strength ( Y ~ ( ~ ) ) . 0.10
-
I
0.5
I
I
'
1.0
1.5
I
/
0.05
TABLE IB ml = 0.010754 m2
A E , mv.
0.0 .03685 .1142 .2132 .3397 ,4503 .7161 1.1063
0.0 7.99 11.57 12.67 12.01 10.72 5.85 -3.31
-log
Yl
(0.0450) .1125 .1428 .E20 .1465 .1356 .0944 .0170
hydrochloric acid is made twice that for calcium perchlorate, as t he eleciirical (Debye-Huckel) component of log y should be approximately twice as great for the 2 : l electroly1,e. It should be remembered that the values for calcium perchlorate as a single electrolyte, being computed from isopiestic vapor pressure measurements, involve some uncertainty due to the difficulty of extrapolation from 0.1 M to zero. The cross-over of the log yZ(o)and log y(o)z curves would be eliminated if the former curve were boldily displaced downward by about 0.01 in log y. It is clear that with the possible exception of this region below the cross-over, the replacement a t constant ionic strength of calcium perchlorate by hydrochloric acid raises the activity coefficient of calcium perchlorate, and a t all concentrations the replace-
~
0
0.5
~~~
2.0
Fig. Bb.-Activity coefficients of hydrochloric acid at vanish) ing concentration in calcium perchlorate solutions ( ~ ( 0 ) ~ compared with those of hydrochloric acid in water at the same ionic strength (YUO)).
ment of hydrochloric acid by calcium perchlorate a t constant ionic strength lowers the activity coefficient of hydrochloric acid. There is a very pronounced difand 2 log y(o)labove 0.1 ionic ference between log y(o)2 strength, though up to that limit the curves are close together, in accordance with the prediction of Guggenheim's theory4 of mixed electrolytes.
JOHNROBERTS AND WILLIAM H. HAMILL
2446
Vol. 67
TABLEI1 ACTIVITYCOEFFICIENT OF CALCIUM PERCHLORATE AT VANISHING CONCENTRATION IN HYDBOCHLORIC ACID SOLUTIONS AKD IN ITS AQUEOUSSOLUTIONS
TABLEI11 ACTIVITYCOEFFICIEXT OF HYDROCHLORIC ACID AT VANISHING CONCENTRATION IN CALCIUM PERCHLORATE SOLUTIONS AND IN ITS AQUEOUS SOLUTIONS
Y ( O ) P= activity coefficient a t vanishing concentration; yZ(o) = activity coefficient in aqueous solution”; ionic strength I = m: in hydrochloric acid solutions and 3mz in aqueous calcium perchlorate solutions.
Y ( O ) I = activity cocfhient a t vanishing concentration; yl(0) = activity coefficient in aqueous solutions”; ionic strength I = ml = 377~~.
I
lag
rwa
log
-
+ +
I
YZ(0)
... .. ..... .....
-0.088 .152 .1 - .203 -25 - .249 -0.238 .5 - .265 - ,264 .7 - .262 - .268 1.0 - .243 - ,264 2.0 - .131 - .210 3.0 ,017 - ,123 4.0 .191 ,016 a R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworths, London, 1959, Appendix 8.10. 0.01 .04
-
As far as we have been able to determine, this is the first investigation of mixed electrolytes of two different valency types with no common ion; the pattern of behavior is generally similar to that found by Harned and collaborators1 for the systems hydrochloric acidstrontium chloride and hydrochloric acid-barium chlo(4) E. A. Guggenheim, “Thermodynamics-an Advanced Treatise,” 4th Ed., North-Holland Publishing Company, Amsterdam, 1959, pp. 357, 358.
log
log Y l ( 9
Y(0)l
0.1 -0.1070 .3 - .1393 .6 .1525 1 .O ,1475 1.4 .1345 2.0 - .lo34 3.0 .0395 3.3 - .0194 See ref. a in Table 11.
-0.0991 - .1215 - .1179 .0621 - .0575 .0037 .1192 .1560
-
-
+ + +
(I
ride. There is, however, evidence that in the present case the activity coefficient of hydrochloric acid in mixtures of constant ionic strength cannot be represented adequately by the linear form of Haraed’s rule log
7 1 =
log
Yl(0)
-
a112
where I , is the component of the ionic strength due to electrolyte 2. This conclusion is reached by comparing - log ylc0,)/1 (Table 111) with values of (log values of (log y1 - log yl(o))/Izcomputed from the data of Table Ia; the latter are numerically smaller.
IONIC AND FREE RADICAL PROCESSES I N LIQUID MIXTURES CONTAINING HYDROCARBONS’ BY JOHN ROBERTS AXD WILLIAM H. HAMILL Deparltnet~tof Chenaistry and Radiation Laboratory, University of Notre Dame , Nolre DanLe, lndiar~u Received J u n e 6, 1963 Yields of HC1 from y-irradiation of cyclo-C& solutions containing CCla, CHFCL, CFCL, CFZCL, C,F,Cl,, and CzHsCl have been measured over a range of concentration. G(H2) for C Y C ~ O - C ~ H ~ ~ - C Ywith C ~ O0.03 - C ~M H ~1 2~, G(CHa)for n-butane-cyclo-C6H1~,and both G(H2) and G(CH4) for n-C6HI~-CH31 have also been examined, all a t ca. 20’. Mixtures of CZHJ in 80% alkane-20% alkene and also in methyltetrahydrofuran were irradiated a t - 196” and analyzed subsequent to thawing for G(H,), G(CzH4),and G(C2Hs). All results are considered in relation to ionic processes in irradiated organic glasses.z
This work extends a series of studies on ionic reactions in liquid solutions of cyclohexanea and benzene4 which are supported by direct observations of ionic species in organic glasses.2-5 We shall also freely use information gained from mass spect’rometry, both qualitatively and quantitatively. I n particular, this work has been influenced by recently available data for appearance potentials of dissociative electron atOachment processes of various halide^.^ Experimental Materials.-Fisher certified reagent grade cyclohexane and nhexane were passed through a 50-cm. siiica gel column and used (1) This article is based on a thesis submitted by J. Roberts in partial fulfillment of the requirements for the Ph.D. degree a t the University of Notre Dame. The Radiation Laboratory is operated under AEC contract AT(ll-1)-38. (2) M. R. Ronayne, J. P. Guarino, and W. H. Hamill, J. A m . Chem. Soc., 84,4230 (1962). (3) L. J. Forrestal and W. H. Hamill, ibid., 83, 1536 (1961). (4) W. Van Dusen, Jr., and W. H. Hamill, ibid., 84, 3648 (1962). (5) J. P. Guarino, M. R. Ronayne, and W. H. Hamill, Radiation R e s . , 17, 379 (1962). ( 6 ) W. M. Hickam and D. Berg, J. Chem. P/wY.,29, 517 (1958).
without further purification. Phillips research grade 3-methylpentane was used as received. Eastman spectral grade cyclohexene and Phillips pure grade 2-methylpentene-1 were treated with Na-I< and used without further purification. The purification and handling of 2-methyltetrahydrofuran has been described.a Fisher certified reagent grade methyl and ethyl iodides were fractionally distilled. Carbon tetrachloride (Fisher certified reagent), benzyl acetate (Eastman White Label), and triphenylmethane (Eastman) were used without additional purification. Propane (99.5%), ethyl chloride (99.5%), trichlorofluoromethane (99.9 %), dichlorodifluoromethane (98.1 %), dirhlorofluoromethane (99.07,), and 1,2-dichlorotetrafluoroethane, all Matheson Company chemicals, were collected in a storage bulb after several trap-to-trap distillations. Sample Preparation .-Pyrex cells used for -&-radiations were 16 mm. o.d., approximately 15 em. long, and were equipped with side arm and breakseal. Solids were weighed, liquids pipetted, and gases measured by PVT. Ten-milliliter samples were outgassed by trap-to-trap distillation using suitable refrigerants. Irradiations were performed in the Hochanadel-Ghormley Coo* source2 and dose rates were established by Fricke dosimetry. Analysis.-Gaseous products were separated using a micro( 7 ) M. Burton, J. A. Ghormley, and C. Hochanadel, Nucleonics. 13, 74 (1955).
