VOLTSUE CHANGES ON MIXINGOF ELECTROLYTE SOLUTIONS
Nov., 1963
rate of increase of Pn is accelerated while that of pw becomes relatively constant. From the figures representing Pn, P,, and H.I., it is evident that a small amount of chain transfer to monomer has an important effect on P , and Pvl but that the H.I. remains relatively unaffected. Although the general shapes of the Pn and iswus. per cent conversion curves are not altered by chain transfer, its inclusion lowers them considerably. This effect is most apparent, a t low catalyst concentrations. To observe the effect of tempera,ture on the variation of 2", and P,, a few calculations were made for polymerization of styrene a t 100'. While larger rates of increase in both Pn and P , were indicated, a limiting value for H.I. of 5.0 was found. These considerations are merely qualitative, however, since styrene undergoes appreciable thermal polymerization a t this temperaturelsthe effect of which was assumed to be negligible in these calculations. Polymerization of Isoprene.-The kinetic constants for the bulk polymerization of isoprene at various temperatures have been determined recently using the dead-end polymerization t h e ~ r y . Using ~ these kinetic constants (Table 11) and applying the expressions developed in this paper, the cumulative number and weight average degrees of polymerization were computed for isoprene a t 80' assuming no chgin iransfer to monomer. The calculated values for Pn, P,, and H.I. are listed in Table 111. (8) R. F. Boundy and R. F. Boyer, Ed., "Styrene, Its Polymers, Copolymers and Derivatives," Reinhold Publ. Corp., New York, N. Y , 1952, p. 218. (9) R. H. Gobran, M. B. Berenbaum, and A. V. Tobolsky, J. Polvmer Scl., 46,431 (1960).
R A CONSTANTS' ~ FOR
2339
TABLE I1 POLYMERIZATION OF ISOPRENE RY
THE
Azo-1 AT 80' f = 0.60 k d = 1.0 X 10-4/sec. k,/kt'/Z = 1.1 x 10-2 M o = 10 See ref. 9.
HETEROGENEITY INDEX IN Fractional conv.
0.02 .06 .10 .14 .18 .22 .24 .26 .28
Cum.
TABLE I11 THE POLYMERIZATION OF ISOPRENE
Pw
Cum.
97.5 184.8 238.5 281.0 320.5 363.3 389.1 421.4 468.9
F,,
H.I.
58.4 60.1 62.2 69.3 75.5 82.3 86.4 91.2 96.7
1.67 3.07 3.83 4.05 4.25 4.41 4.50 4.62 4.75
The technique suggested in this study might well be used to prepare polymers of desired molecular weight and molecular weight distribution. However, one should bear in mind that at the onset of diffusion controlled termination2s4 these theoretical calculations become inaccurate; hence, a polymerization should be quenched before this effect becomes dominant. Acknowledgment:.-The partial support of the Army Research Office (Durham) and the Goodyear Tire and Rubber Company is gratefully acknowledged.
VOLUIKE CHANGES ON MIXING SOLUTIONS OF SODIUM CHLORIDE, HYDROCHLORIC ACID, SODIUM PERCHLORATE, AND PERCHLORIC ACID CONSTANT IONIC STRENGTH. A TEST OF YOUNG'S RULE1
Kr
BY HENRYE. WIRTH,RICHARD E. LINDSTROM, AND JOSEPH N. JOHNSON Department of Chemistry, Syracuse University, Syracuse 10,New York Received May 1, 1963 The volume changes on mixing two solutions of equal ionic strength were determined for the six possible combinations of the four electrolytes, NaC1, HC1, NaC104, and HClOI, at two concentrations, 1.000 and 4.1724 m. A dilatometer capable of measuring volume changes to ic 1 X ml. in a total volume of 100-300 ml. was used. It was found that the volume change on miking two heteroionic electrolytes (NaCl and HC1O4, or NaC104 and HC1) could be calculated from the volume changes observed in homoionic solutions. I n the most unfavorable case the mean apparent volume calculated by Young's rule is in error by 0.6 ml. (2%), and the corresponding density is in error by only 0.2%.
The mean apparent molal volume of a mixture of electrolytes (@I is defined by cp=
V - 55.51D1' m2
+ m3
(1)
where V is the volume of solution containing 1000 g. of water, D'I is the molar volume of pure water, and m2 and ms are the molalities of the two electrolytes. Young and Smith2 have shown that their mixt,ure rule (1) Preaented in part a t the 144th National Meeting of the American Chemical Society, Los Angeles, Calif., April, 1963. (2) T. F. Young and M. B. Smith, J . Phys. Chem., 68,716 (1954).
4,=
m2+2
m2
+ ma43 + m3
(2)
accurately represents data for KC1-NaCl13 KBrNaCllS and NaC104-HC1044 mixtures. I n eq. 2, 42 is the apparent molal volume of one of the electrolytes in a solution containing only water and this electrolyte a t an ionic strength pw corresponding to m2 m3, and 43 is the apparent molal volume of the other electrolyte in a binary solution a t this same ionic strength. A
+
(3) H. E. Wirth, J. Am. Chem. Soc., 69, 2549 (1937). (4) H. E. Wirth and F. N. Collier, Jr., ibid., 72, 5292 (1950).
2340
HENRYE. WIRTH,RICHARD E. LINDSTROM, AND JOSEPH X. JOHSSON
I
0 HC10A
I
I
0 25
0 5
Vol. 67
I
0 75
i n HCI
Sa.
Fig. 3.--T’olume changes on mixing equimolal solutions of HC104 and HC1: upper curve, 1.000 m; lower curve, 4.172 m.
n
-0
Fig. 1.-Dilatometer
(schematic).
06
e;
z
4
> E c- -0.10 d
-0.15
ni”. NaClOa
0 25
0.50 Sa.
0.75
1.0 iYaCl
Fig. 4.-Volume changes on mixing equimolal solutions of NaC104 and NaC1: upper curve, 1.000 rn; lower curve 4.172 m.
One consequence of Young’s unmodified rule is that there should be no change in volume on mixing solutions of equal ionic strength. Since such information can be obtained from the data in the literature only by interpolation it was felt desirable to make a direct test of this prediction. Experimental
0 KaCl
0 50 53.
0.26
0 75
1.0
HC1
Fig. 2.-Volume change on mixing equimolal solutions of NaCl and HC1: upper curve, 1.000 m; lower curve 4.172 m.
small correction term D has to be added to eq. 2 to give complete agreement for ?;aC1-HC16 mixtures. The where Sg = m2/ ‘suggested form of D is S2S3pLwK, i(nLz m3) and SO= m3/ (mz m3).
+
‘(6)
+
E. Wi&~+yl,Am. Chem. SOC.,61, 1128 (1940).
Materials and Apparatus.-Stock solutions of NaC1, HC1, NaC104, and HC104 were prepared from C.P. chemicals. The concentrations of the salt solutions were determined by evaporating weighed portions t o dryness and heating a t 350-400”. The acid solutions were analyzed by weight titration methods previously describe@ using constant boiling HC1 as the reference standard. Solutions exactly 1.0000 and 4.1725 m were prepared by weight dilution of the stock solutions. Volume changes on mixing solutions of equal ionic strength were determined using a dilatometer (Fig. 1) similar t o that described by Geffcken, Kruis, and Solana.6 About 100 ml. of one (6) W. Geffoken, A. Hruis, and L. Bolana. Z . p h y s i k . Chem. (Leiwig), B36, 817 (1937).
VOLUMECHANGESON MIXIXGOF ELECTROLYTE SOLUTIONS
Nov., 1963
solution was introduced from bulb B into A (volume 350 ml.) through the four-way stopcock a. The amount introduced was determined by weighing the mercury displaced through the capillary tube a t the left of the apparatus. A second solution filled the bulb C and all connecting tubing. Stopcock b was opened to the position shown and mercury from A displaced the second solution into the first through a. The bulbs permitted the addition of 1, 4, or 14 ml. of the second solution and were calibrated by weighing the mercury required to fill them to reference marks on the connecting capillary tubing. After addition of the socond solution, the solution in -4was thoroughly mixed by the magnetic stirrer S. Any volume change was reflected by an increase or decrease in weight of mercury in a weighing bottle around the capillary tip. Weight changes were determined to rtl mg., corresponding to a volume change of rtl ml. Stopcock b was turned to permit the mercury in the X bulbs to flow into the bottom of C, and more of the second solution could be added. The pressure at the capillary tip was adjusted in order to keep the pressure on the solution in A constant. The apparatus was immersed in a thermostat a t a temperature of 25” maintained constant to i0.0006”. The volume of the first solution Vz = nlB~’ ~z$z, where nl is the number of moles of water, n2 is the number of moles of electrolyte, and 42 is its apparent molal volume in this solun&. tion. The volume of the second solution T/3 = ni’Bio The total volume V is VZ V3 Au, where Av is the observed change in volume on mixing. By definition, the mean apparent molal volume 4, = (V - nl”olo)/(nz i- na), where nl’l = nl f nl’. Substituting, @ = (n2+2 n&)/(m n3) Av/(n2 n3). The first termis Young’s rule, and D = Av/(np na). Values of +Z and (pa were determined by direct density measurements using the sinker method.4 A few values of D were obtained by direct density determination on mixed solutions.
2341
+
+
+ +
+
+ + +
+
Results and Discussion Results obtained are given in Fig. 2 through 7. I n these figures open circles (0) designate points obtained by adding solution 1 to solution 2, while points labeled were obtained by adding solution 2 to solution 1. Overlap of these points near a mole fraction of 0.5 indicates the reproducibility of the experimental procedure. Points labeled o were obtained by direct density measurements and are generally in good agreement with the dilatometer values, although they are much more sensitive to experimental error. Points are calculated for a 1 m solution from the marked values in 4.17 m solution, assuming D is linearly dependent on pLw. Tables I and I1 give the constants for the equatiolis which represeni, the experimental results in 1.0 and 4.17 m solutions for the six possible mixtures. The results in 4.17 m solution had to be represented by the relation D = kXi% iC’~S’2~83, since in all cases D was not symmetric around a mole fraction of 0.5. I n the Na-
+
ClOpHC104 mixture the maximum value of D was a t mole fraction 0.61 of HC10,. I n 1.0 m solution the data could be adequately represented by the expression D = kS2X3, although there were some indications that the curves are not completely symmetrical. TABLE I1
RESULTS FOR 4.17 m SOLUTION D = kS?& k’S22S3
+
Ys k k’ HC1 HC104 -0,3270 -0.1250 NaCl HC1 - .5071 .1466 NaC104 HC104 ,1228 .OS13 YaC1 hTaC1O4 - .4805 - ,2256 Y2
HCl XaC1 NaC104 KaCl
B
Av. dev., ml./mole
HC104 HC1 HClO4 n’aC104
- 0 0744 - ,1290 - ,0686 - ,1087
f 0 0008 f 0009 f 0005 =t 0004
-0 0186 -0,0323 -0.0172 -0.0272
2 0 = -0.0953
EaC1o4 XaC1
-
HC1 HClO4
+
,8150 ,4251
f ,0016
zx 1/2(‘$NaClOa
+
$€IC1
-
dNaCl
-0 2038 $0.1063
f ,0017 =
Difference = - $“ClOi) =s 1/2R
-0.0975 0.3101 0,307
E
hv. dev..
D0.6,
ml./mole
ml./mole
&0.0007 - 0.0974 f .0004 -0.1085 f ,0008 - 0.0205 i .0012 - 0.1488
- 0.3747 - 0.6470
20 =
NaC1O4 HC1 NaCl HC104
1/2(dJriaCIoa
-2.7810 +1.4907
+
dHCl
+
.3859 i .0019 - ,6944 i: ,0027 +0. 2859
- @Nit01
2 X = -0.3611 Difference = 0.9329 - ‘$“Clod) = 1 / 2 8 = 0 922
TABLEI11 YZ
Do.6, ml./mole
+ +
-
-Electrolyte
pair
YS
10 HClOi
8s.
Fig. 5.-Volume changes on mixing equimolal solutions of NaCIOa and HClO,: dashed curve, 1.000 m; solid curve 4.172 172.
CONSTANTS FOR
TABLE I RESULTSFOR 1 m SOLUTION D = kSaSa
0 75
0.50
SaClOa
+
--Electrolyte Y2
0 25
0
HC1 SaCl YaC104 NaC1 NaC1O4 NaCl
THE EQUATIONS: k = CUM^
+ p&
AND
k‘ =
y@,,.2
pair-
Ys HClO4 HC1 HC1O4 NaCIOe HC1 HC1Oa
P
a
-0.0731 - ,1314 - ,0809 - .I067 - ,8618 .4465
+
-0.0013 .0024 ,0123 - ,0020 ,0468 - ,0214
+ + +
Y
-0.0072 0084 .0047 - ,0130 0222 - ,0399
+ + +
While this work is primarily concerned with the deviations from Young’s rule, it should be emphasized that these deviations are small, and that the rule gives a remarkably good first approximation. For example, the maximum contraction observed on mixing 500 ml. of a 1 m solution with 500 ml. of another 1 m solution containing a common ion is 0.03 ml., or about 0.1% error in the value of the mean apparent molal volume.,
HENRYE. WIRTH,RICHARD E. LINDSTROM, AND JOSEPH N. JOHXSON
2342
Vol. 67
TABLE IV CONSTANTS FOR THE EQUATION : $ = a bpw"' ~ p , ~ . dpw3/a epW2
+
+ +
+
Av. dev. a
b
16.6516 17,8479 44.2441 42,9242
1.72081 1.78964 0.87571 1.94690
Electrolyte
NaCl HC1 HClOI NaC104
dobsd
c
0.00831
- 1.11631
-0.74702 - .43780
-
Ooa,lod.,
d
e
ml./mnle
0.15844 .56722 .18627 .39198
-0.05266 - ,10709 - ,02715
f .021
*0.010
*
.010 i. .008
- .09914
in discussing results on the heats of mixing of homoionic and heteroionic solutions, it was found that in 1 m solution (Table I) the sum of the deviations (Do.6) on mixing the four pairs of homoionic solutions to give 50-50 mixtures ( 2 0 ) was equal to the sum of the deviations on mixing the two pairs of heteroionic solutions (8X) mitliin the experimental error. In 4.17 m solution ( 8 0 - ZX) = -0.0135 ml./mole (Table 11). This difference is considered to be outside the experimental error and could be due to different degrees of ionization of the perchloric acid in the presence of various salts. Except a t infinite dilution the apparent molal volumes of electrolytes are not additive functions of the apparent ionic volumes. For the set of four electrolytes, KaCl, HC1, NaC104, and HC104, the net departure from ad~ H CI 4 ~ ~ ditivity (&) is given by R = (bNaC10, C$HCIOA, and for purposes of calculation can be attributed to one of the electrolytes, i.e., HC104. At a given ionic strength, the apparent molal volumes of the electrolytes are then given by 4 ~ =! ~( P N ~~ 4 1~ 1 (PHC1 , = 4H 6 2 1 , 4NaClO4 = 4% (Pc1Oal and 4HC104 = $H -k @Cl04 R, where 4 ~ 4 ,~ &4c1, , and 4C104 are the apparent ionic volumes of the ions. The mean apparent molal volume of a mixture containing equal concentrations of all four ions as calculated by the unmodified Young's rule for the electrolyte pair HCI-NaC104 is 1 / 2 ( @ H $. d T 1 4Na 4Cl04) and is 1 / 2 ( 4 N a (bel .f 4~ 4- 4 ~ 1 0 , - R ) for the pair NaC1-HC104. The difference between these two calculated values is 0.5R and is equal to the algebraic difference between the observed D values for the 50-50 mixtures for HC1NaC104 and NaCl-HCIOk (Tables I and 11). On the basis of these relationships it is possible t o design a synthetic equation which will represent the mean apparent molal volumes for all possible combinations of the four electrolytes, using the constants obtained experimentally for the four homoionic pairs. I n 4.17 m solution this equation is
+
0
0.25
NaClOi
0.50
0.75
88.
1.0 HC1
Fig. 6.-Volume changes on mixing equimolal solutions of NaC104 and HC1: upper curve, 1.000 m; lower curve, 4.172 m. I
I
I
I
I
+-
NaCl
0.25
0.50
Sa.
0.75
1.0 HClO4
+
+
+
+
+
0
-
Fig. 7.-Volume changes on mixing equimolal solutions of NaC1 and HCIO,: upper curve, 4.124 m; lower curve, 1.000 m.
Only in heteroionic solutions or a t high concentrations are the deviations larger than the errors in the equations representing the apparent molal volumes of pure salts (Table IV). If we consider the array EaC1o4 ++ HC104
I >c s
NaC1++ HC1 sipilar to that used by Young, Wu, and Krawetz7 (7) T.F. Young, Y. C. Wu, and A. A. Krewetz. DiscussiOn8 Faraday Soc., 24,m (1957).
fiCl((kJC1 fiC1O4(&104
f
SNaSHkCl
+
+
sNaSHkC104
+
s2iiaSHk'Cl)
f
+
s2KasHk'C104)
(3)
+
where SNa = m N a / ( m N a m ~ ) Sa , = mcl/(ma mc104), etc., and k ~ and , J C ' N ~ are observed values of k and k' for the pair KaC1-NaC1O4 with sodium as the common cation, kcl and k'c1 are for the pair SaC1-HC1 with chloride as the common anion, etc. If this equation is rearranged to represent XaC1HC104 mixtures by setting S N=~S c l = &"&cl and h" = Sao, = SHCIO~, it becomes
~
1
VOLUME CHANGESON MIXINGOF ELECTROLYTE SOLUTIONS
Xov., 1963
*
= XNaCI4NaCl
k I o 4 f8)
+
+
sHCIO44HC10,
S2NaClSHC1O4(kNa
+
k‘Na
+
k‘Cl)
2343
f + + - k~ - kclo, + + SN&l#HC104(kH
kcl
82NaC182HC10,(k’H
- k’Na - k‘cl)
k’C10,
(4)
The value of D calculated from eq. 4 agrees with the observed data for this mixture (Fig. 4) with an average deviation of *0.0047 ml./mole. In a 50-50 mixture Do.5
+0.25R
=
46.4
+ 0.125Bk + 0.062521~’
-8 d.
Rearranged to represent NaCIOd-HCl mixtures by setting X N ~= XcloI = S N ~ C and~ SH O ~= Sa = S H C ~ eq. 3 becomes
CP =
0
z
+ X H C ~ ~ H+C IX N ~ C ~ O ~ S H C+~ ( I C H $. + k ’ ~- R ) fi2NaClO,XHCl(1cNa
- kCl --
k’H
f
IC’CIO,)
f
k‘Cl
IcCl04
S2NaC10,82HCl(k’Na
- k’Cl0,)
- k’H
44.8
+
(5)
For this system the average deviation (Dcaicd Dobsd)is ~t0.0044ml./mole in 4.17 m solution. This is only twice the deviation found with the empirical equation (Table 11). I n a 50-50 mixture 00.5
=
-0.25R
+ 0.12521~+ 0.06252k’
The sum of these two values (2X) is 0.258k f 0.125%’ and is equal to BU . The difference is OAR. In one molal solution the synthetic equation represents the data for NaC1-HC1O4 mixtures with an average deviation of +0.0017 ml./mole, and the data for NaC104-HCl mixtures with an average deviation of h0.0016 ml./mole. The synthetic equations which contain only the arbitrary constants derived from data on homoionic systems represent the results on heteroionic systems as well as does the empirical equation. The mixing of four ions therefore involves no interactions not already taken into account in mixtures containing three ions. Comparison with Previous Results.-In order to compare the results obtained here with data in the literature, it is necessary to make some assumption as to the dependence of IC and k’ on the ionic strength. It was assumed that k = a p U w P p w 2 and k’ = ypw2. The values of a,P, and y are given in Table 111. The apparent molal volumes of the pure salts were represented by equations of the form @ = a bpW’/z cpw dpw’/’ e p W Z . The constants given in Table IV for the electrolytes investigated are based on the original data for HCl,5 NaC1,5 HC104,4 and SaC1044 solutions, except that the data of Redlich and Bigeleisen8 were used for dilute HC1 solutions. It should be emphasized that these equations are valid only for interpolation between 0.04 and 4 m. Values of 4’ are best obtained by extrapolation of equations involving volume concentrations and the theoretical limiting slope. Values of CP were calculated from the original data on HC1-KaC15 and S a C 1 0 ~ - H C 1 0mixtures, ~~ and compared with those calculated from the equation
+
+
CP
4
Xxacio,@Naclo,
ICCl JCH
45.6
= X242
+
+
+
x343
+ S2X3(a~w+
Dpw2)
+
+
8 2‘ 8 3
YPw 2
(6)
( 8 ) 0. Redlioh and J . Bigeleisen. J. Am. Chern. Soc.. 64, 758 (1942); cf. also ref. 1, p. 721. (91 0.Redlich, J . Phva. Chem., 67,496 (1963).
44.0
0
1.0
2 0
Fw%.
Fig. %-Partial molal volumes of NaCl in HClO4 solution and HC104 in IiaC1 solution ~ t 8a function of the ionic strength: curve 1, g3 of the electrolyte in pure water; curves 2 to 6, & of one electrolyte in 0.04, 0.16, 0.36, 1.0, and 2.25 m solutions of the other electrolyte; dashed curves are the partial molal volumes of one electrolyte in a solution containing only the other electrolyte (note that the HClO, scale is twice that for KaCl).
The average deviation was found to be h0.012 ml./ mole (max. dev. 0.054) for HCl-Sac1 mixtures, and h0.015 ml./mole (max. dev. 0.087) for T\;nC104HClOl mixtures. Partial Molal Volumes.-If eq. 1 and 6 are combined, and solved for V , differentiation with respect to m2 or m3 gives the partial molal volumes g2 and g3
and
m2a
+ 2mm3P + mz2@ + r> (8)
These equations are valid only for uni-univalent electrolytes. The values obtained are in agreement with those previously calculated for KaCl-HC1 and NaC1O4HClO4 mixtures with an average deviation of .t0.025 ml./mole, except for the KaC1 in 4 m solution. It is felt that the equation for HCl (Table IV) yields the incorrect slope in 4 m solution, since no experimental points a t concentrations greater than 4 m were used in obtaining the equation. These equations were also used to calculate the partial molal volumes of the four other combinations of electrolytes. The results for the pair KaCl-HC104 are given in Fig. 8. I n this combination the two slopes (d4/dpw’/Z)differ by the largest amount, and the deviation terms are also larger than for any of the electrolyte pairs investigated. The original observationS that the partial molal
L.R. SNYDER
2344
volume of a salt depends only on the total ionic strength of the solution is valid only if d$z/dpw‘/z= d$3/dp,1/2, and a, p, and y are negligible. Iii this case eq. 8 reduces to: Os = 43 ( ~ ‘ / ~ /(d+s/dpcw1/2), 2) and g3 is independent of the value of m2. I n some cases the correction terms partially compensate for the difference in slopes for one member of the pair of electrolytes. For example, in l m solution the partial molal volume of XaC1 is 19.49 ml. in pure KaCl and 19.30 ml. in pure NaC104 solution, while the partial molal volume of NaC104 is 45.65 ml. in pure KaC104 aiid 45.61 in pure XaC1 solution. I n 4.17 m solution the corresponding values for KaC1 are 22.52 and 21.82 ml.; for NaC104, they are 48.34 and 47.92 ml. Choice of Variable.-Before beginning this work, the possibility was considered that there would be smaller deviations from Young’s rule if molar rather than molal concentrations were used. Preliminary experiments using direct density measurements indicated that the volume contractions on mixing two solutions of equal molarity were of the same order of magnitude as in mixing solutioiis of equal molality. Since such contractions do occur, the resulting solution no longer has the same molarity as the components and further corrections would be required. For practical reasons, molal concentrations were used. With the aid of eq. 6 it is possible to calculate by an iterative procedure the deviations between the value of @ a t a given volume concentration and that calculated from Young’s rule using volume concentrations. For example, in a 50-50 mixture of KaC1 and HC1, where the total molarity is 3.8317, the calculated deviation
+
Vol. 67
is -0.110 ml./mole, or almost exactly the same as for 4.1724 m solutions. (A molarity of 3.8317 corresponds to m = 4.1724 in pure NaC1 and m = 4.1586 in pure HCl.) For a NaC104-HC104 mixture a t a molarity of 3.4841 (corresponding to 4.1724 m NaC104 and 4.1268 m Hclod), the deviation is -0.027 ml./mole for a 50-50 mixture, which is a third larger than for equimolal solutions, but the deviations were more nearly symmetrical about a mole fraction of 0.5 (maximum near 0.57 mole fraction of HC104). Calculation of Density.-The density of a solution containing any possible combination of the four electrolytes, NaC1, HCl, NaC104, and HC104, can be obtained at 25” in the range 0-4 m by use of the equation
a=
+
+ + + + +
1000 (mzMz madla . .) 1002.93 (mz m3 . .)@
If @ is evaluated by Young’s unmodified rule, using eq. 2 and the constants in Table IT’, the maximum error in the density in a most unfavorable case (a 50-50 mixture of KaC104-HC1 in 4 m solution) would be about 2 parts per 1000. If eq. 6 with the constltnts in Tables I11 and IV is used to evaluate CP, then the maximum error would be of the order of 2 parts in 10,000 (0.02%). Acknowledgment.-The authors wish to thank Mr. Jeffrey Greenhouse for preparing the computer program for many of the calculations. This work was supported in part by the National Science Foundation, Crant G-14623.
ADSORPTION FROM SOLUTION. 111. DERIVATIVES OF PYRIDINE, ANILINE, AND PYRROLE ON ALUMINA BY L. R. SNYDER Union Oil Company of California, Union Research Center, Brea, California Received M a y 23, 19623 Linsar isotherm free energies of adsorption from n-pentane onto 3.6% HzO-AlzOa are reported for 66 nitrogen compounds related to pyridine, aniline, or pyrrole. A previously developed theoretical model permits the calculation of the nitrogen group adsorption energy for each adsorbate, free from the “normal” contributions to total adsorption energy by other adsorbate groups. I t is concluded that the nitrogen group in the pyridines and rinilines adsorbs with n-electron transfer to an adsorbent site, while the pyrrole nitrogen group adsorbs with proton transfer to the alumina surface. The localization or anchoring of strongly adsorbing adsorbate groups on the adsorbent surface is also discussed.
Introduction Recent communication^^-^ have drawn attention to certain regularities in the adsorption on alumina of the substituted pyridines and related aza aromatics. The contribution of the nitrogen atom in these adsorbates to total adsorption energy is markedly sensitive to the steric environment about the nitrogen atom, adsorption energy decreasing with increased crowding of the nitrogen. This observation has led Klemm2 to post,ulate that the nitrogen atom(s) in the less crowded aza aromatics serves as an “anchoring” group (a concept first introduced by Zechmeister4), with the remainder of (1) L. R. Snyder, J . Chromatog., 6,22 (1961). (2) L. H.Klemm, E. P. Antoniades, G. Capp, E. Chiang, and E. Y . K. Mak, ibid., 6,420 (1961). (3) L. R. Snyder, ibid., 8 , 319 (1962). (4) L.Zechmeister, Ddscusskone Faraday Soc., 1 , 54 (1949).
the adsorbate only loosely attached to the adsorbent surface. The sensitivity of the nitrogen atom adsorption energy to crowding by adjacent substituent groups is regarded by Klemm as resulting from the interference by such groups to a preferred tilted or edgewise configuration of the adsorbate relative to the plane of the adsorbent surface (presumably for optimum interaction of nitrogen and surface site). Klemm also has proposed that the interaction between nitrogen and adsorbent is the result of charge-transfer complex formation involving the nitrogen n electrons, on the basis of spectral evidence for the greater polarizability of the nitrogen n electrons and by analogy with the previously postulatedK a--complexation of aromatic hydrocarbons adsorbed on alumina. A previous study of the variation of adsorption energy
