AQUEOUS SOLUTIONS OF SODIUM SILICATES. V. OSMOTIC ACTIVITY, LOWERING O F VAPOUR-PRESSURES AND FREEZING-POINTS BY R. W. HARMAN
Introduction I n the elucidation of the problem of the behaviour of solutions of silicates, the osmotic activity i. e. the nature of the ions and their concentrations, plays a very important part. The determination and discussion of the concentration and activity of sodium ions and of hydroxyl ions of aqueous solutions of sodium silicates of varying ratios and concentrations have already been communicated.' Heretofore, the silica in solution has always been thought to be colloidal, due, no doubt, to preconceived ideas arising from the colloidal nature of silicic acid, using the term silicic acid in a wide sense to cover all those forms of hydrated silica or hypothetical silicic acids, met with in the literature. From conductivity measurements* and from transport number experiments' evidence has been brought forward of the existence of silicate ions, and further work on diffusion through semi-permeable membranes to be communicated shortly leaves no doubt as to their existence. The determination of the total concentration of the ions is perhaps the most important part of this investigation into the nature of aqueous solutions of sodium silicates. Having obtained a knowledge of the total crystalloidal content of these solutions, together with the hydroxyl and the sodium ion concentrations, the question of the relative amounts of colloidal and crystalloidal silica, with the possibility of ion adsorption, or of micelle formation, may be definitely discussed. Of the many methods by which the osmotic activity of a solution may be measured, the lowering of the freezing point is, omitting exceptional cases, the best. The lowering of the vapour pressure is also capable of accurate measurement and has the advantage that it may be carried out a t any temperature, thus obviating the necessity of correcting the osmotic pressure for temperature. Since a method of measuring the vapour pressure had recently been worked out in this laboratory and its application had met with success in an investigation on the activity of HC1 solutions, it was decided t o try this same method with silicate solutions; but the results as explained later, have not been altogether satisfactory. The freezing point method was then employed and the conclusions deduced herein are mainly from the results so obtained. Aqueous Solutions of Sodium Silicates, 111, IV. J. Phys. Chem., 30, 917,1100(1926). *Harman: J. Phys. Chem., 29, 1155(1925). Aqueous Sdutions of Sodium Silicates, 11. J. Phys. Chem., 30, 359 (1926).
R. W. HARMAN
356
VAPOR PRESSURES Experimental The method was essentially the same as that used by Dobson and Masson' for measuring the vapour pressure of HCl solutions. I t consists in saturating a measured current of gas, (nitrogen) with water vapour, by bubbling the nitrogen through the solution, and then absorbing and weighing this vapour. The vapour pressure follows from the gas laws when we know the volume occupied by the gas in the saturator. The apparatus, made of hard glass, was a double apparatus, the first part consisting of saturators containing pure water followed by an absorber of H ~ S O Ithe , other part, of saturators containing the silicate solution followed by an absorber. The great advantage of this type of double apparatus is that it may be operated in two ways :( I ) to measure the actual vapour pressure of the water and of the solution, called the absolute method, A. ( 2 ) to measure the vapour pressure of the silicate solution relatively to that of the water, relative method, R. I n the first way, the volume and pressure of nitrogen saturated with water vapour, and the weight of water vapour so required to saturate it, must be measured, whence can be calculated both the vapour pressure of the solution and of the pure water, the latter thus serving as a check on the accuracy of the experiment. Operating in this way, the passage of about 10-12 litres of nitrogen meant an increase in the absorbers of from 0.2-0.3 gram. However, the greater the amount of water vapour absorbed and weighed the greater the accuracy of the experiment. This was better achieved in the second method of operation, where the nitrogen was allowed to bubble through for about 24 hours, whereby the amount of water vapour absorbed was from I to 2 gm. I n this method of operation the volume of nitrogen was not measured, so only the vapour pressure of the solution relatively to that of the water could be calculated. The experiments were carried out at 2 5 O C , the apparatue being immersed in a water thermostat electrically heated and regulated to 25' C f 0.01. The solutions used, their composition, concentration and preparation, the precautions taken, etc., were the same as those already quoted in the previous publications on this subject by the author. Accuracy of Results The absolute method, A . The fact that the vapour pressure of water a t 25' C can be calculated provides a most useful check and indication that the apparatus is working satisfactorily. One or two runs with each silicate solution experimented upon were usually made, but the values of the vapour pressure of water or of the silicate solution generally differed by as much as (I)
J. Chem. SOC.,125,
668 (1924).
AQUEOUS SOLUTIOSS O F SODIUM SILICATES
357
error is not surprising nhen we consider that the accuracy depends upon.( I ) The amount of water vapour absorbed. This was about 0 . 2 gm., the total w i g h t of the absorber and the H2S04being about jo gm. The measurement of the excess pressure in the saturator. This (2) fluctuated slightly over a run, but with a constant-level device attached to the aspirator the pressure could be measured to within 0.1 mm. (3) The measurement of the volume of nitrogen collected. This volume was accurate to within 0.017~.By using great care and making several runs with the same solution it was possible to obtain the vapour pressure to within
TABLE I S'apour Pressures
s,
Method
Vap. Press. Soln.
Lowering Mean in mms. Cowering
Ratio 2.427
A
x R
I
,062
A A
R 0.41
.A
R 0.102
A
R
22.61 22.68 22.62
Calc. Expt. lowering Lowering calc. lowering
I:I
1.09 1.02
1.06
0 .jog6
2.08
0.55
0.2230
2.46
1.08
23.20 23.12 23.12
0.50
23.39 23.41
0.30 0.29
0.29
0.08610
3.36
23.63 23.62
0.08
0.08
0.02142
3.73
0.08
0.45
0.42
I
0.30
0.31
0.21
1.49
0.19
0.20
0.105
1.90
0 .IO
0.042
2.38
0.055
0.021
2.61
0.58 0.58
Ratio 1:2 2.0
h
23'24 23.25 23.25
0.46 0.45 0.45
23.39 23.38
0.30
R A R
23.51 23.49
R R
23.60 23.60
0. I O
R
23.65 23.64
0.05
R R 1.0
0.5
0.2
0.1
A
R
.08
0.21
0.IO
0 . ~ 6
358
R . W, HARMAS
0.01mm. With the more concentrated solutions of ratio I : I , where the lowering is in the neighbourhood of I mm., this 17~ error is allowable, hut with dilute solutions, e. g. one containing o.zN crystalloidal matter, where the lowering is only 0.04 mm., the error in the vapour pressure lowering is z jyc. The relative method, R. By allowing the nitrogen to pass through (2) from 24 to 48 hours the weights of water vapour absorbed were increased to 76 gm. and the error due to their measurement practically eliminated. The error introduced by the measurement of the nitrogen has entirely disappeared, the calculation now being independent of the volume of nitrogen. Therefore the accuracy depends almost entirely upon the precision with which the excess pressure in the saturators can be measured, and this as stated previously could be determined t o within 0.1mm. of mercury. This method gave much more concordant readings, the accuracy being within 0.005 mmyc of mercury, but even this means an error of 10% in the lowering of the vapour pressure of a dilute solution containing o.zX crystalloidal mat,ter. Hence the reason for making freezinp point measurements as well.
Results I n Table I are given the results of vapor pressure measurements for ratios h-alO:SiOl, I:I and 1 : ~ . Under the heading method is given the manner (absolute, A, or relat’ive,R) in which the vapour pressure was found. Column 7 contains the calculated value of the lowering of the vapour pressure for the cited normality for an ideal non-associat’ing, non-dissociating compound and column 8 the ratio of the experiment,ally found lowering to that of the calculated lowering, in other words, the van’t Hoff factor “i”. These results will be discussed and compared with the freezing point results given below. However, the older method of calculating the molecular weight or degree of ionisation, involving the assumptions and conceptions upon which the van’t Hoff factor “i” is based is probably not so accurate or in as close accordance with experimental facts as some of the more recent theories. ‘Therefore an attempt will be made to interpret these results from the point of view of the activiby theory. Calculation of Activity Coefficients for Ratios 1:l and 1:2 from Vapour Pressure of Solvent. The method of calculating the activity coefficient of a solute for concent,rated solutions from the vapour pressure of the solvent, given in Lewis and Randall’s “Thermodynamics”, has been strictly followed and the results are given in Table 11, where the notation employed by Lewis and Randall has been followed. The first column gives the molality of NarSiOs, the second gives pl the vapour pressure of water from the solution divided by po the vapour pressure of pure water. The third column, under S1/52 gives the mol ratio of the two constituents of the solution, i. e. the mol fraction of water have been divided by the mol fraction of the silicate. The values of SIISB calculated from the molality m by means of the conversion table.’ If we plot I.ewis and Randall: “Theraodyr.amic8,” Appendix
I,
p. 609 (1923).
AQVEOUS SOLUTIOSS O F SODIGM SILICATES
359
+
S J S , against I O log. pt 'pIo,we get the difference between the two values of log *&(A2 being the activity of the solute) by obtaining bhe area under the
curve. This quantity is proportional to A?, and by taking the fourth root, i. e. assuming v , the number of ions from complete dissociation of the solute molecule at infinite dilution, equal to 4, and dividing by nz, we get a series of values, ky, proportional to y , the activity coefficient.
TABLE I1 m
PI./PIO
Y,/52
Ratio I , 213 0,531
0.200
0.OjI
0.955 0.973 0.988 0.996
0 . j0
0.2j 0. I O
0.05
0.9811 0.9872 0.9917 0,9959 0.9977
'
27.4
57.0 I10
jI0
999
+ log PI/PI0
kr
9,9800 9.9881 9 9948 9'9983
41. j 6 99 63 298.0 999.0
Ratio I .o
IO
I :I
0.824
1,364 I . 625
'
1.930
I:Z
9.9917 9.9944 9.9964 9.9982 9.9990
I
.o
1.8734 3.3016 6.232 8.824
The values of ky in t,he last column of Table I1 give, of course, only comparative values of y over the molalities quot'ed, because no measurements of vapour pressure are accurate enough in extremely dilute solution t o warrant extrapolation to y = I . However, as will be seen later, when y is calculated from freezing point measurement,s, the value of k can be found and hence y from these vapour pressure calculations can be determined. This is done later on where y from vapour pressure and from freezing point measurements are compared. Freezing Point Measurements Experimental The ordinary laboratory or Beckmann method was used. as, at first, these freezing point measurements were intended only as a check on the vapour pressure measurements ; hut when it was discovered t,hat the vapour pressure method was unsatisfactory, except for concentrated solutions, freezing point determinations of all the ratios viz., 2 : 1 , I:I, I : Z , 1:3, 1:4 were made a t concentrations ranging from o . o o j S, to 2 . 0 s,. The usual precautions were taken; the temperature of the cooling bath, was maintained 2-3' C below t8he observed freezing point', and the amount of supercooling did not generally exceed 0.3'c'. The temperatures were read correct to 0 . 0 0 2 ~ C .
U I
Results Table I11 contains t'he results under the headings S, or weight normality; ~molality, i. e. gm. mol. wt. ( S a n O X SiO?) per 1000 gms. solvent; A , ob-
served lowering in degrees; A, m, molecular depression; "i" =
a m X 1.858
, i. e.
R. W . H A R M A S
360
TABLE 111 Wt. Normality..
Sn
Molality.
Observed lowering
Molecular Depression
m
A
A -
Molec. depression molal low. a t inf. dil. for ideal sub.
, =m X A1.858 ~
m
Ratio
I:I
2.435 I ,062 0.204
0 .5 3 1
4,290 2.160
0 .I O 2
0.548
3.525 4.067 5.370
0 .I O 0
0.050
0.291
j ,820
0.05
0.025
0 . I j j
0.02
0.010
0 ,o j o
6.600 7.00
0.01
0.00;
0.036
7.20
0,398 0 .I99
Ratio Z : I 2.22j 5.59 1 '95 5.97 0.495 6.26
0,796 0.398 0 .I59 o.oj96 0.0398 0,0159
I.2Ij
0.079
0,0398 0.0199 o.ooj9
'
0.3002 O.Ij0
0.080
j.54 8.45 10.12
Ratio 2,450
1.225
I . IO0
0 .jjo
2,140 I ,215
0,500
0.250
0.jjo
0.204
0.102
0.41;
0.IO0
0.050
0.25;
0.050
0.025
0,020
0.010
0,010
0.005
0.140 0.060 0,033
.oo
0.j 0
0 .50
0.25
0.20
0.I
1.46; 0.985 0.680 0.405
0.10
0.05
0.220
0.05
0.025
0.02
0.01
0.01
0 ojo j
2.00 I
2.00
I .00
.
'
2.720
4.050 4.400 0.130 5.200 0.055 5.500 0.030 6.000 Ratio I :4
I , 00
1.050
1.050
0.50
I .j90
0 .50
0.2j
0.20
0.IO
0.795 0,540 0.340
0 .IO
0.05
0.21g
2.160 3,400 4.30,O
0.05
0.02j
0.125
5.000
0.02
0.01
0.055
5 ' 500
0.01
0.ooj
0.028
j . 600
I
.oo
3.0 3.2
3.35 4.0 4.5 5.4
1:2
747 2.209 3.080 4.068 5 .IO0 5.600 6,000 6.600 Ratio I :3 1.465 1.970 I
I .89 2.18 2.88 3.13 3.55 3.75 3.87
0.94 1.94 1.65 2.19 2 ' 74 3.01 3.22
3.55 0.j72
1.06 1.46 2.17
2.36 2 73 2.96 3,22 0.565 0.855 I . 16 1.83 2.31
2.69 2.96 3.01
Loomis Kahlenberg and Lincoln 2 . 1
2.8 3.' 3.4 3.5
2.9 314 3.7 3.7
36 1
AQUEOUS SOLUTIOSS O F SODICY SILICATES
the ratio of the observed molecular depression A/m, t o the molal loivering at infinite dilution, 1.8j8, of an ideal substance, (the van’t Hoff factor “z”). The values of “z” calculated from the results of Loomis, and of Kahlenberg and Lincoln for ;\‘atSiOa are given for comparison. Table IT shows the molecular depressions, A l m , at round concentrations collected together for comparison.
Ncrmalifj
Nw.
. t , . . . . . . . . . . . . . . . . . . ~ . . 0
ao
1’0
O‘S
01
FIG.I
The graphs in Fig. I show the molecular depression A Irn plotted against the molality. The horizontal lines indicate the several values of the van’t Hoff factor “i”. TABLE Is’ hIolecular Depression, A/m
xw
m
2: I
1 : 1
I : z
1:
3
1.465
I
:3.9j
2.00
I .oo
4.2j4
3.6jj
1.00
0 .jo
j.29;
4.075
2.265
1.970
1.j90
0 . j O
0.2j
j.667
4 . j;o
2.720
6.410 7.1;; 8.083 9.385
j.3jo
3.105 4.068
4.050
2.160 3.400
5.820
5.100
4.400
4.300
6.600
j.600 6.000 6.600
j.200
5.000
5,500
5 . joo 5.600
0.20
0.IO
0.10
0.0;
0.oj
0.ozj
0.02
0.01
0.01
0.00.5
10.41
j.000 j.200
1.92;
6.000
1.0j0
A i. e. the van’t Hoff factor ‘5” for m X 1.858 all the ratios at round concentrations collected for comparison.
Table V shows the values of
R. W. HARMAN
362
TABLE V Sti
Van’t Hoff factor “i”
m 2 : I
2.00 I
.oo
2.30 2.85 3.05 3.45 3.85 4.35 5.05 5,60
I . 00 0.jo
o..jo
0.25
0.20
0.IO
0.IO
0.05
0.0;
0.02;
0.02
0.01
0.01
0.00;
1 : I I
.98
=
A m X 1.858 ~
I
I : 2
I
.03
2.19
1.22
2.45 2.88 3 ’ I3 3.55 3.75 3.87
1.67 2.19 2 ’ 74 3,01 3.22 3.55
:3
I
:4
0.772
o..j6j
.06 1.46
0.8jj
I
2.17
2.36 2 ’ 73 2.96 3.22
.06 1.83 2.31 2.69 2.96 3 .OI I
Comparison of Vapour Pressure and Freezing Point Results Before discussing the freezing-point results it is interesting t o compare them with those obtained from vapour-pressure measurements. In Table VI are given the values of ‘ ( 2 ’ ’ obtained from v.p. and F.Pt. measurements for ratios I . I and I : 2 .
TABLE 1.1 Weight normality
sw
1Iolecular deprespion molal depr. a t infin. dil. of ideal suhs. Vapour pressures Freezing points
Ratio 2.427 I , 062
0.41 0.I02
I:I
2.08 2.46 3.36 3.i3
Ratio
1.89 2.18 2.60 3.13 I :2
2.00 I .oo 0.jo
1.08 1.49 1.90
0 . 2 0
2.38
0.IO
2.61
For ratio I :I the values from vapour pressure are considerably higher; this is partly accounted for by the difference in temperature ( 2 5 ’ ) as these results have not been corrected for temperature in the comparison. In ratio I :z there is much better agreement. This is probably due t o hydrolysis being greater in I : I than I : 2 , hence the 2;’ difference in temperature will have more effect in I : I than in I : 2 . The agreement between the two niethotls is on the whole quite satisfactory; this is shown graphically in Fig. 2 where the molecular depression is plotted against the concentration. This graph shows A ’m from rapour pressure and F.Pt. measurements and also Loomis’ results from F.Pt.
AQCEOCS SOLUTIOSS O F SODIUhl SILICATES
36 3
Presentation of Results according to the Activity Theory The accuracy of the freezing point results does not really warrant the calculation of activity coefficients therefrom as Lewis has based his calculation upon the very accurate work in dilute solution made possible by the recent development in freezing point technique due to the work of Hausrath, Bedford, Adams, Richards etc. However, useful information mill be gained, but it must be borne in mind that the values for the activity coefficients given below are not claimed to be strictly correct on this account.
t
Calculation of Activity Coefficients at 25°C from Freezing Points
The method of calculation given in Lewis and Randall’s “Thermodynamics” has been followed. A The question of assigning a value to v in the equation1 j = I - - for vXm
SarO.sSIO?where s is I , 2 , 3 , 4 etc. respectively, is a very difficult one. If v be put equal to three for ratios I : I , I : 2 and I :3 quite impossible and absurd A values are obtained. In view of the results already obtained for m X 1.8j8’ it seems most rational, and cannot be very incorrect, t o put v equal to 4 for I : I . I : z , and I :3 ratios. In order to get comparable values on the same basis Y has been put equal to 4 for the other ratios as well.
‘ Lewis and Randall:
“Thermodynamics,” Equation
2,
p. 342 (1923).
364
R. W. HARMAS
I n the following calculations use has been made of the Lewis-Linhart relationship j
=
s,
a pm to determine
L
- j d(1og m) u p to m
= 0.01, by
means
- P . (0.01) a while for values of nz 2.303ff greater than 0.01the graphical method has been followed for the evaluation of of the equation
- j d(1og m)
=
O1
/"- j d(1og m).
J m
I : I follows in Table VII. TABLE T'II Calculation of y for SanO:SiOn,111, from F.Pts. (assuming v = 1 ions) ]=I-A 1 Nw m A log j 2.303
The calculation of y for ratio
2.435 I ,063
1.217
4.290
0,531
2.
0.204
0.I 0 2
0.548
0.2770
0.291 0.16j
0.2IjO
0.5145 0.3108
I60
-
1,jII4
-
0.2234 I319
1.4925
0 .
1.4425
0 . I2 0 3
-
7,3365 0.0942 0.018j 0.1118 i:,0483 0.050 0.025 0.020 0.010 0,070 3- . i 4 3 4 0.02jI 0.0580 0.010 0.005 0.036 0.0313 2.4955 0.0136 From the plot of log j against log m, LY = 0.086,fl = 3.0,whence, by means 0.I O 1
0.050
j d(1og m) = -fl (o.oi)a, valuesof 2.303Ct 0.01have been obtained.
for concentrations o.oo< and j m 0.ooj
1% Y
2.303
Y
0.0218 0.0354 0.921; 0,010 0.0251 0.0263 0.0514 0.8884 0.025 0.0485 0.0602 0.108; 0.7785 0.2037 0.6256 0.109; 0.050 0.0942 0.1203 0.I O 2 0.1836 0.3039 0.4967 0,531 0 . I349 0.4243 0.5582 0.2j66 1.217 0.2234 0.5893 0.812j 0 .I539 TABLE VI11 Activity Coefficient, y, from F. Pt. Based on v = 4>i. e. each molecule gives 4 ions at infinite dilution m 0.005
0.0136
XaOH 0.950
I:I
I : 2
0.922
0.731
0.001
0.920
0.888
0.025
0.867
o.oj0
0.820
0.778 0.626
0.IO0
0.76s
0.497
0,599 0.4j6 0.358 0.259
0.500
0.700
0.280
0.080
I :3
J. .4m.Chem. SOC.,47, 682 (1925).
:4
0.412
0.2j2
0.171
0,342 0.244
0 .I79
0.109
0.052
0.029
0.029 0.680 0.03j 0.192 The values of y for KaOH above are taken from Harried.' These results are plotted in Fig. 3.
I . 000
I
0.604 0,484 0.359
0.015
AQUEOUS SOLUTIONS O F SODIUM SILICATES
36 5
Having calculated y from freezing-points we can now find y from vapour pressure measurements, where the quantity obtained was ky, not y. The comparison is shown in Table IX.
IO
FIG.3
TABLE IX Comparison of Activity Coefficients calculated from V.P.’s and F.Pt’s. m
y
from V.P.’s
Ratio
y
From F.Pt’s.
I :I
219
0 . I 54
0 .I54
0 .j31
0.2j5
0,277
0.200
0.3035 0,3555
0.329 0.626
I.
0.051
Ratio 1:2 0.IO
0.jo 0.2;
0 .I O 0.0;
0.035 0.066 0.116 0.219 0,309
0.035 0.080
0.130 0.539 0.358
Escept in dilute solution (0.05 = m, ratio I : I ) where the percentage error in the vapour pressure measurement is large, the agreement is fair.
Discussion of Results Such a problem, as this, namely of the behaviour and nature of substances in solution, can only be satisfactorily solved when our ideas regarding solutions in general are stabilised. At present the problem of solutions of electrolytes, and more particularly the anomaly of strong electrolytes, is being attacked along two main lines, both having thermodynamic considerations as their basis.
366
R. W. HARMAN
(I) In the first the idea of actual concentration of ions and undissociated molecules is regarded as the fundamental factor in determining the equilibrium between the different species. The conductivity method is regarded as reasonably accurate in determining such concentrations, but since the law of mass action, expressed in such concentration terms is known not to apply, modifications of this expressed by means of empirical coefficients e. g. Storch‘s equation have been applied with reasonable success. In the second mode of treatment, the conductivity method is dis(2) carded, and instead of the older conception of actual concentration of ions and molecules, a newer treatment correlating various thermodynamic relationships involving the effect of concentration or activity has been applied also with considerable success. Considering the first method above, there are three assumptions which may be employed b r the calculation of the degrees of ionisation,(I) The degree of ionisation is correctly given by the conductivityviscosity ratio. (2) van’t Hoff’s law is obeyed by the ions. (3) van’t Hoff’s law is obeyed by the undissociated molecules. Experimental data show that in general only one of these three assumptions can be true in the case of strong electrolytes, the acceptance of any one involves the rejection of the other two. It has been pointed out by Bates’ that the mistake is often made of calculating the degree of ionisation from freezing-point data by using the empirical expression of van’t Hoff, P = iRTC, which implies that assumptions ( I ) and ( 2 ) above are simultaneously true. However, until such time as the problem of solutions in general is elucidated, we can still derive much valuable information by making use of the earlier ionic theory and its underlying assumptions relating t o ideal solutions. This line will be followed now, although the results from the activity standpoint will also be discussed.
Discussion of Results as calculated from the View-Point of the Activity Theory
Secessarily the whole series of results, based as they are on the one set of experimental data, are relatively the same as those observed when the freezing-point measurements are expressed in terms of the ideal ionic theory, but, as is to be expected from the nature of the two theories, the values of y , the activity coefficient, are lower than the value of cy, the degree of ionisation, calculated from conductivity or froni the van’t Hoff factor “i”. I n considering the above values of y in Table I’III, it must be borne in mind that they have been calculated, for all the ratios, (not for S a O H where v = 2 ) on the assumption that v = 4, i. e. that the solute molecule gives rise to 4 ions on complete dissociation a t infinite dilution. J. Am. Chem. SOC., 37,
1421
(1915).
AQUEOUS SOLUTIONS OF SODIUM SILICATES
367
The ratio I : 2 is thus very largely dissociated in dilute solution, but very little in concentrated solution; the almost equal values of y in dilute solution, and the great difference in values of y in concentrated solution, for NazSiOa and S a O H being noticeable from figure 3. In ratio I :4 the percentage dissociation has fallen considerably over the whole range of concentrations.
FIG.4
In Fig. 4, y is plotted against the ratio. As with all the other quantities measured and plotted in this series of investigations of aqueous solutions of sodium silicates, there are changes of direction in the curves a t I : I and I : 2 for concentrated solutions, and a t I : z for dilute solutions. A t all concentrations the decrease in y with increasing amounts of Si02 is practically linear after ratio I : Z . The Results as calculated from the Earlier Ionic Theory
Considering Table V, we see that the greater the proportion of K a 2 0 in the ratio, the greater the value of “i”, i. e. the crystalloidal content of the solutions decreases with increase of silica. This is brought out in the graphs in Fig. 5 where the molecular depression is plotted against the ratio. As was the case when conductivity, hydroxyl ion concentration and sodium ion concentration were plotted against the ratio, changes of direction in the curves
R . W. HARMAN
368
are again noted a t ratios I :I and I : z ; at I : I in dilute solution and at I : z in the more concentrated solutions; while beyond I : z , A/m falls regularly and linearly as the proportion of silica in the ratio increases. Ratio I :I Ratio I :I is the definite crystalline salt, sodium metasilicate, iYa&Os. The value of '5'' indicates a fairly large degree of hydrolysis or ionisation, even in concentrated solution. In the most dilute solution investigated, O . O I K ~ ,
\
Molfculas
D e p r e s s i o n o f F,P%
against
Ratio.
Ratio.
the value 3.87 lies between 3 , expected if total ionic dissociation took place, and 4, the consequence of total hydrolytic dissociation and total ionisation of the NaOH so formed, assuming in the latter case all the silica to be colloidal and to have no disturbing effect on the other constituents of the solution. If the latter view is correct, and assuming the laws of ideal solution to apply, then
3.487 x
IOO
= 97%
hydrolysis takes place, a value in very close agreement
with the figure calculated from conductivity measurements1 and with the 1
Harman: J. Phys. Chem., 29, 1 1 5 5 (1925).
AQUEOUS SOLUTIONS OF SODIUM SILICATES
369
figure assigned by Kohlrausch’ from conductivity measurements and also by Loomis2 from freezing point measurements. However, only 2 7 .8% hydrolysis is found by E. M. F. measurements (Part IV) a value confirmed by Bogue’s E. 31. F. measurements.s Thus we have found 2 j . 8 % hydrolysis by E. M. F. measurements and 97% hydrolysis from freezing point lowering and from conductivity, assuming in the latter case the laws of ideal solution to hold, which at this concentration, 0.005 m, will not introduce a very serious error, and also assuming all the silica in solution t,o be colloidal. These two results are quite incompatible, but the assumptions with regard to the laws of ideal solution can in no way cause such a large discrepancy. Of the two values, the 27.8% found by E. M. F. measurements will be the more correct one. Therefore we can state with certainty that, neither ( I ) z j . 8 % hydrolytic dissociation into 2Na‘ z0H’ colloid H2Si03 alone occurs, as this does not agree with the freezing-point results, nor ( 2 ) is t,he silica or silicic acid formed, wholly, if a t all, colloidal, i. e. SiO3ions must exist in the solution, and both hydrolytic and ionic dissociation must take place. The interaction of sodium metasilicate and water may be represented as follows at very low concentration, where if hydrolysis has taken place in two st,ages the concentration of HSi0’3 will be negligible :-
+
h’a2Si03
+ 2HOH
%
zNa’
%
20”
+
+ +
+
Sios”
zH’
T 1
LT
2NaOH
H2Si03
From E. M. F. measurements there is 27.8% hydrolytic dissociation a t concentration o.oo5m (or ?J, = 0.01). From sodium ion measurements there is 9 j. jyc of the primary reaction
* 2Na‘ + SiO”
h’azSi03
a t this concentration. The H2Si03formed, as indicated above, may be taken as all crystalloiclal, which seems justifiable a t this low concentration, and be capable of dissociating into H and Sios ions, a reasonable possibility, in spite of the general belief to the contrary, and one which receives so much support from experimental evidence based upon conductivity measurements,transport number experiments, diffusion experiments, apart from the favourable evidence adduced herein, that it appears almost a certainty. Calculating the van’t Hoff factor “i” upon this basis and making use of the OH and Na ion concentration, we get I i i ” = 3 . 5 2 , whereas “i” from F. Pts. is equal to 3.87. This is fairly good agreement, considering that it depends on ordinary laboratory freezing point technique, and on two independent sets of E. XI. F . Z. physik. Chem., 12, 773 (1893).
U-ied. Ann., 60, 531 (1897). J. Am. Chem. SOC., 42, 2575 (1920)
370
R. W. HARMAN
measurements, and it not only supports the view that both hydrolytic and ionic dissociation take place but that a fairly correct percentage value has been obtained for both these dissociations. Let us consider almost complete hydrolysis into NaOH and colloidal HZSi03,according to the theory put forward by Kohlrauschl and by Loomis,2 the extent of such hydrolysis, to be determined by the concentration of sodium ions,8 but assuming the OH ions to be adsorbed to a large extent by the colloidal silica so that the actual OH ion concentration agrees with the percentage hydrolysis found by E. M. F. measurements. On this basis, for concentration N, = 0.01, i. e. 0.005 m, “i” = 2 . 5 3 , whereas from F. Pt. measurements “i” is 3.87. This non-agreement, clearly outside the bounds of experimental error, appears to afford definite proof against OH ion adsorption. Ratio Here there are three possibilities:(I) definite salt KaHSiOa (2) definite salt NalSiz05 ( 3 ) aggregates or micelles. (I)
1:2
dejinite salt NaHSi03. KaHSi03
+
HOH
+Is
Na’
6
OH’
+
1 T KaOH
+ HSi03’ + + H‘ 4T
H2Si03
Following the same reasoning as already given for ratio I :I, and taking the valoes found for OH ion and Iia ion concentrations, communicated in two previous papers, as giving the percentage hydrolytic and percentage ionic dissociation respectively, we get a t concentration m = 0 . 0 5 , since percentage hydrolysis equals 0.051 and percentage ionisation equals 0.60, “i” = 3.34, taking into account that the concentrations expressed herein are in terms of NasO.2 SiOz. (2) definite salt XazSi05. IiazSipOj +Is zNa’ SizOs”
+
zHOH
i=s
+
z0H’
+ + + H‘
LT
lt
aNaOH
HZSizO5
For the same concentration, 0.005 m, where percentage hydrolysis equals 0.051 and percentage ionisation equals 0.60, “i” = 2 . 5 . Since ‘5’’from F. Pt. equals 3.50, on this evidence alone one would say that it is extremely probable that the salt XaHSiO3 exists in solution. Z. physik. Chem., 12, 773 (1893). W e d . Ann., 60, 531 (1897). Harman: J. Phys: Chem., 30, 922 (1926).
AQUEOUS SOLUTIONS OF SODIUM SILICATES
37’
aggregates or micelles. Several suggestions could be put forward to explain the values of “i” obtained but as all of these would be largely hypothetical, it seems better todefethis for the moment, except to state that from transport number experiments we know that one proportion of Si02 carries one charge of electricity and SO the ion is not the simple ion Si03,and from freezing point measurements the existence of the salt NaHSi03 seems most probable. Thus for ratio I : 2 the existence of the acid metasilicate IrTaHSiO, agrees very well with all the experimental data so far given. (3)
Ratios I :3 and I :4 When we consider ratios I :3 and I :4 and bear in mind the result of transport-number experiments a t moderate concentrations, where it was found probable that there were three and four proportions of Si02 respectively per divalent charge we admit two possibilities:( I ) definite salts, N a 2 0.3 SiO~aq. Na2O.qSi02aq. ionising to give sodium and silicate ions of composition (3SiO~aq) and (4SiO~aq.) (2) Aggregates or micelles of the composition [m.Si03.n.SiO~aq.]~-‘ where (m+n)/m equals the ratio, or an aggregate containing amongst other constituents a number of Si02 equivalents approximately equal to the ratio per divalent charge. Let us consider these two possibilities. (I) Definite salts. Calculating ‘5’’as before for concentration m = 0.05,since hydrolysis is practically negligible and the percentage ionisations as given by Na ion concentration are 0.70 and 0.55 respectively for ratios I :3 and I :4 we get ratio “i” calculated ‘5’’from F. Pts. I
:3
2.40
3.22
:4 2.10 3.00 Hence the existence of definite salts so ionising seems very unlikely. (2) Aggregate or micelle formation. In very concentrated solution the silicate probably exists as a very complex aggregate, which not only breaks up on dilution but also gives rise to Na‘ and Si03”or other simple silicate ions, these latter coalescing to form ionic micelles. Only on some such theory can the results from conductivity, transport numbers, hydroxyl and sodium ion concentrations, and freezing points be explained. I n solutions of these higher ratios the OH ion concentration is practically negligible, especially in concentrated solutions, and the sodium ion concentration as found by E. M. F. measurements accounts for only a small fraction of the total crystalloidal content as calculated from the lowering of the freezing point. I
372
R. W. HARMAS
For example, at concentration N, = 0.01, the normality due to Na ions is the total normality as found from freezing-points is 0.03, thus leaving 0.019 K to Ee accounted for either by the silica present, or by some form of undissociated silicate, or both. In more concentrated solutions, e. g. 0.1 iYW,1:4 ratio, where the total normality is found to be 0.23, the normality due to the Na ions is only 0.05. I t is not’ proposed to go into this question in this paper, but ic is hoped to give a rational complete theory shortly when all the experimental data obtained have been published. It will be sufficient to indicate here that at present’ it appears that the ratios higher than I : z are not definite salts giving definitely determinable silicate ions in solution. Rather, having regard to the fact that the value for “i” is abnormally low in concentrated solutions and exceptionally high in dilute solutions, and to the results of transport number experiments, ionic micelles of the composition (m.Si03.n.SiOzaq.)mappear to be present, where m n/m equals the ratio; and thefollowing equilibria existj( I ) Sios” [colloid Si02 as.] % [m.Si03.n.SiOzaq.]“-and (2) [Colloid SiOsaq.] % crystalloidal H2Si033 zH‘ Sios.” Evidence for equation ( I ) is also obtained from transport number experiments, while in a later paper it will be shown that equation ( 2 ) is not only true but t,akes place to a much greater extent than commonly supposed even in moderately concentrated solutions. Until further work is done with the specific purpose in view of determining the exact constitution of the silicate in these high ratios i. e. of proving conclusively that it is or is not the SiOs ion which is here formed in dilute solution, and until more exact knowledge is gained concerning H2SiO3itself, we can only state that micelle formation offers the best explanation of the experimental data given herein, I t must be emphasized that the foregoing suggestions of the existence of aggregates and ionic micelle are only tentative. 0.011,while
+
+
+
Summary Measurements of the lowering of vapour-pressure have been made by a dynamic method, for ratios Ka20 : SiOz, I :I and I : z over a concentration range 0.1 - z.5Xja,and the results expressed in terms of the earlier ionic theory and also in terms of the more recent activity theory. (2) Lowering of freezing-points by the Beckmann laboratory method have been found for ratios Z : I , I : I , 1 . 2 , 1:3 and 1:4 over a concentration range o . o I - z . o ? ; ~ ~ and the results expressed in terms of t,he van’t Hoff factor “i” and in terms of the activit,y theory. (3) The results from V. P. and from F. Pts. are in fair agreement. (4) Ratios z : I and I :I, and’to less degree I : z , exhibit a high degree of osmotic activity, more especially in dilute solution. Ratios I :3 and I :4 show an abnormally low osmot’icactivity in concentrated solution but unexpectedly high in dilute solution. (I)
AQUEOUS SOLUTIONS O F SODIUM SILICATES
37 3
( 5 ) From the results it appears that ratio I :I is the salt IiasSi03undergoing both hydrolytic and ionic dissociation giving rise to Na’, OH’ and Si03” ions and H2Si03, most of the latter being crystalloidal. Ka2SiO3is practically completely dissociated in dilute solution but only z 7 .8Yc hydrolytically. Ratio I : 2 is the definite salt ?;aHSi03, behaving like XasSiOs and giving rise to Sa’, OH’ and HSiO; ions and H2Si03. There is 0 . 6 0 7 ~dissociation a t concentration 0.005 m hut only 0.057~ hydrolytic dissociation. The results from ratios I :3 and I :4 are not in accord with the view that these ratios are definite salts but agree well with the existence of complex aggregates in concentrated solution and of ionic micelle of the composition [m. SiO3.n .SiOnaq.Imwhere m n/’m = ratio; the following equilibria also existing
+
+
Sios‘’ [colloid SiOz aq.] 5 [mS;Os.n SiO, as.]”-[colloid SiO~aq.13 crystalloid H2Si03% 2” SiO3”
+
I wish to thank the Commissioners of the 18j1 Exhibition for a Scholarship which has enabled me to carry out this investigation, and to express my gratitude to Professor Donnan, at whose suggestion this work was undertaken, for his constant kindly interest and advice. The Sir William Ramsay Lahoratories of Physical and Inorganic Chemistry, Cnioersity College, London.
