STUDIES ON THE FORMATION OF LIESEGANG RIXGY B Y PHAKI BHUSAS GANGCLT
In the following pages an attempt has been made to study the Liesegang phenomenon from a colloid-chemical point of view. Peptisation plays an important part during the formation of periodic precipitates in gels. Gelatine, agar-agar, etc, which are generally used for the formation of periodic structures have, as is well known, very pronounced stabilising properties. During an experiment on the growth of Liesegang rings, say in a test-tube, the concentration of the gel is t'he same throughout for that experiment, consequently whatever peptising or other influences it exerts are present more or less throughout the whole mass. What however are changing from layer to layer are the concentrations of the reacting substances I t thus becomes evident that in order t,o get a better understanding of the phenomenon, in addition to the stabilising influence of the gel, the influence of the presence of an excess of one of the reacting substances, on the nature of the newly formed subst,ance,must be definitely knot$-n. I t is well known that the charge on a colloid particle can in many cases be traced t,o the presence of adsorbed ions. In certain cases by the introduction of suitable ions, the sign of the charge can be changed a t will.1 Lottermoserz obtained silver halide sols which were positively or negatively charged according as an excess of silver saks or of t'he halide salts was used. Thus the sign of the charge was directly dependent' on the nature of the common ion which was present in excess and was capable of being adsorbed by the precipitate. Evidently then if silver chromate be capable of adsorbing both silver and chromate ions, one would expect' the presence of an excess of eit,her of these ions to have a distinct influence on the nature of the freshly precipitated silver chromate, it may be produced in any form from that of a coarse precipitate to that of a well dispersed colloidal sol. In the following experiments therefore, the stabilisation of the chromates of silver and lead by gelatine and agar-agar respectively, and, what seems more important, the influence of an excess of one of the reacting substances on the nature of the newly formed substances, have been studied. An at'tenipt has also been made to calculate the concentrations of the reacting substances at different layers of the gel, by means of a formula derived from Fick's diffusion equation in the following way. Let, us consider a column of gel of length I , with a concentrat,ed solution of silver nitrate, say 0.5 1'1,diffusing into the gel from the top region OE, wit'h a certain amount of potassium chromate uniformly distributed throughout the gel from 0 to F. We shall first' consider the distribution of silver nitrate in t,he gel after any time t , neglecting for the time the presence of Cf. Alukherji: Trans. Faraday Soc., 16 (Appendix), 103 (1921). Lottermoser: J. prakt. Chem., ( 2 ) 75, 293 (19071.
482
PHANI BHUSAN GANGULY
potassium chromate in the gel. Since the concentration of silver nitrate is fairly large, if t be not very great, we can reasonably suppose that the concentration of silver nitrate a t 0 remains constant. The diffusion follows Fick's law,
6v
-
6%
- - D@ at
(1)
At any layer B a t a distance x from the top a t any time t , the concentration of silver nitrate is given by:
(2)
FIG.I
where C is the initial concentration of silver nitra,te above 0. / x
writing we have from Equation
(2)
The values of the function 8 (x) for different values of z are known1 whence the value of v for different values of x can be obtained from equation (3). Now as silver nitrate diffuses in, it reacts with the potassium chromate present and destroys the equivalent amount of the latter. Let us suppose that the concentration of the potassium chromate initially had a value A, and that silver nitrate destroys a times its weight of potassium chromate. Kow let us follow the change in the concentration of the potassium chromate after a time interval t. At a distance z in time t , the amount of silver nitrate present in the gel is, from equation (3), equal to C
{
I
-@(*)I
This will react with the potassium chromate and thus destroy the quantity
aC
{
I -8
( & ,) of potassium chromate.
The amount of potassium chromate present at the layer D will thus be
This will be the amount if there were no diffusion of the potassium chromate. Actually however, the potassium chromate is diffusing simultaneously with the silver nitrate. The change in the value of A, owing to the diffusion of the potassium chromate must therefore be taken into consideration. 1
Trans. Roy. Soc., Edinburgh, 39, 257 (1899).
FORMATION OF LIESEGANG RINGS
483
The initial condition is that the concentration of potassium chromate throughout O F is A. If O F be sufficiently long and t be small, we have at any time 1, concentration a t 0 = o (Zero) concentration a t F = A. The diffusion follows the Equation: 6%
6t
X?
Solving this equation with the above mentioned conditions and evaluating the constants as in a Fourier's series, the solution is given by . --Djm2s2t mnx A l2 sin - - x mn 1 1 ~~
+
Kow when the diffusion of potassium chromate is also taken into consideration we shall have to put the above value of 0 , in place of A, in equation (4) The amount of potassium chromate present at any distance 2, after a time t , would thus be
where D1 is the diffusion coefficient of potassium chromate. This equation has been used to calculate a series of values for the concentrations of the reacting substances at different layers of the gel, and an attempt has been made to locate the approximate positions of a few top bands by correlating these values with the experimental data obtained in this investigation.
Experimental When a certain quantity of the stabiliser was used to peptise gradually increasing quantities of the precipitate, it was found that the change from transparent sols to turbid precipitates was not sharp eough to make it possible to determine by means of the eye the limiting concentrations corresponding to the maximum amount that can be peptised by a certain weight of the stabiliser. To get a sharp point the nephelometer devised by Kingslakel was used with a slight modification. The standard used was a gelatine gel containing o.ogco barium sulphate. Instead of comparing the intensity of the scattered beam, the emergent beam after the incident beam had traversed a column of the liquid under examination, was compared with the standard. The observation tube was cut shorter, and a brass cap C , carrying a mirror m inclined a t an angle of 45' to the emergent beam was fixed just above the observation beam. The position of the brass cap was so adjusted that the reflected beam illuminated the central slit usually occupied by the scattered beam. A slit s cut in the side of the brass cap came just in front of the mirror, and thus cut off any light likely t o interfere with the standard. The arrangement is shown diagrammatically in Fig. 2 .
zco
Trans. Optical Soc.,
(2)
26, 53 (1923-24).
484
PHANI BHUSAN GANGULY
The maximum amount of precipitate which can be peptised by a certain weight of the stabiliser was first determined. The precipitates were formed by the interaction of the solutions of the respective nitiates with a potassium chromate solution. Gradually increasing volumes of the solutions of the nitrates, which were exactly equivalent to the chromate solution, were added to corresponding volumes of the chromate, the quantity of the stabiliser being the same in every case. The resulting solutions were then examined on the nephelometer. Experiments were performed with different concentrations of r - - - the gelatine. The results obtained are given in Table I, and Fig. 5 . I n a second - - - -- --series of experiments the quantities of the stabiliser and one of the reacting substances, were kept constant, the other reacting substance being added in gradually increasing quantities. The above experiments were repeated with different I I quantities of the stabiliser but the same I amount of the reacting substances. The FIG.I FIG.2 results are given in Tables I1 and 111. In the beginning the solutions were mixed by rapidly pouring from one tube into another. Various anomalous results were obtained, which were found to be due to irregular mixing, it being altogether impossible to have homogeneous mixing by any such means. With the help of the apparatus shown in Fig. 3, the solutions could be mixed simultaneously and uniformly. By means of the screw clips at c and cl, the flow was so adjusted that the liquids from both the limbs ran out at the same time, there being no lag in the flow. Reproducible results could be easily obtained when this process of mixing was adopted. TABLE I I O ccs of solution containing gradually increasing amounts of AgN03 and 0.004 gm of gelatine, were each mixed with I O ccs of exactly equivalent IC2Cr01solutions also containing 0.004 gm of gelatine.
a@
Amount of Ag C r O P Sephelometric readings formed 15.4 I. 0.0039 15.4 2. 0.0078
0.0097
11.2
0.0117
11.8
5. 6. 7. 8.
0.0136 0.0156
12.4
9.
0.0214
3. 4.
0.0175
0.0195
16.8 18.2 '9.4 Very clear
i\mount of Ag CrOd formed
Sephelometric readings
0.0234 0.0254
Very clear Very clear
12. 13. 14.
0.0273
19.2
IO. 11.
0.0293
17.5
0.0312
13.1
15.
0.0332
9.2
16.
0.0351 0.0370 0.058
17. 18.
7.0 Very turbid. Completely precipitated.
FORMATIOX OF LIESEGANG RINGS
485
From Table I it will be seen that whereas 0.008 gram of gelatine is capable 0.25 gram of silver chromate in one case, the same amount of gelatine fails to peptise a lesser amount of the chromate viz. 0.0097 gram in another case. I t thus becomes clear that peptisation by gelatine is generally dependent on the concentration of the substance peptised, in a remarkably specific way. The scale reading of the nephelometer is a function of the turbidity of the solutions examined, a higher reading being obtained with a more transparent and consequently better peptised solution, a lower reading corresponding to a semitransparent or partially peptised solution. If the scale readings from Table I, be plotted a curve (Fig. 4) is obtained which shows two distinct minima. These points correspond to the concentration at which the resulting mixture is more or less a precipitate, the peptising power being at its minimum. I t thus becomes evident at once that there are two distinct zoneb for the concentrations of the reacting substances at which precipitation occurs, even when the quantity of the stabiliser present is capable of producing a transparent sol with a much larger quantity of the precipitate at a different concentraFIG. 3 tion of the reacting substances. In Fig. 5 are plotted the results obtained with gelatine solutions of increasing concentration, the reactinr substances being mixed in equivalent quantities as before. Similar coagulation zones as in the first case are also obtained with 0 . 2 % ~ 0.4'Jc, and 0.8% gelatine solutions. As the concentration of the gelatine solution used increased, the amount of silver chromate formed at the first coagulation zone also increased. This increase is seen clearly from Fig. 6 where the concentration of the gelatine solutions have been plotted against the amounts of silver chromate present at the coagulation zones. Thus from the above experiments we see that there is no simple proportionality between the amount of the stabiliser and the quantity of the precipitate which it will peptise. For a gelatine solution of given concentration, two equivalent solutions producing silver chromate will have the greatest tendency to form a precipitate only when the amount of silver chromate formed has a value approximating to the quantity at the first coagulation zone or when it has a value in or beyond the second coagulation zone. I n the next series of expeximents t'he influence of common ions on peptisation of the cromates of silver and lead by gelatine has been followed. I n these
of peptising
-
486
PHANI BHUSAN GANGULY
experiments the concentrations of the gelatine solution and that of one of the reacting solutions were kept fixed, the other reacting substances being added in gradually increasing quant,ities.
\
\ ,0039
4
d if p7upLfaL fd. FIG.4
I n Table I1 the influence of an excess of silver ions is shown, the chromate ions being all used up to form silver chromate. With a 0.08% solution of gelatine there is the maximum tendency for precipitation when the quantities of the reacting solutions are nearly chemically equivalent. The precipitation
487
FORMATION O F LIESEGASG RISGS
continues till there is an excess of unused silver nitrate. The same weight of silver chromate viz. 0.0084 gm is formed in all mixtures, therefore if precipitation depended on the quantity of the stabiliser only, excess of silver nitrate
CmLJ&r
0%
$,&e
SOU&
FIG.6
TABLE I1 ccs of solutions containing gradually increasing amounts of silver nitrate and 0.004 gram of gelatine, were each misctl with I O ccs of solutions containing . o o j gm of potassium chromate and 0.004 gm of gelatine. IO
Amount of silver chromate formed
I.
0.0032
gm
8.4
-
=
0.00843 gm.
Excess of Sephe1ometric;Colorimetrio common ion readings readings
Execess of Sephelometric Colorimetric common ion readings readings
7.
0.0912
8.
0.1912
9.
0.2912
IO.
0.5912
11.
1.1912
12.
1,3912
S'ery clear
1.1
cc
1.1
j CC
AgSOa 2.
0.0053
3. 4.
0.0073 0.0113
j.
0.0312
6.
0.0512
18.5 -I-eryclear ,, 1 . 0 cc >, 1 . 1 cc 14.2
>I
,, ,, >2
1.35 CC 1.4
cc
1.5 cc 1.9 cc
having no influence on the process of peptisation, all the subsequent mixtures as they contain the same amount of gelatine, should show the same opacity. On the cont.rary as the quantity of unacted silver nitrate in the mixture increases beyond a certain limit, an increase in the peptisation of the precipitate sets in, showing thereby that a certain excess of silver nitrate has a distinct stabilising influence. The quantity of free silver nitrate can he increased to an extant without any subsequent precipitation occurring. As will he seen from Table 11, X o . 1 2 , the amount of silver nitrate which is left unacted upon is about 300 times the weight of silver chromate formed, hut the resulting solution is still a peptised sol.
488
PHASI BHUSAS GASGULY
The influence of excess of chromate ions on the peptisation of silver chromate is shown in Table 111. Xs in the above case the maximum turbidity occurs when the reacting solutions are nearly equivalent, there being very little escess of either of the reacting ions left unacted upon. Excess of unacted potassium chromate gradually brings about peptisation till for the mixture S o . 8, a very clear completely peptised sol results, which does not get precipitated el-en when the potassium chromate is present in large quantities. Thus like the silver ions chromate ions also act as a stahiliser.
TABLEI11 ccs of solutions containing gradually increasing aiiiounts of Ii?C'r04 and 0.004 grain of gelatine, vere each mixed with I O ccs of solutions containing in each case o . o o 8 i j gram of silver nitrate and 0.004 gram of gelstine. IO
Aniount of silver chromate formed Excess ?E common ion
= 0.00843
Sephelomptric readings
I.
0.002
gni of &CrOr
12.0
gin.
Excess of Srphrlomrtric common ion readings
6.
0.015
2.
0.003
12.5
I '
0.02:
3. 4.
0.004
'3.3
0.09j
0.0oj
14.5
8. 9.
3'
0.010
18.4
IO.
('leu
0.19j 49.;
0
A? ill be seen from Table 111, in presence of an excess of silver ion5 coagulation of the precipitate occurs only over a certain range of concentration of the free silver nitrate. This range of concentration over xvhich the maximum turbidity occurs. however. .shifts in a very reniarka1)le way with the concentration of the gelatine used. Esperiments have heen j~erformetlwith different concentrations of gelatine and the results are given in Table II-. A n examination of t.he table s h o w that as the concentration of die gelatine solution increases. the amount of silver nitrate present at the points corresponding to the zone of inasiniurn turbidity, also increaw. Thus with :i 0.0 jc; gelatine solution thr masiniuin turliidity occurs when there is practically no excess of silver nitrate. with a 0.087; gelatine solut,ion, the rriasirriuni turbidity occurs in the presence of 0.0032 j gni of unactecl silver nitrate. and so on till finally for the 1.65%gelatine solution the maximum turbidity occur,3 in the presence of a relatively large amount of silver nitrate viz. 0.01gram. I t would thus mean that the stabilisation of the precipitate by silver nitrate is greatly dependent on the concentration of the gelatine solution used. For a certain weight of silver chromate as the concentration of the gelatine increases. silver nitrate u p to a certain concentration seems to act as a coagulating agent, but beyond that concentration it serves to stahilise the sol, which then becomes very stable and does not get precipitated on further increase of concentration of silver nitrate.
489
FORMATIOX OF LIESEGANG RINGS TABLE
Iv
ccs solutions cont,aining gradually increasing amounts of AgS03 and 4 ccs of a gelatine solution of given concentration were each mixed with IO ccs of solutions containing 0.00 j gram of K2CrOl and the same amount of gelatine. IO
*lmount of silver chromate formed = 0.00843 gm. Excess of common ion
Sephelometric Readin s (Concentration of gelatine soyitions.)
2.
0.00224 ”
Very t,urbid 6.8
3.
0.
0032j
7.0
4.
0 .0042j
10.0
11.;
11.2
5. 6. 7. 8. 9.
o.ooj2j 0.00625
‘3 0 16.j
o.ooj2j
17.9
0.0082j
IO.
O.OIO2j
Clear Clear Clear Clear Clear
14.2 ‘7 9 18 5 Clear Clear Clear Clear Clear
10.8 14.I I8 2 18 6 Uear Clear Clear Clear
I.
0,00024
gm
AgSO3
0.0092 j
”
11.6
Clear
11.4
10.6
16.8 1j.7
Clear
,,
Clear j s
,,
19
16 8 I4
0
I2 0 12
4
18.2 Clear Clear Clear
18.6 I j . 2
16.8 Very clear I t may incidentally be remarked here that the peptisetl sols obtained when the excess of silver ions present was beyond a certain limit, showed a gradual increase in the intensity of coloration with increase of the amount of free silver nitrate in the mixture. To follow this change a colorimetric. estimation was done. All the various solutions were diluted with known volumes of water so as to bring the depth of coloration to that of one from among the series of mistures chosen arbitrarily. The results are shown in Table 11. It would be seen that, generally speaking, as the quantity of the silver nitrate increased the intensity of coloration of the solution also increased. It seems probable that as the amount of unacted silver nitrate increases, a change in the size of the peptisetl particle sets in, which brings about a corresponding change in the depth of coloration of the final mixtures. The peptisation of lead chromate by agar-agar has also been followed. I t will he seen from Table T, that wherever there is an escess of lead ions or an excess of neither ion, the maximum turbidity appears. \Then however there is an excess of chromate ions in solution, a more or less peptised sol is obtained. As the quantity of the chromate ions c o n h u a l l y increases the sol at first gets more and more stahle, but later on it gradually gets turbid, and finally gets precipitated when the quantity of chromate ions in excess becomes very large. Evidently chromate ions to a certain extent can peptise lead chromate, but lead ions do not seem to have any such peptising influence. It can be easily shown that lead chromate adsorbs only chromate ions and not lead ions. It is well known that if a substance be precipitated in presence of such ions as it can adsorb, the precipitate can generally be subsequently peptised by washing. This has been done in a number of cases. Thus the 11.
0.011 2 5
12.
0.0212j
*
490
PHANI BHUSAN GANGULY
TABLE V ccs of solutions containing different amounts of K2Cr04 and 0.004 gm of agar-agar, were each mixed with I O ccs of solutions containing different amounts of Pb(XO3)z and 0.004 gm of agar-agar. IO
Amount of lead chromate formed = 0.00429 gm. Excpss of. common ion present
Sephelometric readings
I.
0 . 0 0 5 7 gm of
Completely precipitated
2.
Pb(NO3)z 0.0037 ”
3.
0.0017
”
4.
0.002
”
j.
6.
e
0.003 gm of K2Cr04 0.00018 ”
, 1)
,)
Excess of, common ion present
Sephelometric readings
7.
0.00028 gm of
8. 9. 11.
0.00038 ” 0.00048 ’’ 0.00148 ” 0.00198 ’’
12.3 18 ,,o 19. I 18. j
12.
0.00248
17.2
IO.
”
7 . 4 cms
silver chromate precipitated in presence of an excess of either silver ions or chromate ions, could under both the circumstances be easily peptised by subsequent washing. Evidently then silver chromate is capable of adsorbing both silver ions and chromat,e ions. \Then lead chromat,e was precipitated in presence of an excess of lead ions, the precipitate could not be subsequently peptisedat all by washing. This clearly shows thatleadchromatecanadsorbonly chromate ions but not the lead ions. Thus it explains the ability shown by chromate ions alone, of peptising lead chromate. The sign of the charge of the peptised silver chromate was determined in a number of cases, and in every case it was found that it was guided by the nature of the free common ion present, being positive when an excess of silver nitrate was used to peptise the sol, and being negative in presence of a n excess of chromate ions. This clearly shows that peptisation by one of t,he reacting substances is brought about by an adsorption of one of the common ions, the resulting sol having the same charge as the adsorbed ion. As a result therefore of the foregoing experiments one is thus led to the conclusion that a solution of silver nitrate reacting with a potassium chromate solution, will form a turbid precipitate of silver chromate only when one of the following two conditions is fulfilled:( I ) Unless very concentrated, if the two reacting solutions he equivalent, they will be precipitated only when the quantity of silver chromate formed is a certain definite amount (which will be dependent on the concentration of the gelatine solution used.) When the quantity of silver chromate formed is either p e a t e r or smaller than this amount, a peptised solution will result. When one of the reacting substances is used in escess, for a given (2) weight of silver chromate and a given gelatine concentration, precipitation will occur only when a certain concentration of one of the reacting substances is left in excess. If the amount of the substance left in excess be greater or less than this quantity, a peptised sol instead of a precipitate will result.
FORMATIOX O F LIESEGANG RINGS
49 I
The same sort of condition will presuinably hold for the case of lead chromate, but there will be the important difference that whereas in the case of silver chromate both the ions will ha\ye a peptising influence in the case of the lead chromate, lead ions will not function at all in its peptisation. These results thus throw a great deal of light on the Liesegang phenomenon. To take the case of silver chromate rings in gelatine, as the silver nitrate diffuses into the gel! it meets the potassium chromate in all different relative concentrations. But, as we have seen above precipitations will occur only in t,hose layers where the conditions given above are fulfilled. One would thus expect the silver chromate to be formed as a precipitate in certain layers and as a peptised sol in other layers. The same will probably happen in the case of lead chromate. But in the case of lead chromat,e as one of the factors producing peptisation is absent viz. the peptising influence of the lead ions, the frequency of occurence of the precipitate layers will be greater, which seems to be quite in accordance with the actual experimental structures obtained with lead chromate in gelatine gels. It, appears now that it will be interesting to calculate the distribut,ion of concentrations of silver nitrate and potassium chromate in different layers of the gel. By using Equation (6) a series of values have been calculated and are given in the following table. The value of D,, t,he diffusion coefficient of K2Cr04, could not, be found in any of the usual tables. It has been calculated by using Kernst’s equation viz,
D=RT-
2 uv u f v
which when expressed in C. G. S.units gives
D
=
uv
o.o448j-----[1 +0.0034 (t - 18)]. U S V
(cf. Sernst : “Theoretical Chemistry,” pp. 435.) Taking t = I Z ’ , ~ = 6 4 . j , and v = j 2 > ‘ we get the value of D1 = 1.49 for a dilute viz a AI 300 (about 0.006jot) solution of potassium chromate. The value of D, the diffusion coefficient of silver nitrate, has been obtained by plotting the values of Thovert* for different concentrations of silver nitrate. The value for a 0.5 Jl (S.49Vc) solution of silver nitrate is thus found from the curve t o be 0.933. These values of D and D, have been used in the following calculations.
x i e ’’
Dlm2rr2t
The series
-
sin
m 7rx - was found difficult to sum, so in the 1
following calculations sufficient number of terms have been taken in order to get values correct to the second place of decimals. Taking t = I hour and 1 = I O cnis, a series of values have been calculated and are given in the following table. (Table TI.) 1
Landolt, p I 124. Compt. rend., 134, j95 (1902).
PHANI BHUSAN GANGULY
492
TABLE TI Distribution of concentration in the gel after 1/24 day crns.
1
(I
hour) taking
= IO
so.
Concentration of Ii2Cr04
Concentration Of .igXOs
Excess of AgS03
S/150 solution used.)
(0.511 used)
present
X
(cm)
I
.I
,0014
N
si2 ,356 r\;
2
. 2
.002j2
T\T
,2345
3 4
.*5
,00335
N
,182
.4
.0049j
5
'5
6
.6
7 8
'13
9 IO
N .ooj63 N ,00604 S ,00652S , 0 0 6 j9 r\' ,0066 ;h; ,0066 ?i
- I
.8j I
.o
1.2.;
Excess of
K2Cr04 present
=
0735
s K N
S ?: ,003 j X ,035
,015
,001
,3566 r\' . z 3 I 78 N ,1786 N ,0685 S ,0294 ,009
-
s
0. 0.
N N 003 ?u' 0056 S 0066 K 0066 ?u'
An Explanation of Liesegang Ring Formation In the foregoing experiments it was found that two equivalent reacting solutions will give a precipitate only when forming a definite amount of silver chromate, the amount^ depending on the concentration of the gelatine solution used. The values obtained experimentally for different gelatine concentrations are given in Table TII:
TABLE VI1 Concentration of gelatine solution. I.
0.04%
2.
0.
3.
0.2%
4.
0.4%
lyO
Amount of silver chromate formed a t the first precipitation point. 2 0 ccs, i. e. I '367 N.hg,CrOi gm in 2 0 ccs, i. e. I '330N.Ag,CrO? 0 . 0 1 3 3 gm in 2 0 ccs, i. e. I '248 N. ' I 0 . 0 1 4 9 gm in 2 0 ccs, i. e. 1 , ' 2 2 2 N. "
0 . 0 0 9 gm in 0.01
The above amounts of silver chromate formed a t the first coagulation points have been plotted against the gelatine concentrations in Fig. 6. From this curve the amount of silver chromate at the precipitation point' for a 0 . 8 7 ~gelatine solution is found t o be about 0.017gram in 2 0 ccs i. e. o.oojz S silver chromate. Therefore in a 0 . 8 7 ~gelatine gel, one would expect the silver chromate to be a precipitate when the two reacting solutions are each about o.ooj2 S . This condition is very nearly satisfied between 0.6 and 0 .j j cms fiom the top of the gel as can be seen from Table VI. In Fig. j , the concentrations of silver nitrate and potassium chromate have been plotted against distances of various layers of the gel, and it is found from the curve that a t a distance of about 0.69 crns from the top the two solutions are equivalent, each being 0.006 S . Thus in this layer 0.006 N silver chromate would be formed. One
FORMATIOS O F LIESEGASG RISGS
493
would therefore expect this layer to be a precipitate, because it has been shown by actual experiment that 0.0052 N silver chromate when formed in 0.87c gelatine is a precipitate. From Fig. 7 we also find that 0.0025 S . silver chromate would be formed at a distance of about 0 . 1 7 j cm from the top of the gel. From Table IT-, however, we find that 0.0084 gram (is e. 0 . 0 0 2 5 S . ) of silver chromate when formed in 0.87~ gelatine comes down as a precipitate only in presence of 0.01 gram of silver nitrate, but is perfectly peptised in presence of larger quantities
xur.&-d
FIG.7
of silver nitrat,e. From Table VI, we again find that there is a very large amount of silver nitrate present in that layer, in fact much larger than 0.01 gram per 2 0 ccs. Evidently then at that layer there will be a perfectly peptised sol. If we consider the layer of the gel say at, 0.0j cin from the top, the amount of silver nitrate present in excess in that layer is enormously large, about ;oo times the amount of potassium chromate. So one would expect precipitation in that layer. From the above considerations, therefore, we clearly see that there mill be layers of precipitate at dist,ances of o . o j and 0 . 7 cm froin the top of the gel. There mill also be a layer a t a distance of 0.175 cm from the top of the gel in the neighbourhood of which, all the silver chromate mill be in a stabilised or colloidal form. Other layers will be expected intermediately, near o..i cm from the top, depending on the particular concentration of silver nitrate that is capable of producing a precipitate with a certain concent,ration of silver chromate. In the above calculations a static state of affairs has been assumed for a period of one hour. This assumption gets more and more justifiab!. as the
494
PHANI BHESAN GASGULY
period decreases. There seems however every reason to suppose that there is no intrinsic change in the nature of the reaction, as the period, over which the diffusion process takes place, gets longer. In an actual experiment, therefore, as the silver nitrate diffuses in, it meets a layer of potassium chromate and being itself in a very large concentration, f o r m a layer of precipitate. As it travels down in the gel, its concentration gets less and probably attains such a value that the amount of silver nitrate present in excess. is the amount just wanted for the peptisation of the amount of silver chromate formed in that layer. This layer is thus a peptised layer. Later on as the silver nitrate travels further in the gel, i t , in all probability, meets the potassium chromate in equivalent concentration (or very nearly equivalent), and if the concentration has a certain value, the silver chromate formed in that layer conies down as a precipitate. It thus gives rise t o a layer of precipitate. This process repeats itself as the silver nitrate diffuses onwards into the gel. and a series of alternately precipitated and peptised layers are thus oiitainetl.
Summary The stabilisation of silver chromate by gelatine and of lead chroniate by agar-agar, have been studied. The above chroniates were otitainetl by mixing solutions of the respective nit,rates with a potassium chromate solution. The concentrations of the various reacting solutions. and of the stahilisers, were varied. one a t a tiine, to studv their respective influences on the stabilisation of the above nientioned ,substances. 2. By measuring their capacit>y.it has been possible to get a coriiparative measure of the estent t o wliich the various resulting inistures have Iiecn stabilised. For this purpose, the nephelometer devised by Kingslake, has been useti with n slight iiiotiification. 3 . To get wprotiucilile results. it \vas foiintl necessary to mix the a1iol-r. reacting solutions uniformly and siiiinltaneously. An arrangeinent has licen set up which meets the above purpose. 4. When graduallx increasing niriounts of silver chromate were foriiied. by the addition of a series of solutions of silver nitrate of gradually increasing concentrations, t o a corresponding series of solutions of potassium chromate, the concentrations of each pair of t,he reacting solutions being exactly equivnlent, it was found that the turbidities of the resulting mixtures varied in it periodic manner, although the airiount of the stabiliser mas constant throughout. There were two distinct zones at which the resulting mixtures showed the maximum turbidities. j . The influence of the concentration of the stabilising solution, on these coagulation zones, has been studied. It, was found that with increasing concentrations of the stabiliser, these zones becoiiie less and less prominent. 6 . The influence of an excess of either -1g or C r O 4ions on the st'abilisation of silver chromat,e by gelatine has been studied quantitatively. It has been found that both the above ions have a distinct stabilising influence on silver chromate. I.
FORMATION O F LIESEGANG RINGS
49 5
7. I n the case of stabilisation of silver chromate by an excess of free Ag ions, a critical concentration was found; the .4g ions acted as a stabiliser, only when present in concentrations greater than this critical concentration. Free Ag ions, when present in concentrations below this critical value, had a distinct, though slight, coagulating influence. 8. The stabilisation of lead chromate by agar-agar has been studied. I t has been found that the presence of an excess of free chromate ions greatly helps the peptisettion of lead chromate by agar-agar, but lead ions do not, seem to have any such effect. 9. It has been shown that lead chromate can adsorb chromate ions, but not lead ions. A colloidal solution of lead chromate has been prepared through the stabilising influence of chromate ions. I O . . As a result of the foregoing experiments, it has been found that a solution of silver nitrate reacting with a potassium chromate solution, mill form a turbid (precipitated) mixture, only when one of the following two conditions, is fulfilled: ( I ) Unless very concentrated, if the two reacting solutions be equivalent, they will be precipitated only when the quantity of the silver chromate formed is a certain definite amount (which will be dependent on the concentration of the gelatine solution used). When the quantity of silver chromate is either greater or smaller than this amount a peptised solution will result. ( 2 ) When one of the reacting solutions is used in excess, for a given weight of silver chromate, and a given gelatine concentration, precipitation will occur, only when a certain weight of one of the reacting substances is left in excess. If the amount of the substance left in excess, be greater or less than this quantity, a peptised sol instead of a precipitate will result. 11. The distribution of concentrations of a pair of silver nitrate and potassium chromate solutions of given concentrations, in a gelatine gel, has been calculated by using Fick's diffusion equation. 12. By correlating the values from the above calculations for the concentrations a t different st,rata of the gelatine gel with the experimental observations, it has been shown that certain layers of the gel will contain Ag2Cr04 in a peptised form, whilst other layers will consist of precipitated silver chromate. In conclusion the author wishes to express his thanks to Prof. Donnan, for his many valuable suggestions and for his kind interest in this work. The WilZiam Ramsay Laboratories of Physical and Inorganic Chemistry, Cniversify College, London. October 20, 1926.
