T H E PREPARATION O F A LEAD SULPHIDE HYDROSOL AND I T S COMBINATION WITH PHOSPHATE I O N S BY J. BROOKS
The present paper describes (a) the preparation of a colloidal solution of lead sulphide, and (b) measurements of the rate of combination of the colloid particles with phosphate ions. It was necessary that the sol2 should (I) contain a fairly high concentration of colloid (up to 0.5 per cent lead as lead sulphide), ( 2 ) be free from any but negligible amounts of ionic lead, (3) be ’ stable on boiling in the presence of one per cent sodium chloride.
Preparation of the Sol A stream of H2S was led into a stirred solution (300-400 revs. per min.) of lead acetate containing 0.5 per cent gelatin. After the passage of excess hydrogen sulphide sufficient N. NaHC03 was added to neutralise the acetic acid present. Excess H 2 0 was then removed by passing nitrogen through the boiling sol.8 Coarse particles of PbS were removed by centrifuging and the lead concentration estimated by the method of Fairhall et al.4 The sol remained stable indefinitely; it appeared black in thick layers, and the particles were negatively charged. The untrafiltrate (pH ca. 7.0) contained a negligible amount of ionic lead. The amounts of colloid formed depended on the initial concentration of lead acetate. Above a certain concentration, the fraction converted into colloid decreased sharply, the lead sulphide being mainly in the form of coarse flocks. The results which were reproducible to within 5 per cent are given in Table I and Fig. I. Gelatin from the same sample was used throughout and the conditions were uniform. TABLE I Grms. lead per 100 cc. Initial as Final as colloidal lead acetate lead sulphide
Per cent conversion into colloid Observed
Caleds ted
0.75
0.48 0.66
97 96 88
99 96 86
I .o
0.52
52
1.25
0.26
21
1.50
0.11
7
59 26 6
1.75
0.05
3
I
0.2j
0.24
0.so
This investigation was undertaken on behalf of the Liverpool Medical Research Organization, Director: Professor W. Blair Bell of the University of Liverpool. * On account of its possible use as a therapeutic agent. a It was necessary to neutralise the acetic acid as continued removal of H2S at 100’ in presence of acetic acid resulted in the formation of appreciable amounts of ionic lead. “Medicine Monographs,” 7, 25 (1926). 1
1718
J. BROOKS
The results resemble those obtained in the preparation of lead selenide by a similar method' and can be explained on a similar basis. With lead selenide it was shown that the decreased colloid formation in a concentrated lead acetate solution was due to the increased concentration of acetate ion (and acetic acid into which it is transformed). Since the colloid particles when
once formed could not be flocculated by any concentration of sodium acetate, lead acetate or acetic acid the effect was exerted during formation of the sol. It was suggested that acetate ion and acetic acid reduced the velocityof formation of lead selenide nuclei without affecting the velocity of their growth.2 The small number of nuclei formed in cencentrated solutions of lead acetate would then necessarily grow to large non-colloid particles. The calculated values in Table I were obtained by the method used .in the case of lead selenide. Assuming that in each uncentrifuged sol there are particles of all probable masses it can be shown that the fraction of lead converted into colloid, M,/M is c)l - (ml/g)2. e-(ml/a)2. M,/M = I where u is the most probable particle mass in the sol in question and ml is a mass such that all particles of greater mass are removed on centrifuging. 'Brooks: J. Phys. Chem., 32, 698 (1928). 2 Cf. Hiege: Z. anorg. Chem., 91, 145 (1915).
PREPARATION O F .4 LEAD SULPHIDE HYDROSOL
1719
The values of u required for the calculation of Mcj’Mby means of this equation were obt’ained from a relation which fitted the data of Hiege (Zoc. a t . ) on the inhibition by an electrolyte of nucleii formation in a gold sol. In the case of lead selenide the relation was log, u / u , = 4.93 x 10-4 C I 8 S and in the case of lead sulphide log, u / u o = 3.73 x 10-5 c2IZ where bo is the most probable mass of a particle in the hypothetical case of formation in the absence of the inhibiting substance and c is the total concentration of acetate (acetate ion and acetic acid) present during the formation of the sol. It is of interest that in both cases the effect of acetate enters as a function which is approximately the square of the concentration. The Rate of Combination of Lead Sulphide Particles with Phosphate Ions The sol was added to an aqueous phosphate solution in such amounts that excess of phosphate was always present. The mixture was ultra-filtered1 a t intervals and the uncombined phosphate in the ultra-filtrate estimated by Briggs’ modification2 of the Bell-Doisy colorimetric method. The phosphate solution contained sodium chloride (0.16 SI.) and Na2HP04 and KH2P04 in the ratio Na2HP04/KH2P04 = 3.5. Unless otherwise stated, the total concentration of phosphate was o.oo18 SI. The pH of this solution was 7.2. The disappearance of phosphate from the solution was accompanied by a whitening of the black colloid particles. The mean of several final values of the ratio
grm. atoms phosphorus combined was 0.65. grm. atoms lead
Since this value does
not differ greatly from that for the sparingly soluble tertiary lead phosphate Pba(P04)2i.e. 0.67, it may be assumed that the particles are converted into particles of lead phosphate. The pH increases during the reaction which is therefore probably 3 PbS HPO: H2PO: -+ Pba(P0a)z 3HS’
+
+
+
Any oxidation of HS’ by dissolved oxygen would also increase the pH 2 HS’ 0 2 -+ 2 S 20” Two series of experiments were carried out a t 15’ C. Volumes of the same sol (Pb content = 0.512 per cent) were added to solutions containing different concentrations of total phosphate. The values of the ratio grm. atoms phosphorus combined (denoted by P/Pb) are given in Tables grm. atoms lead I1 and I11 and Fig. 2 . The times are reckoned from the time of mixing to the mid-time of ultra-filtration.
+
+
For experimental details, cf. Brooks: Biochem J., 21, 766 (1927).
* J. Biol. Chem., 59, 2 5 5
(1924).
J. BROOKS
1720
TABLE I1 5 cc. PbS sol = 25.6 mg. Pb. IOO
t
cc. phosphate solution.
= ljoc
Phosphate concentration o.0018M. Time (hours) P/Pb k
0.0014M. P/Pb k
27
0.27
0.0051
0.25
48 98
0.45 0.63 0.67
0.0057
0.39 0.63 0.66
170
0.0054
0.0oog M.
0.0047 0.0047 0.0057
P/Pb
k
0.24 0.40 0.62 0.66
0.0045 0.0049 0.0051
TABLE 111 cc. PbS sol = 51.2 mg. Pb. IOO cc. phosphate solution. t = IS°C IO
Phosphate concentration Time (hours)
0.0018M.
P/Pb
26
0.23
47 97
0.36 0.53 0.63
2 00
k 0.0046 0.0045 0.0041
0.0025 M.
P/Pb
k
0.24 0.36
0.0049 0.0045 0.0044
0.55
0.63
I n the experiments in Table 11, there was no sedimentation of the particles during the period of the reaction, and slight sedimentation after approximately 200 hours. When twice the amount of colloid was present (Table 111) there was slight sedimentation after approximately 80 hours. The p H of the mixtures increased to ca. 9.5 during the reaction. The rate of transformation into lead phosphate is slow in comparison with the rate of diffusion of phosphate ions to the surface of the particle.' It will be seen from Fig. 2 that for a given amount of colloid the rate of transformation is independent of the phosphate concentration within the range investigated. There is therefore no formation of a difficultly permeable layer of lead phosphate round each particle as in such a case the rate of penetrationof thecoating would be proportional to the phosphate concentration. 1 If the rate of dirfusion of phosphate were the governing process, the velocity of renction would be represented by the Sernst-Brunner equations, 2. physik. Chem., 47, 5 2 , 56 (r904,. &/dt = kl I C 7 x i a ) where (c - x) = concentration of uncombined b) phosphate at time t. k, = D.w.'\ 6 D = diffusion constantof thephosphate ion. 6 = thickness of the diffusion layer. Y = volume of mixture w = area of surface .\ mean value of kl was obtained from the results in Table I1 by means of (a) and substituted in ib). D was taken as 8 x Io*/cm.2 'see and w calculated on the aasumption of an average radius for a particle of 5opp. ;is this gave impossibly large volumes (several cms.) for the thickness 6 of the diffusion layer round a colloid particle, it may be concluded that the measured rate is slow compared to the rate of diffusion to the surface.
PREPARATIOS OF A LEAD SULPHIDE HYDROSOL
1721
Assuming that the velocity of reaction is proportional only to the surface of unchanged particle we would write dx/dt = k(a - x)" where a is the final value of P / P b and z is the value a t time t , whence k = I/t[a" - (a - x)'] The calculated values of k are given in Tables I1 and I11 and are reasonably constant. The relation would not hold if there was any aggregation of the
0.6
-
P HO S P H A T E
1
0
1
20
1
TIM€ f HONRS)
1
40
1
1
1
60
1
80
1
1
100
1
1
1
120
FIQ. 2
particles which caused a decrease of reacting surface in addition to the uniform decrease due to combination. The decrease in the values of k in Table I11 is probably due to slight particle aggregation ( v i ) . Two alternative explanations of the zero order (per unit area) of the reaction may be suggested (a) the reaction takes place slowly between the PbS surface and adjacent adsorbed phosphate ions, and the number of adsorbed ions per unit area is independent of the phosphate concentration over a wide range (the latter is not improbable in the case of ionic adsorption), (b) the measured rate is the slow evaporation of a poison from the surface,' e.g. a single layer of H2S molecules which had been adsorbed during the preparation. If the rate of evaporation were very small the surface would be practically completely covered and the rate of reaction with phosphate would Cf. Rideal: Trans Faraday SOC., 19,90 (1923-24).
J. BROOKS
1722
be independent of the phosphate concentration and of zero order. This explanation seems less probable than (a) as it must also be assumed that HIS is transferred to the underlying layer of uncombined PbS as the reaction proceeds. The poison could not be HS' since, given the usual magnitude of the electric charge on a particle, the ions could only be relatively sparsely distributed on the surface.
V 1 5 " C.
0.21
A 37.5"C.
$I
u
0
20
40
80 FIG.3
60
100
120
140I.
Similar experiments were carried out a t 2 j' and 37'. j C. The amount of sedimentation was greater than a t 15' C; a t 37.5 O the particles had settled out almost completely after 70 hours. The results are given in Tables IV and V.
TABLE IV t
= 25'C
IOO
Time (hours)
18 47 67 138 306
474
cc. 0.0018M. phosphate solution. 5.0 cc. PbS sol. I O cc. Pb5 sol. P/Pb P/Pb 0.35
0.22
0.57
0.41 0.49 0.60 0.62 0.64
0.59 0.61 0.62 0.62
PREPARhTION O F A LEAD SULPHIDE HYDROSOL
I723
TABLE 5'
t
c
= 37.g cc. o.0018 31.phosphate 5.0 cc. PbS sol. P/Pb
IOO
Time (hours)
18 47
67 138
306 474
39 50 0.54 o 60 o 62 o 62
0 0
solution. IO
cc. PbS sol. P/Pb 0 30 0.40
0.46 0 57 0 63 0 64
Values of k calculated from these results decreased with time, the decrease being greater a t 2 7 . 5 ' . The results with 5 cc. sol for the three temperatures are plotted in Fig. 3.' It will be seen that while the initial rate of combination increases with temperature the reverse is the case towards the end of the reaction. The decrease in rate corresponds with the observed increased rate of particle aggregation. It appears therefore that aggregation of the particles causes a decrease in the reacting suface. This is supported by experiments a t 25' and 37.5' where the sal was added to a phosphate solution containing 0.5 per cent gelatin. There was then practically no sedimentation of the particles. The quantitative results were irregular (the passage of small amounts of gelatin through the ultra filter interfered with the subsequent estimation of phosphate) but together with the rate of colour change they showed that the reaction was faster throughout a t 37.5O.2 The aggregation of the particles must be attributed to a t least a partial removal of the protective coating of gelatin on dilution with the phosphate solution followed by a slow flocculation by the electrolytes present. The falling off in the rate of reaction when the amount of colloid present was increased indicates that the rate of aggregation, in addition to being a function of the temperature, is also a function of the concentration of colloid particle^.^
summary I. A method for the preparation of a lead sulphide sol is described using gelatin as a protective agent. 2. The percentage transformation of lead acetate into colloidal lead sulphide is dependent on the initial concentration of lead acetate. This is attributed to a decrease in the velocity of nuclei formation in concentrated acetate solutions whilst the velocity of growth of the nuclei remains unaltered.
I t was found that the rate of combination at 25' C was independent of the phosphate concentration. * It was possible to obtain a rou h value for the critical increment of the reaction from these results, namely of the order o f 15,000 calories. * Paine: Proc. Cambridge Phil. SOC.,16,430 (191~-12)found that in the slow flocculation of a CuO sol by electrolytes the rate was duectly proportional to the square of the initial concentration of colloid.
I724
J. BROOKS
3. The rate of combination of lead sulphide particles with phosphate ions has been measured. The rate is slow compared with the rate of diffusion of phosphate ions to the surface and is independent of the phosphate concentration over the range investigated. 4. The results a t 15' C are in agreement with a rate of reaction proportional to the surface of unchanged particle. At higher temperatures aggregation of the particles causes a decrease in reacting surface in addition to the decrease due to combination. d probable explanation of the zero order of the reaction is that combination takes place between the surface and adsorbed phosphate ions, the number of asdorbed ions per unit area being independent of the phosphate concentration over a wide range. Muspratt LabOTatOTy of Physical and Electrc-Chemistry, University of Liverpool. May 83, 1928.
