1319
d G I T G O F DRY SILVER BROMIDE
tion of terl-butyl acetate is small, as would be expected from the known small inductive effect of the methyl group. The frequency factor is lowered slightly and the energy of activation decreases by only about 1300 cal., from 40,500 cal. t o 39,160 cal. SUMMA R T
1. The thermal decomposition of terf-butyl propionate follows the reaction:
C,H&OOC(CH3)3
(CH3)2C=CH?
-+
+
C2HbCOOH
2. The kinetics of the decomposition have been studied in the temperature range from 239.9' t o 296°C. and a t pressures from 17 to 125 mm. of mercury. 3. The reaction is first order. The relationship between velocity constant ( k ) and absolute temperature ( T ) is given by the equation: log k
=
12.794 -
39,160 2.303R T
~
4. Like the thermal decomposition of tert-butyl acetate, the decomposition of tert-butyl propionate appears t o be a unimolecular process. REFERENCES BRUINSAND CZARNECKI: Ind. Eng. Chem. 33, 201 (1941). ESSEXA N D CLARK:J. Am. Chem. SOC.64, 1290 (1932). FUQASSI A N D WARRICK: Ind. Eng. Chem., Anal. Ed. 16, 713 (1943). NORRISA N D RIGBY:J. Am. Chem. SOC.54, 2088 (1932). PALOMAA: Ber. 68B,303 (1935). RUDYA N D FUOASSI: J. Phys. Colloid Chem. 62,387 (1948). SCHULTZ A N D KISTIAKOWSKY: J. Am. Chem. SOC. 66, 395 (1934). TRAUTZ A N D MOESCHEL: Z. anorg. Chem. 166, 13 (1926).
STUDIES Or\; AGIn'G OF PRECIPITATES AKD COPRECIPITL4TION. XLII
AGINGOF SILVERBROMIDEIS
THE
DRYSTATE'
I. SHAPIROZAND I . 11. KOLTHOFF School of Chemistry, Unieersity of Xinnesota, M i n n e a p o l i s , Aiinnesota Receiked K a r c h 10, 1948
From previous work carried out in this laboratory it appeared that freshly precipitated silver bromide has a large surface development and is subject t o thermal aging a t room temperature in the air-dried state (2). The degree of 1 This paper is based on a thesis submitted by Isadore Shapiro t o the Graduate Faculty i f the University of Llinnesuta in partial fulfillment of the requirements for the degree of Doctor of Philosophy, August, 1944. * Present address: U. S. Naval Ordnance Test Station, Pasadena, California.
1320
I. SHAPIRO AND I. M. KOLTHOFF
aging had been followed by measuring the decrease of the specific surface, as indicated by the amount of woo1 violet adsorbed on the surface saturated with the dye, and by determining the speed of penetration of radioactive bromide ions into the inactive precipitate when the latter was shaken with a solution of the former. I n the present work the degree of aging as followed in an unique manner by determining the change in the electrical conductivity of the dry powder as a function of the “heat-treatment” of the porn-der. It has already been shown that the electrical conductivity of silver bromide pellets at low (viz. room) temperatures is essentially a “surface conductivity” and can be expressed (5) by
x
=
B&-rJ/hT
(1)
where x is the specific electrical conductivity, li is 311 energy term showing the magnitude of the potential barrier which an ion must surmount in order to migrate t o another position, T is the absolute temperature, X is the magnitude of the active surface, 1’2 is the Boltzmann factor, and R is a constant. Thus, by determining a t a constant (room) temperature the electrical conductivity of silver bromide samples which had been subjected to various heat-treatments, it is possible to relate the active surface directly to the electrical conductivity of the pellets. Since the aging of freshly precipitated silver bromide is very pronounced even at room temperature, i t is expected that compression of the silver bromide powder under high pressures will accelerate the rate of aging. Thus the active surface of the loose powder will be greater than the active surface obtained from the electrical conductivity data of the compressed pellet. Since it is practically impossible to measure directly the electrical conductivity of a loose powder, :i method has been devised t o extrapolate this value from conductivit?.-pr~ssur.c. measurements. The method for calculating the specific conductivity of compressed pellets is to measure the current flowing through a pellet of a certain size under the influence of a definite potential difference, and t o applJr the formnla
‘xl
‘ = E
A
where x is the specific conductivity in Q-lcm. --I , I is the current in amperes, E is the applied voltage, 7 is the length of the pellet (Le., the distance between the electrode.) in (’entimeter,, and i-; the cro+--wtional area of the pellet in square centimeters. I n the caye of the compies5etl pellets the d u e s for I and L4 eSsen tially do not c*linngenuwh u-ith pressure and can be taken as equal to the experimentally meawred dimensions of the pellets Tvithout Perious error, because the apparent densities of the pellets are approximately the same as the density of a fused mas4 (6). Ilon.ever, the application of equation 2 for loosely formed pellets is complicated by the fact that both 1 and A are varying with the applied pressure. A s a first approximntion the ralue of I n.ill be taken as the experimentally m e a s n r ~ ~length, l designated by I,, of the pellet and the value of A
AGING OF DRY SILVER BROMIDE
1321
will be calculated always by the following relation:
9,
w-
= 1, Pa
where W is the weight in grams of the silver bromide sample, and ps is the density of a fused mass of silver bromide ( p s = 6.478 g./cc. (1)). By plotting log x (using values of I, and A , in equation 2) against pressure for a pox-der mass of well-aged or fu5ed silver bromide, one obtains a characteristic curve, represented by curve in figure l a . The experimental points a t the higher pressures fall nearly on a straight line, which can be represented by line B in figure l a . It is quite probable that the function of log x with pressure in this case is analogous to that for compressed pellets (6). The increase in conductivity (curve A, figure la) a t the lower pressures can be attributed to the better contact between individual particles with increasing pressure, while the decrease in conductivity a t the higher pressures is caused by a decrease in active surface. Actually both phenomena 2
r 0
>
k
E".v)
2
a t W
+
0
--o-
--
-d-
---
/-
b.
0
LI
4 .
0
4
* In this article the subscript e refers to an effective or corrected value, and the subscript z t o a n apparent or measured value.
1322
I. SHAPIRO .4KD I . bf. KOLTHOFF
At the same pressure p l the deviation of the logarithm of the apparent density from that of the true density is given by 2 (figure lb), where
If the deviation of curve A from line B in figure l a is attributed to the use of the apparent value of (Z/A) instead of its effective value (which corrects for the porosity of the pellet), then one would expect a plot of log 4) against log
(1DL (from equation (”ALi)e
(from equation 5) to be linear, with the line passing through Pa
the origin. Such relationships have been found in which the slope of the lines is constant for powders of silver bromide of widely different values of electrical conductivity and “age.” Hence by this method of extrapolation it has been possible t o differentiate between “pressure aging” and “thermal aging.” EXPERIMENTAL
The preparation of silver bromide powders aged in different ways and the subsequent measurement of their electrical conductivities and compressibilities are described in previous publications (5, 6) and in greater detail in the thesis of the junior author upon which this paper is based. The silver bromide was prepared by a precipitation method (carried out in photographically inactive red light) and 71-ashed successively with copious volumes of mater, acetone, and benzene and then air dried with dry air. Portions of the silver bromide powder v-ere “thermally aged” by heating to various temperatures for different periods of time. -4brief description of the thermal treatment of the various samples of silver bromide used in these experiments is given in table 3 . The compressibility and electrical conductivity measurements on the powders were carried out in a specially constructed die ( 5 ) . Weighed portions of the fresh and “aged” silver bromide p o ~ d e r s\yere compressed between two silverplated plungers which also served as electrodes, and the electrical resistance of the povder mass between the electrode. nas measured as a function of the applied pressure. The thickness of each pellet as a function of pressure was measured with a cathetometer to =t0.02 mm. xnd then checked with a micrometer after the pellet had been removed from the die. All powders were compressed t o a maximum pressure of 3000 a h . Tlw electrical conductivity x i s measured at a constant temperature of 2.iT ’ I H \\SFLRl.\(
1, 111. i>l I t L V l A T \
Since preliminary experiments had shov n that the electrical conductivity of fresh silver bromide may be as much as lo4 times as great as the values reported by Lehfeldt (4) on fused silver bromide, the possibility of electronic conductance was considered. Several grams of freshly prepared dry d r e r bromide powder were slightly compressed between two silver electrodes and connected in qeries
.IGI?;G
1323
O F DRT SILVER BROMIDE
with a silver coulometer to several dry cells. The silver bromide between the electrodes mas replaced each hour with freshly prepared powder, because the silver bromide ages even at room temperature (2). The replacement of the powder in this manner had the further purpose of preventing the formation of dendritic silver bridges in the silver bromide between the two silver electrodes. At the conclusion of such an experiment it was found that the loss in weight of the silver anode equalled the increase in weight of the silver in the coulometer; hence it is concluded that fresh silver bromide is essentially an ionic conductor similarly to fused silver bromide (7). Next, experiments were carried out to measure the transference number of silver and bromide ions by utilizing the method of weighed pellets. I n this procedure a series of three pellets and the two electrodes are weighed individually before and after a quantity of electricity (as measured by a coulometer) is passed through the system. The migration of ions across the middle pellet will be reflected in changes in weight of the electrodes and the two outer pellets, dependTABLE 1 W e i g h t s of pellets a n d electrodes in transference n u m b e r experiment WEIGHT BEFORE
WEIGHT AFTER
DIFFERENCE I N WEIGHT
grams
mg
-~
Silver Silver Silver Silver Silver Silver
+
silver iodide cathode.. . . . . . . . . . . . . . . . . . . . bromide pellet S o . 1.. . . . . . . . . . . . . . . . . . . . . . bromide pellet KO.2 . . . . . . . . . . . . . . . . . . . . . . . bromide pellet KO.3 . . . . . . . . . . . . . . . . . . . . . . . anode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . coulometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-
grams
1.42592 2.30195 2.05457 1,94550 0.32303 8.55448
,
1.43218 2 30195 2 05156 1.91517 0.31643 8 56105
__
+6.56 *O
-0.01 -0.03 -6.60 +6.57 --
ing upon the transference numbers of the cations and anions. In order t o measure the true changes in weight of the outer pellets, the n-eight of the middle pellet must remain unchanged throughout the experiment. First attempts a t this type of experiment proved unsuccessful, because it was found impossible to separate the pellets once they had been pressed together. Later this difficulty was overcome by using high pressures (3030 atm.) to form the pellets but low preswres (ca. 10 atm.) to hold them together during the co~irseof the experiment. In order to prevent the formation of dendritic silver bridges, a pellet of silver iodide in conjunction with a silver plate JTas used as the cathode. All weighings n-ere made on a Kuhlmann microbalance. The weights of the pellets and electrodes before and after a transference experiment arc given in table I . The data indicate that only silver ions are migrating through the silver bromide pellets. That the bromide ions essentially do not migrate through the silver bromide pellet can be demonstrated further by radioactivity experiments. Radioactive silver bromide was prepared by adding a silver nitrate solution to a sodium twomide solution which had been shaken previously with ethyl bromide contnining radioactive bromine. (The ethyl bromide had been expovd t o R radon-beryllium
1324
I. SHAPIRO A S D I. 17. ROLTHOFF
bulb for 16 hr.) A pellet of radioactive silver bromide \\as placed in contact with a n inactive pellet, and a direct current T T - ~passed S through the pellets until the silver bridges which formed caused a short circuit (approximate time of contact of pellets was 8 hr.). The radioactis-e pellet had been placed at t h r cathode end, so that the electric field would favor a movement of radioactive bromide ions into the inactive pellet. The radioactivity was measured n-ith a. Geiger-Muller counter. Experiments were performed in which the pellets were prepared under different pressures; in no case was there any evidence of the radioT$BLE 2 Conductivity correction j o r effective length of silver bromide pellet
I PRESSURE,
9
NO. 1 FUSED, COOLED SLOWLY,
alm.
_
_
,1
10 POWDER AGED ONE MOXTR IY COSCENIR4TED AMUONILX HYDROXIDE
gramrjcc.
4.76 5 04 1 5 47 5.75 5 92 6 04 1 6.16 1 6 24 6 26 6 32 I 6 35 6 36 6 37 I 6 37 6.38 6 39 6.40 6 41 _
-~ - .
Xa x 107 ' log2 XO ____ -- _-
Pa
205 304 465 616 770 925 1085 1245 1400 1555 1715 1870 2045 2216 2380 2550 2710 2873
NO.
POI\DERED
- - --___
--
-
loge
I
_
2 00 2 31 2 56 2 76 2 88 2 93 2.93 2 88 2 83 2 71 2 62 2 49 2 36 2 25 2 13 2 02 1 94 ~
PO
Po.
grams, cc
0 0 0 0 0 0 0 0 0
x
x
106
-~
R-'crn.-1
1 76
~-~
0 0 0 0 0 0 0 0 0
395 327 242 178 124 086 057 035 021
*
133 109 073 051 038 030 021 016 014
4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6
*
I
__
-
24 53 97 27 51 70 88 98 07 13 22 26 26 28 32 33 34 35 -
R-'cm
-1
2 24 2 68 3 53 4.05 4.48 4 90 5 21 5.40 5.48 5 55 5 45 5 30 5.13 4 96 4.70 4.52 4 33 4.13 - -
I
I
0 571 0.482 0.345 0.266 0.206 0.149 0.103 0.069 0.046
*
0.183 0.155 0.114 0.089 0.069 0 055 0.041 0.034 0.027
*
- --
* Values no longer significant a t higher pressurw
active bromide ions migrating into the inactive pellet. It is pointed out here that the above evidence of the immobility of bromide ions does not exclude the possibility that bromide ions in freshly prepared silver bromide can move on the surface from one position t o a neighboring position in an irreversible manner. CORRECTIOS F O E E F F C L T I Y L U I M L S S I O X b O F PELLETS
Plots of the logarithm of the specific conductivity (log xn) against pressure for fused and well-aged samples of silver bromide powders as the powders are compressed give curves similar t o the characteristic curve A of figure 1. I n order t o show that these curves actually correspond to straight lines when the data are corrected for the porosity of the pellets, the data for two samples of silver
1325
A G I S G O F DRY SILVER BROMIDE
bromide which show the characteristic curve but differ most widely in their values for conductivity are tabulated in table 2 . Tlic cliaracteristic conductivity curves n-ith the extrapolated straight lines (ZIA )e for the.se tn o ~ . ~ n i p lare c s shown in figure 2. The values for log (Z,/l)a ~ - and log Ps Pa
from tahle 2 are plotted in figure 3. At the very high pressures the ratios of (Z,’A) c / ( l / A ) aand p I / p a are practically unity, so that these values a t the very high pressures are without significance in figure 3. As is to be expected froni the i n ? 0
c
t
4
L
t 0 3
n
z
0 0
0 k
0
W
a cn L
0
-6.5
-
I I
k a d
I s
s
-6.8
0
200
400
600
800
1000
1200 1400 1600 I800 2000 2200 2400 2600 2800 3000
PRESSURE
IN ATMOSPHERES
P
FIG.2. Apparent and corrected conductivities of silver bromide powders during compression.
previous discussion, the data in figure 3 fall nearly on a straight line which passes through the origin. The empirical relation between (Z/A)e/(Z/A)a and ps/p. can be expressed as:
By applying the correction (equation 6) to the conductivity values for the fused and well-aged samples of silver bromide4 and by plotting the resulting data, one obtains curves (figure 4) that can be represented by straight lines. It is pointed out here that the identical relationship as given by equation 6 or figure 3 could For the sake of brevity the tabulation of d a t a of the conductivity values for the variously aged samples of silver bromide have been omitted here, but they can be found in the thesis upon which this paper is based.
1326
I. SHAPIRO AND I. M. KOLTHOFF
have been obtained from the data of any curve given in figure 4 instead of the data given in table 2. This agreement with the theoretical aspects of the problem gives credence to the conception of conductivity taking place by way of “paths of surface.”
0 =SAMPLE NO. IO A = SAMPLE NO. 1
FIG.3. Conductivity correction for effective length of pellets COXDUCTIVITT O F FRESH SILVER BROXIDE
Plots of the logarithm of the specific conductivity (uncorrected) against pressure for pellets prepared from fresh silver bromide powders exhibit the general shape of the characteristic curve found in the case of the well-aged and fused silver bromide, but the maximum in the curves appears a t lower pressures for the fresher samples. By applying the same correction (equation 6) to the data for the fresher products of silver bromide, one observes that the resulting curves
1327
AGIXG OF DRT SILVER BROMIDE
(figure 5) deviate considerably from a straight line. These deviations are attributed t o the rapid aging iyhich takes place when fresh powders with a high surface development are subjected to pressure. Cnder the conditions of the experiments as carried out here thederivative of theslope of the curveswith pressure (d21nx/dp2) a t a given pressure can be considered as representing the rate of aging. The conductivity-pressure-time sequence followed a rhythmic pattern. An increment of presswe, say 150 atm., was applied to the powder-pellet and the conductivity, i.e., current flowing under a definite potential difference, was noted as a function of time. The major portion of the change in conductivity (the incrense or decrease in conductivity depends upon the value of the pressure)
a
a
-6.2
-
(3
3
-6.3 0
1
1
200
400
1
600
1
800
1
1
1
1
1
1
1
1
1
1
1
1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000
PRESSURE I N ATMOSPHERES
P
FIG.4. Conductivity corrected for length of pellet as function of pressure (wcll-aged silver bromide samples).
took place within a matter of seconds after the increase in pressure and before the current values could be read on the micromilliammeter.’ The conductivitytime function a t each pressure reading approached a fairly constant value in the course of half a minute, though there mas a slight drift in current values with time for the fresh samples. Evidently the fresh silver bromide continues to age regardless of the experimental conditions. From figure 5 it is noted that the slopes of the curves have the greatest numerical values at lorn pressures and tend t o approach values which are comparable t o the values for the well-aged products a t high pressures. 6 A continuous current could not be maintained on the silver bromide sample during the compression because of the tendency of the migrating silver ions to form dendritic bridges through the pellet.
1328
I . SH \1’1RO
AKD 1. Y. KOLTHOFF
DISCUSSIOK O F RESULTS
The values of the slopes of the curves for the various well-aged samples of silver bromide (figure 4) cannot be compared directly with one another, since it
PRESSURE I N
ATMOSPHERES
P
FIG.5 . Conductivity corrpcteci for length of pellet as function of pressure (fresh silver bromide samplesl
is known that the slopes in compressed pelletb vary ivith the conductivity (5) Hen-ever, by taking the difference in the slopes of the curres on pellets obtained on compression of the powder and on recompression of the pelletc, one can
AGING O F DRY SILVER BROMIDE;
1329
calculate the ratio of the conductivity in the loose powder to the conductivity in the compressed pellet by the following equation: In--xo
=
-(k2 - k J . p m
=
-Ak.p,
XP
where xo is the conductivity of the loose powder a t zero applied pressure (extrapolated), x p is the conductivity of the compressed pellet at zero pressure (extrapolated), li, is the slope d In xldp for the compres3ed pellet ( 5 ) , k , is the slopc d In x d p for the compression of the powder, and p m is the maximum pressure applied to the pellet (i.e., 3000 atm.). The value of A, is independent of the magnitude of the applied pressure, but the value of k 1 will be a function of the maximum pressure applied to the pellet. The significance of the value for x[,x,, is that it represents the relative decrease in surface when a loose pon-der is compressed under an external pressure. The values for the relative decrease in conductivitj. from a loose pon-drr to H compressed pellet (considered over a pressure range of 3000 atm.) for the variow samples are given in table 3. I n the case of the fresh zamples the values for xb were estimated from the curves in figure 5 . Since the slopes of these curves at zero pressure probably are greater than the values indicated in figure 3 , the values for xu for the fresh powders may he considered as minimum values, so thcb ratio of x0 to xr,may be greater than listed. I n table 3 the values for xo xI for the more aged samples vary from 1.1 to 1.5, whereas the ratio for the fresh powders may be higher than 10. Thus, pressure has a hrge effect on decreasing the surface of fresh powders hut very little effect on the well-aged powders. Since the latter had been aged drastically previous to the application of pressure, one would not have expected any further aging by pressure to take place foi these powders. The decrease in surface brought about by pressure for the fused and n-ell-aged silver bromide powders can be termed a “mechanical aging” or “mechanical sintering” process. Consider a fused powder. -45 pressure is applied to the powder, the conductivity decreases according to the value of k2 (table 3 ) . Kheri pressure is released, the silver bromide is in the form of a pellet and the slope of conductivity curve \yith preswre is given by ( 5 ) . -4s long as the silver bromide remains compressed in a pellet, the conductivity will follow reversibly the slope given by h.1, providing the pressure does not exceed the ma.;imum pressure applied previously, but if the pellet is crushed and powdered again, the conductivitj- will folloiy the slope given by k2 until the maximum pressure has been reached, and then it will follow the slope given by 7~1. Since this cycle can be considered as reversible, the decrease in surface from pon-der to pellet in this case is pnrcly :t mechanical one. I n contrast to this process the cycle described above is not reversible for the fresh samples, because they had undcirgonc a true aging procebs with pressure. The aging process in these instance5 (’:in be called “pressure aging.” It is pointed out here that the values for x0/xP (table 3) show only the relative decrease in surface of a powder by pressure. In order to compare relative sur-
1330
I. SHAPIRO AND I. M. KOLTHOFF
TABLE 3 S u r f a c e conductivity a n d decrease in surjace w i t h pressure f o r silver bromide powders at room temperature SAMPLE NO. (CORRESP O N D S TC CURVE NUMBER I FIGURES AND 5) .
$
