I
THE KINETICS OF THE HETEROGEXEOUS REA-
-&
POTASSIUII PERM.ASGAS;ITE ASD TT700L P. ALEXASDER
AND
R. F. HUDSOS
Department of Inorganic a n d Physical Chemistry, Imperial College of Science a n d Technology, L o n d o n , E n g l a n d Receiaed M a r c h 83, 1.948 ITTRODUCTIOh
It has been shovn (1) that acid permanganate solutions (pH < 2.5) render n-ool unshrinkable to washing. The technical aspects of this process and the effect that it has on the ~ ~ o have o l been recorded elsenhere ( 2 ) ; the present paper is confined to the kinetics of the reaction, n-hich nere studied in detail. -4 comprehensive re\-ien- of felting, containing all relevant references, has been given by Freney (6);cf. also Martin 17). Qualitative experiments shon-ecl that in dilute solutions of potassium permanganate (& and $ per cent) the surface of the fibers becomes slightly discolored, but in more concentrated solutions the reaction medium rapidly becomes :loudy ith a thick precipitate of manganese dioxide. The fiber surface is also :overed n i t h a thick depo4t of the oxide, only a limited quantity of nhich may 3 6 removed by physical method., such as rinsing n ith u ater or n-ashing in soap qolution. -4naly-is of the reaction mixture shoned that in 0.5-2 per cent periianganate solutions the concentration of manganous sulfate is negligible hroughout the course oi the reaction. -4t loner concentrations some manulfate is found in the solution. This is of importance n hen the mechaiism of the oxidation is considered. EXPERIJlESTlL
I . I'elocity of reactiou
The material used was knitted fabric made from a high-quality cross-bred 'aril. The only chemical treatment to n-hich the fabric had been subjected n-as nild n-ashing in soap to remove \roo1 grease and any contamination introduced luring the spinning and knitting. Each piece of n-eighed fabric (approximately g.), previously purified by extraction Jyith ether and alcohol in a Soshlet exractor, was immersed for several hours, so as to produce thorough and even Tetting, in either sulfuric acid solution a t pH 2 or borax at p H 9.2, depending on he subsequent treatment. 1 potassium permanganate solution of the required mcentration was made in 3 per cent sulfuric acid solution a t pH 2 or in saturated oras a t pH 9.2, and the resulting p1-I tested by means of a pH meter. Khen le reaction was complete the pH was measured again and in no case was found have changed by more than 0.1 of a p H unit. -4knon-n volume of this solul volume of solution, on, calculated to give the required ratio of weight of ~ v o o to as transferred to a 300-nil. beaker immerqed in a thermostat. The fabric was i33
734
P. ILEXASDER . I S D R. F. H T D 3 0 S
fitted to the stirrer, n-hich TWS in the form of a cylindrical glass cage, G em. high and 5 em. in diameter, which could be lovered into the reaction medium. The axle of this cage n-as secured to a small electric motor, the speed of nhich could be regulated and was measured n i t h a tachometer. Samples of the reaction mixture were withdraim a t timed intervals and placed in small tubes fitted to a centrifuge. hfter centrifuging for approximately 10 min. the supernatant liquid was transferred to a cell inserted in a Spelilier photometer and the reading converted to permanganate concentration from a calibration graph. Other samples xere analyzed chemically by adding a 3-ml. portion to a solution of potassium iodide and titrating against sodium thio>ulfatesolution. As similar results TT ere obtained from both methods, it v a s evident that all the suspended manganese dioxide must have been removed by the centrifuging process adopted. To eliminate, as far as possible, the effect of stirring on the rate of reaction, experiments ivere performed (see table 3) in which the frame to uhich the v-ool v a s attached was stirred at different rates. It was found that the rate of reaction became almost independent of stirring rates above a certain limiting yelocity. -111 experiments were therefore carried out a t a speed of 350 R.P.M., which was found to be Jvell within the region of stirring insensitivity without causing a large vortex in the liquid. -is the reaction is rather fast, all experimentij. unless othervise stated, liere carried out at 0'C. in an ice bath. The temperature was not allon-ed to rise above 0.1"C. 2. Esfin?afionof manganese dioxide deposited o n the j b e r s
One-gram pieces of n-ool TI ere immersed in separate beakers containing 150 ml. of potassium permanganate of known concentration acidified 11-ith 3 per cent sulfuric acid at 0°C. After lmonn time>, each piece was removed, washed, and placed in 25 ml. of a 1 per cent sodium bisulfite solution. lTThenall the rnariganese d i o d e had been removed, which TT as shov n by the complete decolorization of the fabric, 10 ml. of the solution v a s removed vith a pipet and boiled for 15 min. to remore sulfur dioxide. Approximately 20 ml. of 2 per cent potassium periodate solution in dilute sulfuric acid vas added and the solution boiled until no deepening in color n-as evident. Thi> solution was made up to 50 nil. and a sample transferred to a glass cell inserted in a Speklier photometer. The readings were con\-erted to n eight of potassium permanganate per gram of wool. Check experiments TI ere carried o u t by oxidizing the manganous sulfate v i t h sodium bismuthate and titrating n-ith ferrous ammonium sulfate. In some cases the manganese dioxide deposit n-as removed by immersion in concentrated potassium iodide solution in 3 per cent acid, and the liberated iodine titrated v ith sodium thiosulfate solution. The n-ool was not allowed t o remain in contact n-ith the potassium iodide solution for longer than necessary, owing to the slow absorption of iodine by the ~ o o l . REbULTS
1. T'elocity of rcactioii It n-as found that the graphs of log, a ( a - x) against t TI-ere linear in acid solutions at concentrations of less than 0.5 per cent permanganate ( a is the initial
REACTIOS BETWEES POTASSIUlI PERlLiSGISITE A S D W O O L
'735
concentration of permanganate and .2: the quantity reacted in time t ) . Deviations from linearity were observed in alkaline solution (figure 1) and concentrated acid solution (figure 2). Owing to the impossibility of finding a representative velocity constant for the alkali and acid reactions, the rates of reaction are compared in table 1 by means of half-life values. The modified rate and form of the reaction progress indicate that the reaction in alkali is quite different chemically from that in acid (tide infra); the latter only is considered in detail in this paper. IOOI
0
10
40
30
PO
50
60
70
80
T/ME-MIN
FIG.1. log10a,(a - T ) against t in alkaline solution. Four grams of wool iiiimersed in 100 of solution.
111.
Results are given in table 2 for the effect on the rate of changing the initial *oncentrationof potassium permanganate at pH 2 with a constant ratio of n-eight )f TI--001to volume of solution. (Results using a larger n-eight of n-ool per volume If solution are given later (page 740).) The half-life values are recorded and lso pseudo-unimolecular constants calculated from the simple relation : 1;
1
= -
t
log,
U __ U - %
The results in table 2 shon- that a t lon- permanganate concentrations the rate goT-ernetl by the qimple first-order law. -It higher concentrations, however, le rate decrease, rapidly, so that n-hen T T - O O ~is immersed in a 1 per cent perianganate solution, 1e.s permanganate reacts in a giT-en time than when an lual n-eight of wool is immersed in a 4 per cent solution. The velocity constnnt
ACID
011
0
1
KMnO,
u t O'C.
W O O L TO SOLUTION
\
I 0.1
wrio
ISO:I
'\
1
40
30
20
IO
60
50
70
80
T / M f -M/N
FIG.2. loglo ( a - z) against t in acid solution. One gram of wool in
150 ml. of solution.
TABLE 1 T h e half-life values i n acid and a l k a l i m e d i u m with varying i n i t i a l permanganate concentrations Four parts of wool fabric by weight per 100 vol. of solution KbhOd
COXCENTRATION
11 2
____
AT
,
pH 2
11 2 A t pH 9.2 -
~
per cent
min.
min.
12
36 32 28
4
-
i
4 4.8
1 3
-12
18
TABLE 2 Half-life values and oelocity constants i n acid solution One gram of wool in 150 ml. of 3 per cent acid solution of permanganate KMnOc
COXCENTBATION
I
I
k
fl ?
(UNIXOLECUL\R)
~~
per cent
0.104 0.255 0.272 0 311 0.510 0.55 0.701 0.765 1 08 1.06
mzn
5 6 7 8 5 18 30 47 59 150 137
min-1
I
I
0 063 0 065 0.040 0 029 0 016 0 011 0 0068 0 0052 0 0022 0 0026
736
I
1
(KMnO#
'
1
k(KiMn0a)z
1
I
'I 1
1
o
075 0.096 0.25 0.30 0.49 0 585 1.17 1 12
'
0.0030 0 0028 0.0010 0.0033 0 0033 0 0031 0 0026 0 0039
737
REACTIOS BETWEES POTASSIUM PERMASGASATE B S D \TOOL
is a function of the initial concentration of permanganate a t a given n-oo1:solution ratio. Table 2 s h o m the following relation to be obeyed approximately: a2 a k = - log, -
t
a--a
The graphs of loglo a / ( a - x) against t are shon-n in figure 2, from which it is observed that linearity holds for the majority of the reactions for initial permanganate concentrations up to 0.: per cent, whereas for 0.75 and 1 per cent the lines are not linear. The significance of this observation and of the peculiar law relating rate to initial permanganate concentration is discussed later (page 745). It is unlikely that such a law receives a true explanation on kinetic grounds, but it probably has a physical explanation, as shown by later work. Before this is described, the effect of temperature and stirring will be considered. The rate at various stirring speeds, expressed in table 3 in the form of half-life values, was found to increase oyer the 100-250 R.P.BI. range and then become TABLE 3 Halj-life valztes at different stirring speeds ~~~
t i ? A T THE
TEUPERATURE
"C. 0
15 25 35
100 r.p.m.
200r.p.m.
min.
min.
16
5 2.5
-
,
POLLOWISG STIRRISG RATES
300r.p.m.
'
min.
,
min. I
G 4
1.5
2.0
400r.p.m.
15
5.7
3 1.5
~
~
I
,
500r.p.m.
min.
15 3
constant. It was shon-n that a stirring rate of' 350 R.P.11. with rotating fabric is equivalent to a rate of 1200 to 1500 R.P.11. if the solution alone is stirred with an ordinary paddle stirrer. \Then this is taken into consideration, it is highly probable that the diffusion layer on the wool surface is reduced as completely as possible. The courses of these reactions are given in figure 3, from which the stirring effect may be observed more clearly. From the calculated first-order velocity constants a t high stirring rates the temperature coefficient may be obtained and the graph of log k against 1/T constructed (example, figure 4). The slopes of these graphs, which are approximately linear, n-ere used to calculate values of the apparent activation energy of the rate-controlling process a t different COIIcentrations (table 4). I n the case of a 1 per cent permanganate solution, the initial velocities at 0" m d 25°C. n-ere used for the purposes of calculation, as the rate does not obey a simple relation a t this concentration. For per cent pernianganate solutions, .he half-life values a t 0" and 25°C. w r e employed. The>e data and calculated tctivntion energies are giren in table 4. The results recorded in tables 5 and 6 refer to the reaction at pH 2, using solu-
+
738
P. ALEXASDER A S D R . F. HCDSON
tions of $ per cent and 1 per cent permanganate, respectively, with varying weights of wool in 100 ml. of acid solutions. From figure 5 and table 3 it is seen that the rate of reaction for lo\\ permanganate concentrations is approximately proportional t o the Tveight of wool in solution and consequently t o the surface area exposed. At high conwntrations, 0.5
0 . '
2
F Q
0.3
c
2 y1
U
0"
5
0.1
0.I
W O O L 70 S O L U T I O N
0
R A T I O 150:I
20
IO TIME
30
- MIN.
FIG.3. The effect of stirring rate on the rate of reaction of B 0.5 per cctlt solution of permanganate Tyith 1 g. of n-ool per 150 ml. of solution: I, alkaline solution a t 25°C.; 11, acid solution at 0°C.; 111, acid solution at 25°C.
honever, this relation no longer holds. It is seen from table G that the rate is approximately proportional to the square of the n-eight of 11-oo1 ininlersed in a given volume of solution. Thia relation is, hon-ever, only approximate, as the constant i: and half-life tl give rough measure3 of the rate of reaction. In addition, the pori-er appears to change 11ith the n-eight of v-001and for lon. 11 eights the rate tends to becoinc proportional t o the n-eight of n-001. This is discussed in the light of subsequent data in the discii4on (page T43).
I.a
1.6
I .4
* 0
1.2
?
p 1.0 0
-4
0.8
0.6
0.4
FIG.4. loglil100 k , against 1,'T for 0.5 per cent permanganate solution. One gram of no01 in 150 ~ i i l of . solution. T.iBLE 4 The eflect of tenzpernfrcre o n late of reaction ~~~
~
K I I n O l COSCESTBATIOS
RATE A T
O'C.
RATE A T 2 Y C .
p e r ce?:!
miri.
1
niin.
5 15 0.0125
1 -
2
1*
* Iiiitinl rates expressed
8s
ACTIVATION EKEBGY
___
~.
641.
I
1.5 3 0.100
8,000 12,000 13,500
,
per cent of permanganate reacting per minute.
TABLE 5 Reaction a t p H 2 ncifh 1 / 6 per cent permanganate ITEIGHT OF U'OOI.
6.07 5.0 4.0 3.33 2.5 2 0
11 2
5 7.5 10 12 17 22
I
fi
0.120 0.093 0.069 0 050 0 040 0.031 739
I 1
L
WEIGHT OF WOOL
0 018 0 018 0.017 0 018 0 016 0.016
' W E I G H T OF \\ 'JOL
,
1
I
,
I
x li ?
33.5 37.5 40.0 40.0 42 5 44 0
__-
i40
P. ALEXAKDER A S D R. F. HUDSON
TABLE 6 Results a t p H 2 with 1 p e r cent permanganate
,,
grams
6.67 5.0 4.0 3.33 2.0
I I
1 ~
_____
-
min.
I
I
262 225 208 205 196
5.9 9.0 13.0 18.5 49.0
I
102 101 104 110 140
1
0.049 0.031 0.021 0.0143 0.0054
1.10 1.24 1.30 1.29 1.35
1
i
7.0
; U
5.0
-
0
-5 Z
4.0
0
3 U
3.0
$ 2.0
-a
0
.02
.04
.05
.06
1.0
1.2
K
TdBLE 7 The relation bcticecn k a n d iniiial c o n c e n f m t i o n Four grams of ~ o o per l 100 nil. of solution KhlnOa COSCEXTRATION per c e n t 1 -
5
1 -
,
I! 2
I
I
-3 1 lf 2
k
(UEIMOLECULAB)
mia.-'
0.58 0.66 0.7
I
1 I -
I
4.2
7 12 26 36
0.77
0.12 0.20 0.15 0.09
210 232 225 217
REACTIOX BETWEEN POTISSIURI P E R M S ~ G A ~ A T A E S D WOOL
74 1
It has already been seen (page 735) that the rate is approsimately proportional to the square of the initial concentration of permanganate, with a small quantity of fabric immersed in a large volume of liquid. This relationship was investigated with a considerably larger weight of wool per volume. Table 7 records half-life values and first-order constants n-ith 4 g. of wool in 100 ml. of solution. This table shows that the retarding effect is dependent to some extent on the quantity of n-ool surface available and decreases with an increase in the available surface. This effect is shon-n by the following relations: a2 1 g. of \I-ool in 150 ml. of solution: k = - log,
t
a3 '2
G g. of wool in 150 ml. of solution:
k
= -
t
log,
a
___
a-x
a __ a-x
In addition, the concentration a t which the simple first-order relation deviates is higher the greater the weight of wool in the solution. These generalizations will be explained after the n-ork on the deposit on the surface has been described. 2. T h e e$ect of the manganese dioxide deposit
hlthough a high degree of accuracy 'iws not expected in these esperiments, in n-hich the amount of manganese dioside retained by the n-ool was determined, satisfactory results of a semiquantitative nature were obtained. I t is seen from figure G that the amount of manganese dioxide deposited on the ~t-oolin a given time is a function of the permanganate concentration. The results are summarized in table 8, n-hich gives the lveight of manganese dioxide deposited from the three different solutions of permanganate in three different times, and also the initial rate of deposition of dioside. The rate of deposition of manganese dioxide is thus related to the concentration of the solution by a general equation of the type Weight of M n 0 2 = a(K-11n01)2 where a is a constant. To study the effect of the oxide deposit on the kinetics of the reaction with acid permanganate of different concentrations, two typical kinetic esperiments were carried out, but in one case the piece of n-001 was removed after a given time and immersed in a 1 per cent acidified solution of sodium bisulfite until the deposit was removed completely. It n-as shon-n (1) that the brief immersion in bisulfite does not attack the wool, as the cystine content and the elastic properties remain unchanged. The wool was then washed n-ith running water, followed by a 3 per cent acid solution, and again placed in the reaction bath. The rate if the continued reaction was then followed as before. The results of several wns are shown in figure i . It is seen that at low permanganate concentrations and 2 per cent) a very small discontinuity results from the clearing process. ?or higher concentrations, however, a very distinct break in the curve is observed, nd it is also seen that the rate of reaction immediately after the clearing of the
+
742
P. ALEXLKDER .43D R. F. HUDSON
wool piece is almost equal to the initial rate of reaction. It appears that the rate does not decrease so rapidly when the reaction is continued after clearing as does the rate of the control reaction, presumably because a t the permanganate concentration corresponding to the clearing the rate of deposition of manganese
r:
5 U
0
0.5-
i)
0
1, .-
TIME
- M/hj
FIG.6. T h e weight of manganese dioxide deposited on the vi001 in various times with (a)
1 per cent, (b) 0.5 per cent, and (c) t per cent permanganate solutions.
TABLE 8 The relation betueen deposition of manga)iese dioxide and potassium permanganate conccntration VEIGBT OF
I
KMnOd
1.0 0.5 0.25
. . .
ISITIAL R A T E
2.5 min.
5 min.
gram
gram
~
fier cent
___
.\lnO? DEPOSITED
0.125 0,045
0.020
0.20 0.07 0.03
10 min. ~
~
grams
0.30 0.10 0.05
0.10 0.024
0.008
dioxide is greatly reduced. The more important indication, however, is the observation that the initial rate is slightly less than the rate after clearing, in agreement with the observation that the rate decreases with increasing concentration (figure 2 ) . This iiidicates that, a t these concentrations, if manganese
REACTION BETWEEN POTASSIUM PERVAXGAN.4TE
AND T O O L
743
dioxide were not deposited on the wool surface the rate would be independent of permanganate concentration.
0.5
i
0
5
IO
5 TIME
20
- M//Y
as
x,
35
FIG.7 . Interrupted treatments with 3, t , and 118 per cent permanganate solutions at 0°C. with 1 g. of wool in 150 ml. of solution. ( a ) Acid potassium permanganate at 0°C. a t different concentrations. (b) .4t the reaction time indicated by the arrow the deposit of manganese dioxide x a s removed. The reaction was continued in the same solution.
TABLE 9
+
H a l f - l i f e values for treated f a b r i c s and control pieces per cent K M n 0 4 in 3 per cent sulfuric acid; 4 g. wool per 100 ml. of solution TREATUEST
I, 2
min.
Si1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11n 0 2 Method 1 . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . Method 3 . . . . . . . . . . . . . . . . . . . . . . . . .
1.75 2.0 2.25 2.0
The effect of manganese dioxide deposited by the following three independent nethods was investigated: ( 1 ) Each sample 11-as thoroughly saturated lyith a olution of manganous sulfate, which was then treated n-ith alkaline perman;anate for 10 sec. ( 2 ) The oside was precipitated by treatment of the 11-001
744
P. ALEXASDEB AXD R. F. HUDSON
samples soaked with manganous sulfate, with hydrogen peroxide (3 per cent by volume) in 2 it' ammonia for 10 see. ( 3 ) The 11--001 pieces were placed in a 3 per cent alkaline solution of permanganate for 10 min. Before the rate of reaction was determined, the loose oxide was removed by washing in running water. Table 9 gives the values of half-life periods for treated fabrics and control pieces. The deposits appear to have a slight retarding effect, but this is much smaller than the reduction caused by manganese dioxide in the course of the acid permanganate treatment. This suggests that the manganese dioxide deposited from acid solution is held on different centers in the wool fiber and in a different manner from that deposited from alkaline solution and from manganous sulfate solution. Consequently, it is considered that the chemical reaction in acid solution is entirely different from that occurring in alkaline solution. The effect of other oxide deposits on the rate of reaction was also studied under similar conditions. These oxides had little effect on the rate, although a slight acceleration m s noticed after deposition of ferric oxide and treatment n-ith TABLE 10 W e i g h t s of manganese d i o x i d e deposited o n deaminated a n d o n untreated samples TISIE
min
.
5 10 20
30
ammoniacal cupric sulfate. Zinc oxide and manganous hydroxide caused slight retardations of the same order as those caused by external deposition of manganese dioxide (table 9). 3. The effect of nzodijcafion of wool
The reaction n as performed xvith partially deaminated TI-001,and the ir-eight of manganese dioxide depobited in the course of the reaction determined. K o o l was deaminated by the standard procedure ( 3 ) and the extent determined by titration of a weighed sample n-hich had been brought to the isoelectric point. I n most cases, 50-GG per cent deamination v a s obtained. Table 10 compares the weights of manganese dioxide deposited on deaminated and untreated samples after various times of reaction. It is seen that the n-eight of manganese dioxide deposited on deaminated wool was less than the amount on the untreated samples, suggesting that it is deposited mainly on the amino acid chains. KO satisfactory agreement in the rate of reaction of deaminated ~ r o o lwas obtained in the sex-era1 runs performed. This is due to the drastic reaction of the deamination process when appreciable main-chain hydrolysis occurs.
REACTIOS BETWEES POTASSIUM PERMANGASATE ASD WOOL
745
Lastly, the effect of a preliminary disruption of some of the disulfide bonds by dilute aqueous sodium hydroxide, and the subsequent formation of more stable cross links, e.g., -CH2-S-CH2and -CH=S-, was observed. The wool samples were treated as prescribed by Speakman and Xeish (8), and the rate of reaction and weight of manganese oxide deposited n-ere determined. It was noted that no change in the velocity of the reaction took place owing to this treatment. In addition, the weight of manganese dioxide deposited was found to be approximately the same as that deposited on an untreated sample (table l l ) ;hence this deposit alone appears to govern the rate of reaction. T.IBLE 11 Efect of pretreatment o j wool with s o d i u m hydroxide Concentration of Iohition. The temperature coefficient under these conditions has been measired and the apparent activation energy of the rate process found to be approxinately 8000 cal. With high concentrations of permanganate, hon-ever, an empirical relation f the folloIying type has been shown to hold approximately for constant amounts f n-001 in solution:
a''
-
t
log,
a
___
a--5
,here n is a number which varies n-ith the weight of wool in solution. Thus = 2 with small n-eights of ~vooland 1.5 for comparatively larger quantities.
746
P. hLEX.ISDER h X D R . F. HUDSOS
I t was found that the plot of t against log,, a,(a - x) was not linear as in dilute solution, but was taken to approximate to linearity over a small range in order to correlate rates a t high and low permanganate concentrations. The factor an represents a retardation factor which increases rapidly as the permanganate concentration increases. It is considered that this retardation is due t o the deposit of manganese dioxide firmly held on the surface of the fibers. The weight of manganese dioxide deposited after a given time is proportional to the square of the initial permanganate concentration as a first approximation. The reduction in rate thus appears to be approximately proportional to the amount of manganese dioxide firmly held on the fabric. Further evidence of the r81e played by the manganese dioxide deposit is obtained from the interrupted treatments shown in figure i . It is seen that in dilute solution (and also in alkaline solution) no break is noted in the curve of percentage decomposition against time of reaction. This indicates therefore that under these conditions, the manganese dioxide deposit has little effect on the rate of reaction. In more concentrated solutions, however, very marked breaks in the curves are noted, confirming the importance of the dioxide deposit on the rate process. In addition, it is observed that under these conditions the initial rate of reaction is slightly less than the rate of reaction immediately after the fabric has been replaced in the solution. This shows that in concentrated solutions the reaction would follon- approximately a zero-order law if no deposit formed on the surface of the fabric. The curves given in figure 3 shov that the rate of reaction is somewhat dependent upon stirring, a result which indicates that the reaction rate is controlled by some diffusion process 11hich may be in solution or within the swollen fiber. I t is logical to assume that in dilute solutions the state of the surface has no effect on the rate of reaction, whereas in concentrated solutions it is highly important. It is considered that the experimental results show that the over-all rate of reaction is not governed by a chemical process in acid solution. The results indicate that in dilute solution the rate of reaction is governed by diffusion across a liquid barrier at the surface of the fabric. I n this circumstance, the rate of diffusion through the fibers and the rate of absorption are relatively great compared n-ith this solution diffusion. The rate of diffusion across a liquid layer is given by the general relation
where dx is the quantity of solute crossing a barrier of area J in time dt, n-ith a concentration gradient in the barrier equal to (dc),’(ar), If it is assumed that the rate of remom1 of permanganate ions at the surface is great compared with the ixte at which the ions cross the barrier, and also that the concentration gradient 1’, linear, this equation reduces to dz - D 9 - (a - x) dt Ar
-..- -
REACTIOS BETTVEES POTASSIUM PERYASGASATE A S D WOOL
747
where (a - x) is the concentration of permanganate solution a t time t and Ar is the width of the barrier. Thus,
D
=
l-r log, ___ (a) At (a - 2)
This expression is similar to that observed to hold in dilute solution. The effect of increasing the stirring rate is to reduce the width of the diffusion layer, Ar, with a resulting increase in the rate-controlling diffusion coefficient D. When comparatively large quantities of manganese dioside are absorbed on the surface, ions cross this layer a t a greater rate than that at which they can pass through the fibers to the sites of reaction. The manganese dioside deposit may affect both the diffusion through the fibers and absorption on these sites, one of these tn-o processes determining the over-all rate of reaction. The kinetic results will be considered in the light of these two alternatives. It is assumed from the experimental results that the reaction obeys a zero-order law apart from the retarding influence of the manganese dioxide. The wool surface is thus saturated with ions throughout most of the reaction. The retarding influence gradually increases in the course of the reaction, oning to the deposit of manganehe dioxide increasing with time of reaction. The following assumptions viill be macle to account quantitatively for this retarding influence: (1) The Tveight of manganese dioside formed concentration of permanganate above some limiting concentration. The analyses (summarized on page 742) of nianganous sulfate in solution shou- this concentration t o be approximately $ per cent. (2) The u-eight of manganese dioside firmly held on the surface of the fiber is proportional to the xveight formed in solution. (3) The retarding influence is inversely proportional to the weight of oside deposited to some pon-er 2. Thus, for zero-order kinetics
so that
If n = 1 as a first approximation, n-hen a small n-eight of wool is immersed in a large volume of solution, then
Khen t = tl,'?, .x = * a , so that t = a', if. K i t h larger quantities of \~-oo1immersed in the solution, the value of n may tssume smaller values, as the retarding influence is no longer proportional to the r-eight of dioside deposited.
748
P. ALEXANDER AND R. F. HUDSON
If n = 0.5 then
This semiempirical treatment then esplains the esperimental results with relatively large and small quantities of wool in the solution. The plot of 2' against t has been shown t o be linear for 1, 2, and 3 per cent permanganate solutions, with small weights of wool (figure 8). The agreement vith 4 per cent solutions is not so good, as the change-over in mechanism occurs at this order of concentration. Id
9
I6
14
12
IO
x** I
d
8
6
4
2
0
FIG.8. The relation betneen 5 2 and t for t , O"C., with 1 g. of wool in 150 ml. of solution.
3, and
1 per cent acid perniangariate a t
Experiments with varying weights of n-ool show that the rate of reaction is approximately proportional to A', where -4 represents the n-eight of n-ool. This relation, hon-ever, varies with the n-eight of 11001, and with comparatively small quantities of no01 the following relation is found to hold much more closely than the q u a r e relation: li2 a 93'. I t iiould appear at first sight that the rate of reaction is proportional to the sru.f:we nieu of the fahric. -in increa*e in weight of wool, hon-ever, tends to reduce the retardation factor due to the manganese dioxide deposit. The relation I ~ t t ~ t e rate e ~ i and quantity of i\ool bhould then be written as: 1;'
-4
x
(KAjL)
RE-ICTIOS B E T K E E S POT.ISSIL-hf PERMASGASATE I S D K O O L
749
where n may vary from 0 when small weights of u-ool are employed to 1 when larger quantities are employed. The reduction in the retardation factor is then given by IC4 n. Recently, Boyd, Adanison, and Myers ( 5 ) have considered the rate-determining diffusion of an ion through an absorbent zeolite, and obtained a similar but more exacting relation to hold. From the general diffusion equation (dn a t ) = D(d'ri ax'), utilizing the solution given by Barrer (4) for the appropriate boundary conditions, these workers obtained an approximate relation for the quantity of ion J diffused into a porous slab in a given time t , as
x
= 8nr2Cs&%/n
!There r is the radius of the slab and C" is the concentration at the surface. As Cs has been shown to be constant above a certain permanganate concentration, this expression may be rewitten as:
This relation applies strictly for small values of t , for small diffusion coefficients, and or for large particles, where it is assumed that the products of reaction are adsorbed within the solid. The second alternative, the rate-determining absorption, n-ill non- be considered. I t \\ ill be assumed as before that the surface of the fabric is saturated jvith pernianganate molecules. It is supposed that the product of reaction is ahsorbed strongly on the burface and that most of the surface is covered with this deposit. If 8 is the fraction of the surface covered n-ith absorbed molecules, (1 - 0) is the fraction remaining uncovered. Let C be the concentration of the product, manganese dioxide, in the liquid and consider the equilibrium between the removal and attachment of this product on the surface. Then z i l - 8)C' = 08, nhere a and b are proportionality constants, so that
1s the concentration of manganese dioxide in the liquid phase is proportional o the amount of permanganate J which has reacted, this expression may be eplaced by
.Isthe dioxide is absorbed strongly, the rate of absorption determined by a is reat compared with the rate of removal dependent on b, so that a / b and con>quently1;; are large. Hence (1 - 0) = k', x. Xs the concentration of ions on the uncovered fraction of the surface is conant for most of the reaction, the rate equation thus becomes
7 50
P. ALEXASDER A S D R. F. HUDSON
so t'hat
This expression is of the same form as that evolved assuming diffusion within the fiber to be the rate-determining process and is subject t o similar restrictions. Thus, both processes can explain the experimental data. The nature of the specific chemical reaction which leads to an unshrinkable fabric has been discussed elsewhere ( l ) ,and shown to consist of an attack of the disulfide bond. It has been shown that the rate in alkaline solution is much slower than that in acid solution under equivalent conditions (table 1). As the rate in acid solution is highly dependent on the quantity of manganese dioxide on the fabric, it is reasonable to assume that in alkaline solution this reduced rate is due to an even larger deposit of manganese dioxide. The experiments on interrupted treatments in alkaline solution, however, show that no significant break appears in the percentage decomposition-time curve, in contrast t o that obtained in acid solution. I n addition, it has been seen that the resulting deposit of oxide does not decrease the rate of reaction greatly xhen the fabric is treated with an acid solution of permanganate (page i44). It is further noted that the rate of reaction is completely independent of stirring rate, in contrast to the rate in acid solution. It is concluded that the rate measured is that of a slow chemical reaction representing a general oxidation of the keratin macromolecule, n-ith no specific reaction with any particular group. The physical properties of the fibers (1) support this contention. In conclusion, the mode of precipitation and bonding of the manganese dioxide will be considered. The oxidation of the -4-Sbond may be considered as follon-s:
R-S-S-R'
+ 2XnOT t GH+ + RSO,,H + R'SO,H +
2H20
+ 21In++
The manganous ion5 are then osidized by permanganate ions by a series of valency changes, leading t o tetrarnlent manganece ion in solution; this then hydrolyzes t o the dioxide, TI hich precipitates. 31\In-'
+ 2JInO$ + 2H20
+ 5Mn02(s)
+- 4HT
This series of processes occurs on the .iuf'nce of or n-ithin the fiber- Consequently. absorption of a certain proportion of the soluble tetravalent manganese ion on specihc sites occ~ir",follon ed by rapid hylrolysis to the insoluble dioside. It is the eyuilibi iiim betn-een this soluble tetravalent manganese salt and the wool surface TT hich is considered in the absorption treatment given on page '749. The rezulting depoqit firmly held by strong ph>-sical forces or by n-eak coordination bond. reduces the rate of reaction, either by steric hindrance if the ratecontrolling proceqi is absorption or by reducing the rate of diffusion through the fibers if this is the rate-controlling process. The series of graphs (figure 9) c h o ~ ~that . s the amount of manganese d i o d e deposited is very small compared with the total quantity produced, n hich indicates that the retardation is due t o
751
REACTIOS B E T W E E S POT.LSSIUJI PERM.\ZdSGASdTE A5-D WOOL
some such physical factor. The analyses of manganese dioxide deposited on samples of deaminated n-ool and n-ool in which the disulfide bonds had been removed indicate that the dioxide is bound to the amino groups of the side chains of the keratin molecule and not to the disulfide bond. It follow, therefore, that manganese dioxide deposited by other methods, and also other oxide de.. 1.8
I .6
1.4
g
s
1.2
U
0 1.0 &
a
a" & -
0.8
u
0c' 2 0.6 Y
LL
0
0.4
0.2
, . ; - - -_, . . -
. IO
20
,
,
60
70
, ,
(b) 30
40
50
TIME- M/N FIG.9. The rate of reaction and amount of manganese dioxide deposited a t 25OC. Acid iotassium permanganate a t 2 5 T . (a) Quantity of manganese dioxide deposited expressed s weight of potassium permanganate. (b) Amount of potassium permanganate reacted.
osits, do not affect the rate of reaction appreciably, as these deposits are not eld by specific groups in the macromolecules but are distributed a t random along l e surface. It is difficult t o see why such deposits should not reduce the rate F diffusion of permanganate ion through the fibers, unless these deposits are Infined to the exterior of the fibers. On the other hand, if the rate is controlled
'752
P. ALEXAKDER -%?,-D R .F. HUDSOS
by absorption on the disulfide groups, these oxide deposits would have little effect on the rate in contrast to a manganese dioxide deposit held only on amino groups close to the disulfide bonds. SLTJIARI
The rate of the heterogeneous reaction of potassium permanganate n-ith 1~001 has been measured under various conditions, and related by an empirical relationship to concentration and I\ eight of n-001. Different relations and temperature coefficients have been found for concentrated and dilute solutions. In acid solutions, the rate-determining step i y that of a solution diffusion process, a t lorn concentrations, and probable diffusion through the fibers in concentrated solutions. The reaction i q found to ohey a zeio-ortler lan in concentrated solutions, as the surface becomes saturated n ith permanganate ions, but as reaction proceeds the rate decreases, oning t o the deposit of manganese dioxide firmly held n-ithin the fibers. This deposit, uhich i> probably attached to the amino groups of the side chains of the keratin macromolecules, can only be removed by treatment x i t h sodium bisulfite or hydrogen peroxide. -4fter the deposit has been removed, and the reaction continued, the subsequent r3te is of the same order ab the initial rate of reaction. The results obtained uith concentrated solutions have also been discu.wl. assuming absorption on specific sides t o be the rate-determining process, and such a mechanism has been shonn to be possible.
It is a pleasure to aclinon-ledge the helpful discussions with Professor H. TT. A. Briscoe, D.Sc., and the financial assistance of IIesers. TT-olsey Limited, Leicester, n-ithout which this research could not have been underta,kpn. REFERESCES ,1) ALEXASDER. E'.: British patent 586,020 (1947'). SPEAKAIAS, J . B., SILSSES,B . , ASI) ELLIOTT,G . H.: S a t u r e 142, 1038 (193s). (2) &1I,EXANl)ER,l'., CARTER, D., A N D HL-IXOS, It. F.: J. Soc. Dyers Colourists, hpril. 1949. (3) BALDWIS,A . \T., BARR,T., AXD SPEAKAIAS, J. B . : J. SOC.Dyers Colourists 62, 8 (1946). (4) BARRER, 11. 11.:Uij'i'!ision in and through Solids, p. 29. Cambridge Cniversity Press, London (1941). ( 5 ) BOYD,G . E . , . l u . u r s o ~ , .1.W., ASD A I T E R L. ~ , S . : .J. Ani. Chem. SOC.69, 2836 (1947). ,AI. R. : Symposium on Fibrous Proteins, J. POC.Dyers Colourists 57,178 (1941). ( 7 ) NARTIX,-1. J. P . : J. SOC.Dyers Colourists 60, 225 (1944). (8) S P E . 4 K U A S , J. B., .4KD NEISH, It-. J. P . : S n t u r e 155, 4s (1945).
