KINETICSOF
Dec. 20, 1959
THE
FORMATION OF THE FERRIC CHLORIDE COMPLEX
the charge on the cation or anion undergoing polymerization, and E are generally both known, the charge per monomer unit, Z*’ = ( z 3 - T), can only have values between z ? and i 0. I n order to obtain a system corresponding to the one treated in the hypothetical case, i t is necessary to make the measurements a t high values of 5. Under these conditions, $2 is considerably greater than $3, and since ?i will have a sign opposite to z the possible values of Z*’ are limited to a narrow range. I n addition, the use of a weakly complexing ionic medium like NaC104 makes i t very unlikely that 5 will have values greater than about 0.5, I n order to relate the properties of the monomeric component to those of the polymeric component, these quantities are defined
+
+
Z?*/M = Z*’, charge per monomer unit
(17)
J f 2 / N = M‘, formula tvt. of the monomer component (18) m2.N = m‘,molarity of component 2 computed as monomer (19) IC.‘ = (dn/dm’) (23)
Within the relatively narrow range of possible
Z*’values, values of Z*’ are assumed and used to
calculate c2, cp2 and ms*. It is convenient to plot the deviation function obtained by substituting (17) and (18) in (12) and rearranging terms
as a function of
c2
or m‘. When the correct value of
Z*’ is chosen, the plot will have a limiting slope of 0 and an intercept 1/N. This is shown in Fig. 2 in which the turbidity data for the first case in Table I which corresponds to the case with N = 5, M‘ = 200, and Z*’ = 0.8 are plotted as deviation functions. Values of M‘, 6 2 , m3* and cpz were computed for 2”‘ = 0.4 and 1.2 in addition to the correct value 0.8. In this case, the value chosen for Z*’ has a significant effect on the value of ilr; however, the large deviations from 0 slope obtained with in-
[ CONTRIBUTIOS F R O M
THE
6389
0
10 15 20 1 0 2 c (g./ml.). ~ Fig. 2.-Effect of Z*’ on the determination of 11’: 0, Z*’ = 0.4; 0 , Z*’ = 0.8; A, Z*’ = 1.2. 5
correct Z*’ values make a fairly accurate estimate of the charge possible. It should be noted that while deviations from equation 12 limit the accuracy of the determination of Z*’, the effect of Z*’on the intercept decreases rapidly and eventually becomes negligible as the ratio $2/$~3 increases. The analysis of highly polydisperse systems is restricted to those where $2 >> $3 and Z*’ is best set equal to 0 in the calculation of Nw. In summary i t has been shown that the average degree of polymerization N may be calculated from light scattering measurements on systems a t high values of 5. Since N a n d Z*’ may also be obtained from sedimentation equilibrium measurements, a system may be studied by two independent experimental methods. Light scattering measurements provide a means of obtaining information about systems a t high values of N where data from the more usual e.m.f. and cryoscopic measurements tend to be inconclusive and also provide a convenient method for measuring the aggregation as a function of time in systems where the equilibria are not attained rapidly. CHAPELHILL, N. C.
DEPARTMEXT O F CHEMISTRY A S D THE RADIATIOS LABORATOR\ UXIVERSIl Y CALIFORNIA, BERKELEY] I
OF
Kinetics of the Formation of the Ferric Chloride Complex BY ROBERT E. CONNICK AND CLAUDE P. COPPEL RECEIVEDFEBRUARY 6, 1959
A previously described apparatus for rapidly mixing two solutions has been used to sttidy the kinetics of the reaction : F e + + + C1- = FeCl++ in aqueous solution. The forward rate law has been determined to be d(FeCl++)/dt = k l ( F e + + + ) (Cl-) k2[(Fe+++)(C1-)/(H+)]. At 25” and an ionic strength of 1 0 Ad the values of k1 and k2 are 9.4 z t 1.0 i Z P 1 set.-' and 18.0 =k 2.0 sec.-l, respectively. The heats and entropies of activation were calculated from the variation of the rate with temperature. Mechanisms for the observed rate law are discussed and the rate constants and entropies of activation are compared with those for the analogous thiocyanate reaction. A lower limit for the rate of chloride complexing of iron(II1) in 3 M sodium chloride has been obtained from nuclear magnetic resonance studies and compared with the results of the spectrophotometric kinetics studies.
+ +
The reaction in aqueous solution of ferric ion with chloride ion to form the monochloride complex FeClf2 is known to be rapid, but apparently no quantitative study of the rate had been made previously. The present work constitutes a determination Of the rate law using the fast mixing apparatus which had been applied earlier to the
study of the kinetics of the analogous complexing reaction of thiocyanate ion with ferric ion.‘ Chloride Complexing Constants.-In the interpretation of the data it is necessary to know the equilibrium quotients relating the various species (1) J. F.Below, R. E. Connick and C . P. Coppel, THISJOURNAL 80. 2961 (1958).
6390
ROBERTE. CONNICK .4ND
CLAUDE
P. COPPEL
1-01. s1
present. The principal equilibria between ferric and chloride ions a t low chloride concentration are Fe+-
+ C1-
=
FeClt-
QH
2FeOH
t-
=
=
(FeOH ++)( H. _ +) . ~_ (Fe +++)
Fez(OH)2.t4
with QH (25', p = 1.0) = 1.65 X and Qn ( 2 5 O , p = 1.0) = i l l . The equilibrium quotients were corrected to other temperatures using A H where parentheses indicate concentrations in moles values of l 0 . F and ~ ~ - 8.26kcal./mole, respectively, per liter, M. Rabinowitch and Stockmayer2 measured for an ionic strength of 1.OO. in an extensive spectrophotometric study, obtained Interpretation of Rate Data values of Q1 and Qz a t zero ionic strength and 25' As a reasonable working hypothesis, it was asof 30 f 5 and 4.5 + 2, respectively, and from the sumed that the rate law for the ferric chloride ionic strength dependence deduced complex formation could be written as FeCl++
+ C1-
= FeC12+
log Q1 = 1.51 -
Q2
=
"'
1 f 1.5C'
(FeCL +)-
(FeC1+T)TC1-) (a)
+ 0.295~
(3)
where .u is the ionic strength. Their temperature dependence results gave a value of AH1 of 8.5 f 0.2 kcal./mole a t an ionic strength of 0.61. Olerup3 obtained a value of Q1of 5.7 at 20' and p = 2.0, which is t o be compared with the value of 5.5 a t 25' calculated from equation 3 for an ionic strength of 2. Correction of Olerup's value to 25' using the A H 1 value discussed later yields 6.8 for Q1. Values of Q1 calculated from equation 3 were used in the present work. Under the conditions employed by Rabinowitch and Stockmayer2 the polymerization of hydrolyzed ferric ion4 was negligible, both optically and stoichiometrically. The work reported here was carried out a t an ionic strength (pj of 1.0 Jf where the value of Q1 obtained from equation 3 is 4.03 at 23'. This high ionic strength as compared to 0.40 used in the ferric thiocyanate study' was necessary because of the high acidities required to eliminate light absorption of hydrolyzed ferric species in the region of ferric chloride absorption. I t should be noted that there is considerable disagreement in the literature regarding the value of Q1.4a -4 change in the value of Q1 would alter the values of k , k l , k 2 and kz approximately in direct proportion to the ratio of the Q1 values. The primed rate constants in Table I11 would be essentially unaffected. The A H l value (equation 1) of 8.5 =t 0.2 kcal. reported by Rabinowitch and Stockmaye? was not used because their data indicate that somewhat more than 20% of the total ferric ion was present as FeClT- and cn. lCc as FeC12+'. Under these conditions the method of calculation which we infer from their paper would not yield accurate equilibrium quotients. Since no other value was available, A H l was remeasured, as described under Experimental; the value found was 6.0 f 0.1 kcal. Hydrolysis of Ferric Ion.--Xll data were corrected for the hydrolysis of ferric ion. Milburn and Vosburgh4 found the principal equilibria to be (2) E. Rabinowitch a n d W.H. Stockmayer, THISJOURNAL, 64, 335 (1942). (3) H. Olerup, Sucizsk. K e m . T i d s k v . . 55, 324 (1943) (4) R. M. Milburn and W. C. Voshurgh, THISJ O U R N A L , 77. 1352 (19%). (4a) J . Bjerrum, G. Schwarzenbach and L. G. Sillbn, "Stability Constants of Metal-Ion Complexes," T h e Chemical Society, London, 1967: H. Coil, R . V. Nauman and P. TV. West, ihid., 81, 1284 (1939).
Fe+++
+ Cl-
k (8)
FeC1++
k'
the integrated rate law being
(7)
where (Fe+++) is assumed to be constant. Under the experimental conditions used, with a value of Q1 of about 4 and ferric and chloride ion concentrations of 8 X and 4 X Jf,respectively, very little of either the ferric ion or chloride ion is complexed, and therefore the linearity of a log [(FeCIT+), - (FeCl++)]versus time plot does not test directly the dependence of (Fe+3) and (Cl-). Such linearity does establish, however, a firstorder dependence on (FeCI++) for the reverse rate. Such plots of the experimental data were in general linear, deviations being present randomly owing to various experimental limitations. Ferric and Chloride Dependence.-Direct verification of order with respect to ferric and chloride ion concentrations was obtained by rarying the initiai concentrations of these ions and comparing the k values calculated using equation 7. The quantity (Fe-3) in the denominator was almost negligible, %.e., &yoor less of l/Ql, and it was not necessary to know i t with any great accuracy, nor to know the mixing ratio accurately. Table I shows the data for runs made a t varying ferric and chloride ion concentrations. a given acidity i t is seen that the assumed rate law fits the data within the experimental accuracy but that the rate increases with decreasing acidity. These results in conjunction with the linearity of the log [(FeCl+t) - (FeCl++)] plots demonstrate the first-order dependence on ferric and chloride ion concenJrations over the acidity range investigated. The k values a t 25" in the last column of Table I were calculated from those in column 5 using the AH* values which will be discussed under Temperature Dependecce. Acid Dependence.-Figure 1 shows a plot of k a t 25' Z'CYSZLS 1 '(H+). Except for the points a t lowest hydrogen ion concentration, the plot is linear with a finite intercept a t l,'(H+) = 0 and can be interpreted as representing the rate law d(FeC1'+i kl(Fe+T+)(C1-) + kz (___F e & + + )C1-) (__ tl 1
( 5 ) T. 1% Siddall and W. C. vosimrgh, 1 " s (1961). (6) R. A I . hlilburn, ibid., 7 9 , 537 ( 1 9 5 7 ) .
iH
J o L - R N . ~ ~ ,73, , 4270
KINETICS OF
Dec. 20, 1039
T H E FORMMATION O F T H E
FERRIC CHLORIDE
I
280
0.2 0.3
7 . 200
I-
6391
COMPLEX
i
, 0.1 0.08
k! 0.06
--. h r4!
0
2
4
6
8
10
12
14
16
18
0.04
0.02
1/W+). Fig. 1.-The
acid dependence of k a t 25' and (NaC101 added).
p
= 1.0
+
where E = kl k2/(H+) and the back reactions have been omitted for simplicity. The values of a t (H+) = 0.90 and 0.311, which were taken from the temperature dependence data (see later), were given more weight because they represent entire series of runs. TABLE I
K ISETIC DATAON FERRIC AND CHLORIDE DEPEXDESCE (FOR p = 1.0, XaC1O4 ADDED)
2411 237 23 41 22 06 2296 2241 2368 25 75 2480 228 279 266
9 9 5 2
8 5 0 0
5 6 8 5 8 2 17 1 7 3 1 8 1 3 4
4 3 4 3 4 0 18 5 5 3 4 7 4 6 4 5 4 5 159 4 7 154
0.89 .89 . 90 .90 .90 ,156 .I56 ,156 ,156 .0622 ,0622 ,0622
26 8 25.0 22.6 20.0 20.1 88.5 95.0 130 1 109.1 183 259 228
29 29 27 28 26 125 113 118 112 261 227 253
9 4 4 7 2 8 2 0 0
At the lowest hydrogen ion concentration studied (0.0622 M ) significant deviations from the linear relationship appear. These are believed to be due to mixing limitations which become important a t these low acidities, ;.e., the slowness of mixing becomes partially rate determining. At this acidity and a t sweep frequencies of 60 C.P.S. the reaction could only be observed for approximately two sweeps; the mixing process itself took about 1 sweep (16 mseconds) for 83% mixing. The intercept and slope of Fig. 1 give values of k1 = 9.4 f 1.0 M-l set.-' and k p = 18.0 i 2.0
set.-'. Temperature Dependence.-Experiments were run covering the temperature range 16 to 32'; the results are shown in Tabl_e 11. Because of the hydrogen ion dependence of k the runs were made a t two acidities. From the data in Table I1 and the firstfive experiments of Table I, a plot was made of log k / T " K . V e n u s l / T " K . for the two acidities. Since the data showed no significant signs of curvature, the best fitting straight lines were drawn. The
TABLE I1 TEMPERATURE DEPENDENCE RESULTS (AT p = 1.0, Sac104 ADDED) Temp. ("C.)
31.29 31.74 23.95 18.16 15.97 31.72 25.03 22.23 31.45 16.97 24.00 18.40 21.23 26.24 32.28
ZFe(III)" (ZC1-)" x 108) (-M x 103)
(M
6.3 6.6 6.9 6.4 8.0 7.8 8.0 8.0 7.9 7.6 7.8 7.6 7.7 7.5 7.4
4.9 4.7 4.6 4.8 4.7 4.8 4.8 4.7 4.7 4.8 4.7 4.8 4.8 4.9 4.9
$2 0.90 .90 .90 .90 .90 .90 .90 .90 ,311 ,311 ,311 ,311 ,311 ,311 ,311
-k
(A!
-1
sec. - 1 )
59.3 66.5 24.8 12.2 9.45 69.1 30.4 20.0 154.7 23.0 62.9 28.2 40.5 74.3 161.2
Total stoichiometric concentration.
The corresponding entropies of activation a t 25' are ASl* = 2 f 6 e.u. and AS,* = 25 i= 6 e.u. The values of kl = 9.4 M-l sec.-l and kp = 17.5 sec.-l from this plot are in good agreement with the values 9.4 and 18.0 obtained from the hydrogen ion dependence results. The uncertainties were obtained by assuming a possible error of 10% in k1 and kz a t the high and low temperatures.
ROBERTE. CONNICK AND CLAUDE P. COPPEL
6392
Recently King and Gallagher7 have made calorimetric measurements on the heat of reaction 1, AH1, and found a provisional value of ca. 4.3 f 0.4 kcal. rather than 6.0 kcal. measured here. Use of their value would lower AHl* and AH2* approximately 1.7 kcal. and lower ASl* and AS2* approximately 6 e.u. The source of the discrepancy in the AH1 values is not certain. Our spectrophotometric value could be in error through failure of the assumption that the molar absorptivity of FeClf2 is independent of temperatureS; the calorimetric value is relatively sensitive to errors in the equilibrium quotient of reaction 1 a t 25O. Discussion of the Rate Law RIechanisms analogous t o those of the thiocyanate reaction' can be proposed for the two terms of the ferric chloride rate law
ki
Fe(&O),+++ f c1-
%-
Fe(H20)6Clf+
+ EI,O
Yol. 81
model, the thiocyanate ion would be expected to be attracted less strongly than chloride ion since the charge in SCN- is probably spread out through the ion. The weaker hydration of SCN- would, of course, work in the opposite direction. In contrast to the kl values the k2 values are nearly equal. TABLE I11 COXPARISON OF FERRICCHLORIDEAND FERRIC THIOCYASATE KINETICPARAMETERS Chloride"
Thiocyanate b
9 . 4 =k 1 127 rj, 10 1 8 . 0 =k 2 20.2 f 2 kL',sec. 2 . 3 =k 0 . 2 0 . 8 7 =k 0 . 0 7 k?', d l sec.-I 4.5 f0.5 0.13s 0.014 AIli' kcal. 1 0 . 6 =k 2 . 0 14.6 =t1 . 4 1 7 . 3 Z!Z 2 . 0 2 1 . 8 =t1 . 4 AH!'*, kcnl. AS1'*, e.u. -21 i 6 -10 f 5 2 1 6 10 i 5 AS?'*,e.u. Ionic strength 1.0 M . Ionic strength 0.40 M .
k l , J - 1 sec. -1 k2, see.-'
*
(a)
Until the discrepancy in AHl for the chloride reaction is resolved (see above), i t is useful to QH consider AH1'*, AHzJ*, ASl'*, and A&'*, i.e., Fe(HlO)s+++ Jr Fe(H20)60H++ H + (b) the quantities for the rate of decomposition of k3 F e e l + + and FeSCN++, which are nearly indeFe(H,0)60Hf+ f C1- -+- Fe(H2O)dOHCl+ HzO pendent of the choice of AHl. These values are listed in Table 111. The entropies of actiFe(H20)40HCl+-I- H + Fe(H20)6Cl++ vation for the chloride complex decomposition where k3 = ~ ? / Q H . Mechanisms also could be pro- reaction are 11 and 8 e.u. more negative than for posed involving hexa-coordinated activated com- the corresponding thiocyanate reaction. The difplexes, where water is released before the com- ference in ionic strength would not be expected to plexing ligand enters in the rate-determining step. produce this large a change. The explanation lies The value of k~ a t 25' and p = 1.0 is 1.1 X lo4 perhaps in the greater localization of charge on AP-' set.-', compared to kl = 9.4 M-' set.-'. the C1- than on the SCN- so that the electroFrom electrostatics, FeOH + f would be expected static effect of separation of charge in the actito react with C1- more slowly than does Fe+++, vated complex involving chloride is considerably which is opposite to the observed result. This same greater than with thiocyanate. The smallness situation exists in the thiocyanate case and was of the entropies of activation would imply that the interpreted' as being due to the weakening of the solvent is considerably oriented in the activated bonding of the hydrated waters by the negative complex in restricted configurations conducive to OH-, thus permitting easier entry of the thiocya- the separation of the ions. nate ion into the coordination sphere, or to some Rate of Chloride Complexing from N m r . Measelectronic interaction of the OH- with the Fef3, urements resulting in faster reaction with C1-. It might be Paramagnetic ions in solution cause a broadening argued that the greater rate of the hydrolyzed species is evidence for a six-coordinated activated of nuclear magnetic resonance lines of other nuclei complex. The more facile release of electrons from because of the relaxation of the nuclear spin in the the OH- group to the ferric ion could help to com- changing local fields of the paramagnetic ion. pensate better for the incomplete bonding of the It is possible to measure lifetimes of states from incoming chloride ion. relative to the corresponding such line broadening measurements. Wertz'O has measured the broadening of the behavior of HzO. I t can be argued equally well, C13j resonance by several paramagnetic ions. however, that the same effect would operate in the case of the seven-coordinated activated complex, Ferric ion produced a very large broadening efwhere the incomplete bonding of the incoming fect, whereas chromic ion a t the same concentraand leaving groups would be similarly compen- tion produced no observable broadening. Since chromic chloride complexes form and dissociate sated. comparison of the kinetic parameters of the only very slowly, i t is inferred from the above chloride and thiocyanate' reactions in Table I11 results that the rapid relaxation caused by ferric is instructive. I t is to be noted that the relative ion must be occurring almost entirely in the values of kl follow the stabilities of the complexes first coordination sphere. One can then deduce rather than the prediction from electrostatics. that the relaxation rate of the chlorine nucleus The more stable and therefore more strongly (9) Although these differences are within t h e limits of uncertainty bonded thiocyanate complex forms more rapidly of t h e individual entropies, t h e y are believed t o be significant when together, T h e large uncertainty in t h e individual values than the chloride complex. On an electrostatic considered arises from t h e resolution of t h e r a t e d a t a into two separate r a t e con-
+
z-
+
( 7 ) E L. King and K. Gallagher, private communication. ( 8 ) T h e same t y p e of assumption was made in references 2, 5 and 6.
stants.
(10) J. E. Wertz, J . Chem. P h y s . , 24, 481 (1956).
KINETICSOF
Dec. 20, 1959
THE
FORMATION OF THE FERRIC CHLORIDE COMPLEX
is equal to or less than the rate a t which chloride ion enters the first coordination sphere of ferric ion. The broadening of the full width between maxima on the derivative of the absorption curve of C135 in 3.0 M sodium chloride containing 0.1 M ferric ion was measured to be A x = 1.4 X l o 3 sec.-l a t 9600 gauss. Using the expression11
Tz
=
1 V%AV
one calculates the transverse relaxation time to be 1.3 X lo-* sec. Presumably this is an upper limit12p13to the lifetime of a n uncomplexed chloride ion before i t becomes complexed by ferric ion in the solution. From Gamlen and Jordan’s14 data i t is estimated that in 3 M C1- the complexes present are approximately: 10% FeCl++, 30y0 FeC12f and 60% FeC13. Under these conditions i t seems reasonable t o hypothesize that the principal mechanism for entry of chloride ions into the first coordination sphere of the iron will be FeC12+
+ C1-
k’
+ FeC13
and the upper limit for the rate of randomization of nuclear spin configurations will be
--d(C1-*) dt
= k’(Cl-*)(FeClz+) = k(Cl-*)
where the asterisk indicates a particular spin configuration. Therefore
I n the spectrophotometric study these rate constants were measured ki + C1- + FeCl++ k , = 9.4 M-’set.-' ka FeOH++ + Cl-+ FeOHCl+ ka = 1.1 X lo4 X-l set.-' Fe+++
On the basis of the hydroxide catalysis of the first ferric chloride complex formation, one would expect the presence of chloride on the ferric ion to catalyze further chloride addition also, and therefore the second-order rate constant for formation of higher complexes would be greater than k1. T h a t k’ is a t least ca. 30-fold greater than may be plausible, but i t is also possible that the next higher complex is involved, i.e., the chloride ions exchange on the iron by addition of C1to FeCI3 to form FeC14-. It is unfortunate that the n.m.r. measurements are not sensitive enough t o detect the relaxation where only the first complex is important.
Experimental Apparatus and Procedure.-All experimental apparatus and procedures involving the fast mixing device were identical to those reported in the earlier ferric thiocyanate study.’ In the present work, only the box type baffle was used. Since the earlier experiments, it has been learned that bubble formation is not caused by the presence of dis(11) N.Bloembergen, W W. Hansen and M. Packard P h y s . Rev., 70. 474 (1946). (12) H.M. McCounell and S. B. Berger, J . Chem. Phys., 27, 230 (1957). (13) R. E. Connick and R. E. Poulson. i b i d . , 80, 759 (1959). (14) G. A. Gamlen and D.0. Jordan, J . Ckem. SOC.,1436 (1953)
6393
solved gases in the reactants but rather by the presence of gas pockets trapped on the mixer surfaces. Two types of experiments were carried out to demonstrate this effect. First, outgassed solutions were put into the dried mixer by gravitational flow, the mixer being a t one atmosphere pressure. When fired, extreme bubble formation was observed, indicating that wall effects were very important. The next step was to attempt the elimination of such effects by filling the mixer under vacuum with previously outgassed solutions, i.c., by the normal filling operation used in the kinetic studies. This mode of filling is known to eliminate bubble formation. Once the mixer was filled, water saturated with air was forced in at the bottom of the mixer, displacing the outgassed water which was taken out a t the top of the mixer. Care was taken that no bubbles entered the mixer. The introduction of air-saturated water was continued until several times the volume of the mixer had been displaced a t the top. The bulk of the water inside the mixer was now air-saturated and no bubbles had been introduced. When the mixer was fired no bubble formation was observed, thereby demonstrating that bubble formation is not due to dissolved gases. This result does not immediately show a new method for avoiding bubble formation. The filling process described in the experiment above is not practical and in actual kinetic runs it seems probable that vacuum filling with outgassed solutions will continue to be used. It might be possible to coat the walls in such a way as to eliminate bubble trapping. Reagents.-All reagents were prepared by methods identical to those used in the ferric thiocyanate study,’ with the exception of the sodium chloride solution. Stock solutions of approximately 0.3 M sodium chloride were prepared by weight from the dried analytical reagent salt and checked by gravimetric analysis. Analytical Procedures.-The extent of reaction was determined spectrophotometrically as a function of time from the oscilloscope trace. The quantity log [(FeCl++)m (FeCl++)] (see Interpretation of Rate Data) equals log [l:g ( x b / x m ) log ( x b / x ) ] where xb, X - and x are the linear displacements on the oscilloscope of the blank, sample a t infinite time, and sample, respectively, relative to the dark current.’ Although no further experimental data were necessary in order to calculate k, it was desirable to check the experimental conditions. After each run a sample was removed from the mixing apparatus. The optical density of this sample was measured on a Cary spectrophotometer and this value then was compared with the value calculated from the trace on the oscilloscope of the kinetic run. The agreement was in general good to about 5% and this was taken as evidence that the sample removed was a good measure of the final equilibrium state of the sample observed kinetically during the run. A portion of the removed sample was analyzed for total Fe( 111)by adding excess sodium thiocyanate and observing the spectrum.’ From the known total Fe(II1) and the known initial concentration in the ferric solution a mixing ratio was calculated, and in turn the total (Cl-) was obtained. Using the total Fe(II1) and C1- cqncentrations and the equilihrium quotients for hydrolysis, dimerization and complexing, the concentrations of F e + + + , FeOH+*, F e n ( o H ) ~ +and ~ FeCl++ were calculated. From these and the previously measured molar extinction coefficients (Table I V ) , the total optical density of the sample was obtained and compared with that measured on the Cary. This comparison was generally good to about 5y0,indicating that the sample composition was that expected. Molar Extinction Coefficients.-In checking the concentrations of the kinetic runs, i t was necessary to know the molar extinction coefficients of all species present in the reacting solutions. Rabinowitch and Stockmayer’s2 spectrophotometric study was primarily a t wave lengths above 400 m g . Because of the low absorption of FeCle+ above 400 mp, it was necessary to work between 300 and 400 mp and t o determine the molar extinction coefficients in this spectral region. Three solutions were prepared, each containing 0.003764 M Fe(ClO4)s and each a t an ionic strength of 1.15. These solutions had hydrogen ion concentrations (uncorrected for hydrolysis) of 0.250, 0.0528 and 0.0308 hl. Using Milburn and Vosburgh’s4 values for QH and QD, the concentrations of F e + + + , FeOH++ and F Q ( O H ) ~ +were ~ calculated. The optical densities of these solutions then were measured in 2 cm. cells on a Beckman Model DU spectrophotomet,er a t 25
-
6394
JOHN
J. HALLAND SOLTRIEBWASSER I
i
1
Vol. 81
TABLE IV APPROXIMATEMOLAREXTIKCTION COEFFICIENTS USEDFOR CHECKJSGCOSCENTRATIOSS A , mli
sFe+aa
~ ~ ~ ~ ( 0 ~ 1 2 7 4
