1542
JAMES
/(I/ t ti I
KINGAND NORMANDAVIDSON
Vol. 80
We are now engaged in determining d In a*/dc for 12- and 9-phosphotungstic acids from measurements of cells with transference, transference number and dissociation constants. We will report on this work in a subsequent communication.
1
Appendix The correction factor CV' which is the volume seen by the photomultiplier tube in non-aqueous solvents compared to that in water may be derived with the aid of Figs. 1 and 5.
r,
-+-
r,
--
Fig 5 -Didgram of optical system used in derivation of expression for C,
where RV = ratio of volume PW to the actual volume seen by the photomultiplier tube in the presence of a liquid with refractive index n. When the angle m is sufficiently small so that sin m % tan nz, it can be shown that
may be due to the common ion effect. The lower pH favors the formation of more undissociated acid and the system thus approaches the conditions for which the light scattering treatment is valid. For the 9-phosphotungstic acid, the pH has no effect, the turbidity in pure water and a t pH of 2 being identical. This probably is due to the fact that the 9-phosphotungstic acid is so strong that the additional hydronium ion does not produce sufficient undissociated acid to affect the turbidity. In order to relate the light scattering of a nonideal substance to the molecular weight, it is necessary to revert to equation 2 . By utilizing the Gibbs-Duhem relation XI d lnf, + NZd 1n.f~ = 0 (5 ) and N z are mole fractions, it can be shown where that in dilute solutions
and the correction factor for non-aqueous solvents becomes
Thus the determination of the molecular weight requires in addition to the turbidity, knowledge of d In a*/dc. This relation is perfectly general in moderately dilute solutions.
POTSDAM, N. Y .
[COXTRIBUTION No. 2260
and z p = z
It follows that
(a+:+
rl
+ w/2
n.\/ll+;;i>
(9)
The light radiated by the excess volume is only half as intense as that radiated by the volume L2w.l1 The ratio of the light scattered by the volume 1% to the total volume seen by the photomultiplier tube is
(11) C. I. Carr and B. H. Zimm, J. Chem. Phyr., 18, l G l O (1950).
GATESAND CRELLINLABORATORIES OF CHEMISTRY, CALIFORNIA IXSTITUTE OF TECHNOLOGY ]
FROM THE
Kinetics of the Ferrous Iron-Oxygen Reaction in Acidic Phosphate-Pyrophosphate Solutions B\'
JAMES
KING.4ND
xOR?riAN
DAVIDSOS'
RECEIVED OCTOBER 15, 1957 The rate law for the ferrous iron-oxygen reaction in acid solutions (PH -1-2) containing phosphate and pyrophosphate anions is - d(Fe++)/dt = kl(Fe++)(HnPOn-)2Po, k2(Fe++)(H2P;07-)Po, where k l = 1.08(+0.06) X atrn.-'mole-? liter2 sec.-1 and kz = 2.13(=!~0.05) X 10-2 atm.-l mole-' liter set.- a t 30" ( p = 1.0-1.1 mole/liter, SaC104). The activation energies are aH1* = 21( 1) and AH2* = 6( +1) kcal. The rate law and the values of k l and k? both show that H&'?07and HzP04-are independent catalysts and that the unusual quadratic dependence on (HzPO,-) is not due to the equilibrium 2HzP04- F? HZP207- HiO. The mechanism of the reaction presumably involves a s the rate-determining step either the one electron transfer process FeII 0 2 Fe"' 0 2 - or the two-electron process Fe" 0 2 + FeIv 02=, with iron in the transition state stabilized by the complexing phosphorous anions.
+
+
+
+
-.f
+
+
+
Cher and Davidson2 found that the rate law for the oxygenation of Fer*in phosphoric acid solution
is -d(Fe++) 'dt = kl(Fe++)Pop(€12P01-)2.The quadratic dependence on (H2POI-) is somewhat
(1) We are indebted t o the Atomic Energy Commission for support of this research under Contract A T ( l l - l ) - 1 8 8 ; and to t h e Danforth Foundation and t h e General Education Board for fellowships to one
of us ( J . K . ) . This paper was presented in part a t the 129th National Meeting of t h e A. C . S., Dallas, April, 1956. ( 2 ) M. Cher and N. Davidson, THISJ O U R N A L , 77, 793 (1955).
April 5 , 19%
IROS(II)-oXYGEN REACTIONS I N ACIDIC
PHOSPHATE-PYROPHOSPHATE
SOLUTIONS1533
The time lapse between preparation of the samples and unusual. A linear dependence would be expected actual observation of the change in oxygen pressure introin view of: (a) general experience with this kind of duced an error not greater than 3%. This was checked by reaction; (b) the reported first-order dependence determining the F e concentration by permanganate tion (F-) for the fluoride catalysis of the Fe", O2 tration in such a solution three minutes after mixing. All the glass joints were lubricated with Apiezon grease reaction3; and (c) the reported fact that the first (M). Excess grease added to the reaction vessel did not complex formed between F e + + + and phosphate affect the rate. It has been shown2 previously that the reanions in acid solution contains one phosphate per actions taking place in the byarburg reaction flasks are not iron, being either FeHP04+ or FeHZP04++.4s5 diffusion controlled. The quadratic dependence on dihydrogen phosResults phate concentration would be explained if the actual catalyst were dihydrogen pyrophosphate, Effect of FelI and FeIII Concentrations.-The formed in equilibrium amounts according to the rate of oxidation is first order in ferrous iron conreaction centration. This is evident from a study of the variation of initial rate with initial (Fe") a t fixed 2HzPO4HzP207HsO phosphate and pyrophosphate concentration (Table This hypothesis and a general interest in the effects I). Throughout this paper, ill and F stand for of pyrophosphate stimulated the present work. mole liter-' and formula mt. liter-', respectively. Spoehr6 and Smith and Spoehr' have reported The molar concentrations of H3P04, H2P04-, that there is an accelerating influence of pyrophos- H3P207- and H2P207-in Table I are calculated asphate on the Fer1-02 reaction. The latter authors suming acid constants of 0.020 and 0.021 M for claim that the rate law is - d(FeI')/dt = k(Fe") (02) ; H3P04 and H3P207-, respectively. but a later studys of the effects of stirring indicates that the reaction rate was diffusion controlled unTABLE I der the conditions employed. EFFECTOF Fe" ON INITIAL REACTIONRATE Other references to studies of the FeI1-O2 reacm = -d ln(Fe")/dt (hr.-l), ( H + ) = 0.0177 M , (HItion in various media are given in another paper P o l ) = 0.188 M , (HzP04-) = 0.212 M , (HoPzOT-)= from this Laboratory.9 0.0023 M ,(HzP207-) = 0.0027 M , p (ionic strength) = 1.0 - 1.1 M(h'aClO4), Pon = 151 mm., T = 30' Experimental 0.003 (Ferr)o ( F ) 0.010 0,020 The rate of 02 uptake was measured by a manometric ++
+
method with a Warburg apparatus, as described previously.2 T h e apparatus was well thermostated and had provisions for vigorous shaking of the reaction mixtures. Reagent grade ferrous ammonium sulfate and sodium hydroxide were used. Sodium perchlorate, for maintaining ionic strength, was prepared by neutralization of known amounts of 85yo perchloric acid with sodium hydroxide. The commercial redistilled water used in the initial experiments was found t o contain trace amounts of copper. For all the results reported here, water was prepared by redistilling the commercial distilled water in a Pyrex, electrically heated still, to remove the traces of copper. The necessary precautions were taken to exclude dust from the vessels and each reaction vessel was pre-rinsed with the redistilled water. The desired H ~ P O ~ - H Z P O Ibuffer solutions were prepared by the appropriate neutralization of reagent grade phosphoric acid with standard sodium hydroxide solution. Pyrophosphate solutions were prepared from weighed quantities of reagent grade Na4P20~.10H20 and checked acidimetrically. The procedure was t o dissolve separately ferrous ammonium sulfate and sodium pyrophosphate in phosphate buffer. ~ - were made for the Corrections of the H ~ P O ~ - H Z P Oratio effects due t o the conversion of P207-4 to H ~ P 2 0 7 - and ~ H3P207-1. Varying amounts of the two solutions were placed in the 15-1111. reaction flasks, the total volume of solution always being 5 ml. The flasks were then quickly attached to the manometric apparatus and the shaking mechanism started. It required 3-5 minutes for vapor pressure and temperature equilibrium to be established and the initial rapid changes in pressure t o cease. The pressure reading a t this time was taken as that for zero reaction. For reactions in pure oxygen, the gas was bubbled through water, filtered through glass wool, passed into the system through the stopcock a t the top of the manometer and out through an outlet on the side of the reaction flask. Approximately l / 2 liter of gas was passed through the system in about five minutes. (3) J. Weiss, Ezperientia, IX.61 (1953). (4) 0.Lanford and S . Kiehl, THISJOURNAL, 64, 292 (1942). ( 5 ) T.Yamane and N. Davidson, unpublished work in this Laboratory.
(6) H . A. Spoehr, THIS J O U R N A L , 46, 1494 (1924). (7) J. H.C.Smith and H. A. Spoehr, i b i d . , 48,107 (1926). (8) A. B. Lamb and L. W. Elder, ibid., 63, 137 (1931). (9) R. E. Huffman and N. Davidson, ibid., 78, 4836 (1956).
m (hr.-I)
.0789
,0772
.os00
It was not practicable to vary the Fe'I concentration over a larger range than that displayed in Table I. With lower concentrations, the manometer change due to reaction is small compared to fluctuations in the control (no Fe") runs. With higher concentrations, the reaction is too fast. When -In (Fe") is plotted against t, fairly good straight lines (cf., Fig. 1 of ref. 2 ) are obtained. A t about 60% reaction, there was a decrease in slope of 10-20%. Usually a t about 70% reaction, a white precipitate, believed to be ferric pyrophosphate, slowly formed. Addition of ferric ion initially produced the same phenomena immediately. Therefore, a detailed study of the kinetic effects of Fer" addition did not appear to be profitable. Values for rate constants were taken from lines drawn through points up to about 40y0 reaction. Effect of Phosphate Concentration.-In agreement with Cher and Davidson, we find that -d In(Fe")/dt = ~ I ( H ~ P O ~ - ) ~ PThese O , . results are given in Table 11. TABLE I1 PHOSPHATE CATALYSIS OF THE Fe"-O1 REACTION (30°, p = 1.0 - 1.1 M , NaCIOl) pol,
hi. atm. - 1
(Fe")o,
(&POI),
:HnPOa-),
M
atm.
M-2 hr.-l
0.0100
0,200 .200 ,415 .415 ,415 .415 ,800
0.200 I200 ,389 .389 .389 ,389 ,200
0.198 .942 ,198 .942 .198 ,942 .198
4.00 3.95 3.96 3.78 3.64 3.56 4.43
M
.0100 .0100 .0100 .0050 .0050 .010
M
Av. kt = 3.90 (50.22, mean error)
1544
JAMES
RINGAND NORMAN DAVIDSON
The values of kl in Table TI are generally somewhat lower (l0-20%) than those reported by Cher and Davidson2; furthermore the ratio of rates in oxygen and air was close to the theoretical value of 4.8, whereas Cher and Davidson observed about 4.0. These differences probably are due partly to the use of redistilled water containing no C u + + impurity in the present work, although i t seems unlikely that this is the entire reason for the numerical discrepancy. The other causes however arc unknown. Effect of Pyrophosphate Concentration.---Pyrophosphate is an effective catalyst for the Fer*-0, reaction. This is evident, for example, hy notiIiq that the rates recorded in Table I are about 5 times faster than predicted for phosphate catalysis alone. Yost and Russell’O quote values for the ionization constants of pyrophosphoric acid a t 18” as foiiows: K~ = 0.14, K~ = 0.011, K , = 2.1 x 10-7, K 4 = 4.06 X in 1 AT KCl, K 2 = 0.027, Ka = 3 X The species present in significant amounts with 0.01 < (H+) < 0.07 are HYPP07-and H2P107=; i t is accordingly necessary to determine a value of K I under the conditions of our experiments. This was done using a pH meter to measure the hydrogen ion concentration of solutions containing varying amounts of H3P207- and H2P207=a t p = 1.0 (NaC104). X NaCl salt bridge was used because of the insolubility of KC104. The pH meter was calibrated to read 2.09 for 0.00814 44 HCl in 1.00 Af NaC104 at 30’. The results are shown in Table 111. We have used K, = 0.021 M for the concentration ionization quotient of H3P20;-in interpreting the kinetic results (cf., the discussion in footnote 13).
TABLE IV RATESIN THE PRESENCE OF PYROPHOSPHATE (Fe“),, = 0.010 M , T = 30,’, p = 1.0-1.1 111 (SaClOd) Por = 151 mm., k 1 = 0.793 M-* hr,-I (H +), A4
0 0650 0546 0402 ,0176 0176 01;s 0169 0 I. $57
’
TABLE I11 SECOXD IOSIZATION QUOTIESTOF PYROPHOSPHORIC ACID = 1.0 ;If,solutions prepared from staridart1 “ 2 1 and S a 4 P 2 0 7solutions.)
MEASUREMEST OF
( T = 30”, p
up 0.00955 ,00912 .0126 ,0120
THE
(HIPzOT-),
(HzP20i-j.
1.1
If
0,003871 ,00918 ,0118 .0124
0.0021x
.00213 ,00187 . 00 180
(IO) D.
hl. Yost and H. Riissell, “Sy-tematic Tnorgariir ChPmis. S e w Yirr-k. S T I Q l 6 , P 2:’s.
t r y , ” Prcn!icr-Hall, Inc.,
I
15.00 15.91 15.68 15.05 15.10 15.58 14.69 15.29
- d ln(Fe++)/dt = k,(I&PO,-)*Po~ -t k2(HzP&’)Po~ Effect of Surface. Xate measurements in which Pyrex glass woo1 v as added to the reaction flasks were performed in order to investigate possible surface cJtalytic effects. The surface area of the glass fihers2 is estimated as 2300 cm.2 g.-’. The surface area of the reaction flasks is about 50 cm.*. Refore introduction into the reaction flasks, the glass wool was heated to 500’ in an oven for an hour, v ashed vith hot aqua regia, rinsed copiously with nater. dried and transferred to the cells. The resulis, presented in Table V, indicate that there is :I iieyliyilAc amount of surface reaction. TABLE V
.I I
The results of a set of runs in mhich (H,P04-), (H3P20i-) and (HrP,07-) are all varied independently are exhibited in Table IV. These results show that the phosphate and pyrophosphate catalysis are independent and additive; and that the pyrophosphate catalysis is due principally to, and is first order in H2P207=;i.e., that the rate law is -d ln(Fe”)/dt = kl’ (112POa-)2 f k2’ (H2P20i=) (in air, 30”). This result is demonstrated by the constancy of the calculated values of kz’, taking k l ’ = 0.794 AP2hr.-l, with (H2P04-) varied by :I factor of 2. (H2P207-) varied by a factor of 5.7, and (HsP207-)/(H2P2OiP)varied by a factor of 3,s. all independently. Unfortunately, a thoroughly satisfactory study of the effect of O2 pressure on the pyrophosphate reaction path was not carried out. One series of
0 . 00305 0.765 0.235 0.00945 ,268 .01800 . 00730 ,732 ,333 .03280 , 0 1720 .667 .212 ,00225 . 00272 ,188 .427 .00602 00698 .377 .431 .00770 . 00930 ,373 ,435 .00850 . 01050 369 ,224 ,00424 . 00576 ,176 Av. k?‘ = 15.29 ( 1 0 . 3 3 , mean error)
runs vas made a t a time when difficulty with nonreproduci1:le results was being encountered. This series gave ratios of rates in oxygen to rates in air of 3.7-4.3. The air rcsult: showed more scatter than the oxygen results. Coinparison of the most consistent oxygen results obtained a t this time with the consistent air results (Table IV) obtained later gives a ratio of 4.7 ( f0 2 ) . On this basis it seems to us to be clear that the rate of the pyrophosphate catalyzed reaction is essentially proportional to the oxygen pressure and v e ilrite
ICZ,
0.0289 ,0212 ,0200 ,0170
Vol. 80
iii
=
0 030
.02c1 020
. 020 ,020 ,020 .010 ,010
THEEFFECTOF SURFACE ON REACTIOX RATE d lniFe+”)/dt (:r.-ll, p = 1.01-1.1 Af(NaCIO,), T = 30 , PO, = 151 rnm.
0 020 ,020 ,0181 ,0181 .(I165 .01G5 ,0143 .0143
0.200 ,200 ,210 ,210 ,219 ,219 ,234 ,234
0 0 0.00215 ,00215 ,00448 ,00448 ,0083 ,0083
50 985 50 726 50 1007 50 650
0.0396 .0264 ,0625 ,0534 ,1025 ,1040 ,179 ,200
Effect of Temperature.-A set of r u m was performed a t 20’ in air at (H+) = 0.017-0.024, with variable amounts of pyrophosphate. These results gave kl’ (air, 20”) = 0.25 (rt 0.01) M-* hr.-I and k2’ (air, 20*) = 10.70 ( r t l . 0 ) hl-’ hr.-I. For this calculation, i t is assumed that the ionization constant of HzP207- does not change very much between 20 and 30’. It is known that K I and IC2 for HsPQ do not change very much. The activation energies for the phosphate and pyrophosphate p3ths are calculated to be 21 (*1) and 6 (kl)
.April 5 , 195s
IRON(II)-OXYGEN REACTIONS I N ACIDICPHOSPHATE-PYROPHOSP€IATE
SOLUTIONS
1545
It is very unlikely that this estimate is wrong by a factor of more than lo2. It therefore is highly probable that kllkz does not equal Kh, z.e., that Discussion the calculated ratio between them of 7.5 X lo3 is We may summarize the results of the experi- not all due to experimental error and errors in estiments with the rate law mates. There are other arguments that discredit the - d ln(Fe++)/dt = ~ I ( H z P O I - ) ~ P4-O~Z(H~PIO~-)I)POZ ~ (a) withkl = 3.90 (10.22 mean) atm.-l hr.-l (or k1 hypothesis that the catalytic effect of phosphate is = 1.0s (k0.06) X atm. sec.-l) and k, = due to pyrophosphate maintained a t equilibrium by 76.8 (h1.66) a h . - ' h1-l hr.-l (or k2 = 2.13 reaction b. The hydrolysis of pyrophosphate is (d~0.05) X 10-3atm.-1 M-'sec.-l)at 30Oandactiva- known to be too slow to maintain such an equilibtion energies of 21 (fI) and 6 ( * 1) kcal., respec- rium,14 but it can be imagined that there would tively. Of course, the result does not mean that be a catalytic effect of iron ions for reactions b. H3P107- is not a catalyst; but the data indicate However, if such an equilibrium were maintained, that i t is less than, say, 10% as effective as Hf- the pyrophosphate added in our experiments would Pz07-. Correspondingly, i t is quite possible that have hydrolyzed rapidly and almost completely, catalytic effects due to HP207- would be significant thereby increasing the phosphate concentration a t higher pH's where the concentration of this ion slightly and having an imperceptible effect on the rates. is larger. The mechanism of the FeI1-O2 reaction for the The results show that the quadratic dependence case that the rate is first order in FeI1 and first oron (H2P04-)is not due to the equilibrium der in O2 has been discussed frequently b e f ~ r e . ~ * ~ , g 2HzPO4HzP207' H20 (b) The two most attractive possibilities may be written schematically as
kcal. mole-'. Cher and Davidson gave 20 ( A 2 ) for the former.
+
Jr
If such were the case, K h = k d k , = 0.051 M-l. We shall now show that available thermodynamic data and reasonable estimates give Kb = 6.8 X 10-6 A 4 - I (with an uncertainty of a factor of perhaps 10-100). Therefore, the observed value of kll/k2 is too large by a factor of about lo4. For the reaction HzPOd-
+ HPOI'
----f
HP207'
+ Ht0
(c)
5810 (=t130) cal. mole-' l1 (in solutions with p 0.4 M a t 25'). From the empirical formula of Connick and Powell,12 we estimate the entropy of HP207=as -5.4 e.u. and therefore, for reaction c, A S = -1.4 (f 4, estimated) e.u. Therefore A P (reaction c, 30') = 6235 (f 1200), K , = 3.4 x M-l, uncertain by a factor of 7.5. The thermodynamic ionization constant of H2P04- is 6.4 X lo-*; a t p = 1, we take 2 X lo-' M . For the ionization constant of H ~ P 2 0 7a t~p = 1 we take AH
=
N
1.0 x
104.13
Therefore
+
H z P 0 4 - HP04' = HP207' HzPOI- = HPO4H+ Hf HP207= H9P207'
+
+
4-H 2 0 3 . 4 X
(c)
3 x 10-7 1 . 0 X.106
and adding, we get 2HzP04'
= HtPz07'
4- HzO
+ +
+ +
FeII 0 2 FelIl HOz (12) Fer1 HOt +Fe"1 HzOl (3) H202 +further oxidation (fast') FeII (4)
+
or
+ FeIV + H 2 0 ~ 0 + HlO2 +further oxidation
FeII
FeII
0 2
(5~3)
(4)
There is a t present no compelling reason for favoring one path or the other. The occurrence of the first scheme would be proved by observing inhibition by FeIII, corresponding to competition between reactions 2 and 3. I n the present case i t was not practicable to search for such an effect because of the formation of complex ions and insoluble solids containing Fe"' and pyrophosphate. Pyrophosphate is a good complexing agent for FelI1 and undoubtedly also for Fe'". Its catalytic effectiveness probably is due to the stabilization of the transition state for reaction 1 or reaction 5 by complexing the iron ion in the transition state molecule, as suggested by Weiss. A s pointed out prev i o ~ s l y there ,~ is a correlation between the complexing a0inity of an anion X- for FelI1 and its catalytic effectiveness in the bimolecular Fe"-Oz reaction. PASADENA, CALIFORNIA
6.8 X
(b)
-
-
l((CHd4NCI) at 25', where brackets and parentheses indicate activities and concentrations. respectively. We estimate Y H 0.76, so that the concentration equilibrium constant is 1.0 >: 10-4 M. These authors give [Hfl(HzPr0r')/(H1PzOr-) 6.0 ;< 10-1 at p = 0.1 at 25', from which we estimate Kz 8 X 10-4 M at p 0.1 1.0 and 25'. This is to he compared with the value 0.021 M at p and 30' which we have used (cf. Table 111). (14) D. 0. Campbell and M. L. Kilpatrick, i b i d . . 76, 893 (1954).
p
(11) J. M. Sturtevant and N. S. Ging, THIS JOURNAL,76, 2057 (1954). (12) R . E. Connick and R . E. Powell, J . Chcm. Phys., 21, 2206 (1953). We are indebted to Professors Connick and Powell for correspondence concerning this matter. (13) S. hl. Lambert and J. I. Watters, THIS JOURNAL, 79, 4262 (1957), give 7.6 X 1 0 7 for the quantity [H +I (HP*O~')/(HIP,O~-)at
- -
--
