EPHRAIM BEN-ZVI
2698
characterized by pl = 1200 D. and another particle whose main orienting force (producing a positive An) Was characterzed by (maE - ~ 2 =~ 1.2 ) x lo-’’ ~112.~.
Conclusiono--Riearl~ and many low molecular weight globular proteins orient so rapidly that one cannot measure the rise and decay of these times of their birefringence. The calculations show that, so long as one can measure the equilibrium birefringence throughout a sufficiently wide voltage range, electric birefringence studies
VOl. 67
should still yield useful information about their electric and optical properties. As consideration of only cylindrically symmetric models may be inadequate in many cases, whenever possible, the optical and electrical polarizabilities should be completely specified. Acknowledgments*-The authors are indebted to Dr. M. J. Shah for providing manuscripts of some of his work Prior to Publicatsion, to Mr. E. Tinoco for his assistance with some of the Fortran programming, and to Dr. IC. Yamaoka for his helpful criticism.
OXIDATION OF PHOSPHOROUS ACID BY PEROXYDISULFATE. I. KINETICS OF THE REACTION I N NEUTRAL SOLUTION’ BY EPHRAIM BEN-ZVI~ Department of Chemistry, Immaculate Heart College, Los Angeles 27, California Received June l Y , 1963 Kinetics of the oxidation of phosphorous acid by peroxydisulfate Fas investigated in neutral solution. The experimental rate law, d(S208-2)/dt = [kl kz (ZH~P0~)]’/z(S~O~-2)8/~, was adequately explained by a chain mechanism, initiated by two parallel reactions. The rate constants were determined a t three teniperatures between 48 and 57’, and an attempt was made to estimate activation energies of the elementary processes.
-
+
Introduction Peroxydisulfuric acid, H2S20s,and its salts are powerful oxidizing agents. The standard potential of the half-reaction
SzOs-2
+ 2e-
= 2S04-2
(1) is 2.01 v . ~ ;yet, many of its reactions are slow. Kinetically, peroxydisulfate presents an interesting case as its reduction can occur by means of several distinct mechanisms. Kumerous reactions of peroxydisulfate have been investigated. The reader is referred to two reviews which appeared re~ently.4.~ Phosphorous acid, H3P03, is a good reducing agent particularly in basic solutions. Standard potentials for the reduction of &PO4 to H3P03are -1.12 and -0.276 v., in alkaline and acidic solutions, respectively.6 Xot many kinetic investigations have been reported on the oxidation of phosphorous acid. It appears that here, too, several distinct mechanistic paths are available for the process. Mitchell studied the oxidation of phosphorous acid by iodine in acid solution.7 The work was extended by Griffith and McKeown.8 Similarly, with the rethe oxidation of actions of hypophosphorous HaP03in an acidic solution involves a general acidcatalyzed equilibrium between the “normal” and the “active” forms of the acid. (1) Presented, in part, a t the 144th National Meeting of the American Chemical Society, Los Angeles, Calif., April, 1963. (2) (a) A grant from the Petroleum Resesrch Fund is gratefully acknowledged: (b) Patricia Perez assisted in part of the experimental work. (3) W. M. Latimer, “The Oxidation States of the Elements and their Potentials in Aqueous Solutions,” 2nd. Ed., Prentice-Hall, N e d York, N.Y., 1952, p. 78. (4) D. A. House, Chem. Rev., 62, 183 (1962). (5) W. K. Wilmarth and A. Haim, in “Peroxide Reaction Mechanisms,” edited by J. 0. Edwards, Interscience Publishers, New York, N. Y . ,1962, PP. 175-226. (6) Reference 3, p. 107. (7) A. D. Mitchell, J . Chem. S a c , 1’23,2241 (1923). (8) R. 0. Griffith a n d A. MoKeown, Trans. Faraday Sac., 36, 766 (1940). (9) W. A. Jenkins and D. M. Post, J . Inorg. Nuel. Chem., 11, 297 (1959), and references quoted in it.
acid
HJ’Os(normal)
+iodine
HsPOa(active) -+ products
(2) pH dependence of the reaction in neutral solution indicated that only the monohydrogen phosphite ion, HP03-2, is being oxidized; no measurable reaction between 1 2 and H2P08-was detected.* Certain other reactions of phosphorous acid involve, probably, free radicals.10-11 We have observed that peroxydisulfate oxidizes H3P03 over a wide range of hydrogen ion concentration. The present paper reports the results of the investigation in neutral solution, where phosphorous acid is present as the HzPO3- and HP03-2ions.12
Experimental Materials.-Preliminary experiments indicated that the reaction was slower in redistilled water than in the commercial distilled water. Therefore, redistilled water was used in all kinetic measurements. It was prepared as described elsewhere,13 except that the KHSQa step was omitted. Stock solutions were prepared from reagent grade chemicals. Potassium peroxydisulfate was recrystallized from the redistilled water. All other chemicals were of the best available grade and were used without purification. Phosphorous acid was neutralized by the addition of solid NaQH before diluting to mark in the volumetric flask. Xitrogen was the Matheson prepurified gas.13 Procedure.--Predetermined volumes of all the reagents, except peroxydisulfate, were pipeted into the reaction flasks, which were Pyrex gas washing bottles with fritted-glass dispersion tubes. KzS~OE solution was placed in a separate flhsk. Nitrogen was bubbled through all the solutions during the duration of an experiment. rlfter deaeration a t room temperature and equilibration with a constant temperature bath, the reqction was started by pipeting an appropriate volume of KzSzOs solution into the reaction vessel. (10) N. Kornblum, A. E. Kelley, and G. D. Cooper, J . Am. Chem. Sac., 74, 3074 (1952). (11) K. Nertz and C . Wagner, Ber., 70B,446 (1937). (12) HsPOs is a dibasic acid. cf. textbooks of inorganic chemistry, e.g.,
W. 3%.Latimer and J. H. Hildebrand, “Reference Book of Inorganic Chemistry,” 3rd Ed., Macmillan and Co., Ltd., London, 1951, p. 229. (13) E. Ben-Zvi a n d T. L. Allen, J . Am. Chem. Soc., 88,4352 (1961).
OXIDATION OF PHOSPHOROUS ACIDBY PEROXYDISULFATE
Dec., 1963
Aliquots were withdrawn a t intervals and analyzed for peroxydisulfate by introducing them into an acidified Fe(I1) solution. Excess Fe(I1) was back titrated with standard Ce(1V) in the presence of NaBr.I4
2699
50
Results Stoichiometry.-Amording to the equation
+
S ~ O S - ~&Po3
+ H20 = 2S04-2 +
+ 2H+
40
(3) one mole of H3P03 disappears per mole of peroxydisulfate. This was verified when a solution 0.0060 M in Kzs20s and 0.0143 M in H3P03was allowed to react for several hours at 65". When no peroxydisulfate could be detected, the solution was found, by an iodometric analysis,15 to contain 0.0081 M H3P03, a decrease of 0.0062 mole of H3POsper 0.0060 mole of SZOS-~. The Rate Law.-The reaction is 3/2 order in peroxydisulfate. Very good linear plots, down to two halflives, were obtained when (S20s-2) was plotted vs. time. The rate constants, calculated from the plots, did not change when the initial concentration of peroxydisulfate was varied between 4.50 X loe3 and 30 X M (at 0.125 M HaP03). The dependence of the observed rate constant on the concentration of phosphorous acid is represented by the equation kobsd =
[hf h(zH3PO3)
(4)
where (2H3P03) is the formal concentration of phosphorous acid. Plots of k2&d vs. (2H3P03),at three temperatures, are shown in Fig. 1. pH Dependence.--The present work was carried out in neutral solution, where phosphorous acid was present as its salts, E2P03-and HP03-2. Knowing that only HP03-2 reacted with the halogens,* it was of interest to determine the effect of p H on the rate of oxidation of phosphiorous acid by peroxydisulfate. Experiments in the p:H range 5.5-9.5, where the ratio (HP03-2)/(H2P03-) varied from 0.2 to 2000,16 failed to reveal any dependence of the rate on the hydrogen ion concentration. Humerous experiments were carried out at 54.2' with 0.030 Ad H3P03, 0.250 M total phosphate buffer, 0.0080 or 0.0075 M initial K2S20s, and 1.05 M ionic strength, maintained constant by the addition of Na2SO4. The results can be divided into three groups: (a) Eighteen runs in the pH range 5.5-7.5, with an average k of (2.24 A 0.25) X M-'/a sec.-l. (b) Six experiments in the pH range 7.9-9.3, with an average IC of (3.30 :k 0.15) X M - ' l 2 sec.-l. (c) Runs at pH above 9.5 presented in Table I. The lower rate in the runs below pH 7.5 was caused by impurities in the acidic phosphate buffer, HJ'04--. TABLEI E X P E R I ~ ~ EAT XT HIGHER S pH" PH
10sk, , ~ - ' / 2
see. -1
9.32 3.10 9.62 1.70 10.18 1.10 10.78 0.383 11.26 ,183 u0.0060 M K2S208,0.030 A4 H,PO,,O.250 M K,HPOa, variable NaOH and Pu'akDd, 1.05 .Mionic strength, 54.2'. (14) I. M. Kolthofl and E. ;\f. Carr, Anal. Chem., 86, 298 (1953). (15) R. T.Jones and E. H. Swift, ibzd., 25, 1272 (1953). (16) A value of 6.6 X 10-7 f w the second dissociation constant of HsPOp at 1 M ionic strength was taken from ref. 8.
OI'
4 30 I
8 "2
3
3
s 20
10
0.1
0.2
0.3
0.4
0.5
(Z HsPOs), M .
Fig. 1.-The dependence of the observed rate constant on the concentration of phosphorous acid, 0.0060 M K&Oa, 0.050 M KzHP04.
Ample evidence was accumulated in support of this argument, The rate constant was close to 3.3 X lo-* in the absence of any buffer a t pH 6.6. Introduction of the acidic phosphate decreased the rate, in proportion to the concentration of H2P04-. Recrystallization of KH2P04,or replacing it with NaH2P04 (experiments were carried out with the buffer obtained from three different sources), H2S04, H3P04, HC104, or KHS04 did not increase the rate. No H2P04- was added to the runs above p H 7.5. All the six runs described before contained 0.250 M KzHPO4 and various amounts of NaOH. Their rate was identical with the rate in the absence of any buffer. I n order to verify that the faster rate at a higher pH was caused by the absence of impurities in the acidic buffer, enough NaOH was added to 0.250 M KH2POI to raise the p H to 9; yet this run was significantly slower than the six runs a t a higher pH and belonged in the group of 18 experiments with KH2PO4 present. The rate falls off rapidly above p H 9.3, as shown in Table I. This is caused, most probably, by impurity (ies), which inhibits the reaction strongly when it is present in a basic form, but does not affect the rate in its acidic form. The order of the reaction changes a t a lower pH. Preliminary experiments indicated that the acidic reaction was, apparently, first order in peroxydisulfate and independent of the concentration of H3P03. The reaction a t low pH is now under investigation. Effect of Oxygen.-The reaction was investigated under nitrogen, although the rate in neutral pH was not much different in air-saturated solutions. The presence of O2 manifested itself ahi a slight induction period.
2700
Vol. 67
EPHRAIM BEN-ZVI
Preliminary experiments have indicated that oxygen inhibition is more pronounced in acidic solutions. Salt Effect.-No salt effect has been observed in the reaction. Addition of Na2S04, NaC104, or K2HP04 did not have any effect on the rate. CuSO4 catalyzed the reaction, whereas AgN03 had no effect. Inhibition by Allyl Acetate.-Allyl acetate is an effective scavenger of sulfate radical ions and can be used to isolate the chain-initiating step in the reactions of peroxydisulfate. l 3 l7 Several experiments have been carried out a t a constant concentration of K2S2OS, allyl acetate, and phosphate buffer, but variable H3P03. The runs were plotted on a semilogarithmic paper and first-order rate constants were evaluated. These are presented in Table 11. TABLEI1 FIRST-ORDERRATECONSTAXTS IN THE PRESENCE OF ALLYL
ACETATE^ lo%,
(ZH3P08)
hr.-1
4 78 .loo 5 00 .200 G 15 ,400 7.76 a 0.0060 M K2S208, 0.100 M phosphate buffer, 0.046 M allvl acetate, G3.1°, pH 6.
where a, b, etc. are the rate constants for the corresponding reactions in the mechanism. Equation 7 agrees with the experimentally derived eq. 4,when
IC,
s208-2+
SzOs-2
(5a)
2so4-
+ H2PO3- --+ SO,- +
+ HPO3- (5b) Sob- + He0 +HS04- + OH OH + H2P03- +H2O + HP03(5d) HP03- + SzOs-2 -+H P 0 3 + + SO*- (5e) HP03- + HP03- +HPO, + HP03-2 (5f) HSO+-
(ZC)
followed by a rapid acid-base type reaction of HP03 with water. HPOB
+ H2O --+ H2P04- + H +
(6)
Application of the steady-state treatment leads to the rate law
+
-d(S208-*)/dt = [e2u/f e2b/f(H2P03-) 1’” X
(7)
(sz0s-2)3/2
(17) I. M. Kolthoff, E. J. hleehan,and E. 11.Carr, J . Am. Chem. Soc., 76, 1439 (1953).
e2u/fand ic? = e2b/f
(8)
H2P03-, chosen to represent the main species of phosphorous acid in the mechanism, can be replaced by HP03-2. The experimental results do not show any preference for one of the salts over the other. Reactions 5c and 5d may be combined into a single step
Sob-
+ &Po3- +HSOI- + HP03-
(5cd)
eliminating, thus, OH radicals from the mechanism. The derived rate law would be the same. The kinetic data do not distinguish between the two alternatives. It was hoped, that by investigating the reaction a t a higher pH, where the hydroxyl radical is converted to its conjugate base,18according to
0.050
Discussion The Mechanism.-The inhibition of the reaction by allyl acetate, the effect of small amounts of impurities on the rate, its fractional order dependence on the concentrations of the reactants, and the necessity to use NaBr in the ferrometric analysis,l4 strongly suggest a chain mechanism for the reaction. General features of chain reactions of peroxydisulfate have been recently The reactions can be initiated either by a homolytic cleavage of the 0-0 bond in peroxydisulfate, or by a reaction between peroxydisulfate and the reducing agent. The rate law depends on the chain-initiating and terminating processes. The following mechanism is proposed for the reaction between peroxydisulfate and phosphorous acid in neutral solution.
=
OH
+ OH-
==
0-
+ H20
(9)
the problem could be resolved. The independence of the rate law, however, of the rates of reactions 5c and 5d renders it independent of the reaction 9 as well. The falling off of the rate of the over-all reaction a t 8 higher p H (Table I) must be, therefore, attributed to impurities, unless the mechanism of the reaction changes a t a higher pH in such a way as to make reaction 9 important. The problem was not investigated. The simultaneous occurrence of two chain-initiating processes, 5a and 5b, is required by the form of the rate law. Evidence for the presence of two competing chaininitiating reactions is prorided by the experiments with allyl acetate, where SO4- is removed effectively by the scarenger, the chain does not form, and one measures the chain initiation only. When the rate constants from Table I1 were plotted us. (2H3P03)a straight line resulted, indicating that in the presence of allyl acetate the rate law is -d(Sz08-2)/dt
=
[A
+ B(ZH3P0,)](Sz08-2)
(10)
with A = 4.25 X hr.--1 and B = 8.70 X M-l hr.-l. This means that two reactions take place in the presence of allyl acetate, one of which is zero order and the other first order in phosphorous acid. The two chaininitiating reactions, 5a and 5b, satisfy this requirement. The parameters iz and B of eq. 10 should be identical with a and b, the rate constants of reactions 5a and 5b, respectively, provided the inhibition by the scavenger is complete. The rate constant a was calculated from the data of Kolthoff and Miller1$ (for the reaction in 0.1 M NaOH) to be 2.8 x 10W2hr.-l a t 63.1’; the rate constant b was estimated (see Table 111)to be 15.1 x M-l hr.-I. The excellent agreement, within a factor of two, between the calculated a and b and the observed A and B values, respectively, indicates that the inhibition by allyl acetate was quite effective. Free radicals involving phosphorus in the + 3 oxidation state are well established in organic chemistry. Formation of many of these is initiated by peroxides.2u (18) C. R. Giuliano, N. Schwartz, and W. K. Wilmarth, J. Phus. Chem., 63, 353 (1959). (19) I. M. Kolthoff and I. K. Mlller, J . A m . Chem. Soc., 73,30% (1951). (20) 51. Grayson, Chem. Eng. Kews, 40, No. 49, 90 (1962).
Dec., 1963
THERMODYNAMIC AXD PHYSICAL
A free radical mechaiiism was proposed for the reduction of diazonium salts by phosphorous acid.1° The oxidation of phosphorous acid by peroxydisulfate is, thus, assumed to take place by the following sequence.
[
H:i-OH]-
2[.:-OH]
-”,
PROPERTIES O F
2[TIO--;-OH] 0
TABLEI11 RATECONSTANTS AS A FUNCTION OF TEMPERATURE Temp.,
(11)
2701
Logarithms of the square roots of kl, obtained from Fig. 1, were plotted us. 1/T, and the activation energy El, of the phosphorous acid independent rate constant, was calculated to be 32.5 kcal./mole.
OC.
[ ! O H ]
LIQUID FLUORIXE
105 k l , M-1
108 ka,
sec.-a
IM-2 sec.-a
0.88 5.60 14.50
48.0 54.2 57.2
18.7 73.1 139.8
106 b ,
106 a, sec. -1
M-1 see. - 1
0.776 1.92 3.07
16.7 25.1 29 6
From eq. 8 one obtains the relationship
No additional evidence can be presented a t this time for the intermediatm in just the form and order postulated. The mechanism would be the same had an electron been transferred in reaction 5b and H atom in 5e. The sulfate radical ion, SO4-, is well established in the chemistry of pero~ydisulfate~; the P03-2 radical ion was recently identified in the y-ray irradiation of sodium phosphite.21 Activation Energy.-Because of the complexity of the rate expression, a simple, straightforward determination of the activation energy was not possible. The following approach was adopted. At zero concentration of phosphorous acid, eq. 4 becomes -d(Sz08- ”/dl
=
k~1/2(S~08-2)*’e (12)
(21) A. Horsfield, J. R. Morton, and D. H. Whiffen, Mol. Phys., 4, 475 (1961); Chem. Abstr., 56, 10928a (1962).
b
==
a(Lzlk1)
(13)
Values of kl and k2, obtained from Fig. 1, and of a, calculated from the data of ref. 19, were used to calculate b. These are presented in Table 111. From the plot of log b us. 1/T, Ea was found to be 14.0 kcal./mole. From eq. 8 one obtains the following relationship
El
=
E,
+
’/z
(E, - E f ) = 32.5
(14)
Assuming zero activation energy for the chain-breaking process (5f) and inserting E, = 33.5,19E , was estimated to be 15.7 kcal./mole. Acknowledgment.-The author wishes to express his appreciation to Professor W. K. Wilmarth of the Chemistry Department, University of Southern California, for helpful discussions.
THERMODYNAMIC AND PHYSICAL PROPERTIES OF LIQUID FLUORINE AS CALCULATED BY SIGNIFICANT STRUCTURE THEORY OF LIQUIDS BY TOMR. THOMSOT, HER’RY EYRIR’G, AND TAIKYUE €LEE Departments of Chemistry at Arizona State University, Tempe, Arizona, and the University of Ctah, Salt Lake City, Utah Received J u n e 17, 1968 The theory of significant structures has been applied to liquid fluorine over the entire liquid range from its melting point of 53.54”K. to its critical point a t 144°K. Melting point data and such physical constants as atomic weight, moment of inertia, and fundamental frequency of the molecule are the only data used to find the essential parameters for the partition function. The following properties were calculated with reasonably good agreement with experimentally observed values : vapor pressure, density, entropy of vaporization, critical constants, heat capacity a t constant volume and constant pressure, thermal coefficient of expansion, compressibility, i~urfacetension, and viscosity.
Introduction The “significant structure’’ theory of liquids is one that views a liquid as a “solid-like” structure with “fluidized vacancies’’ of molecular size randomly distributed throughout the solid. Molecules adjacent to such holes can assume “gas-like” degrees of freedom in moving into the vacancies. The significant structures of a liquid are thus considered to be the solid-like and gas-like components. The applicability (of this theory lies in the fact that the partition functions for both solids and gases are well known. Since the number of holes, consequently the number of gas-like molecules, increases with the volume of the system, the distribution of the liquid into solid- and gas-like molecules is a volume-dependent one, as given by the general form for the partition function
where V , is the molar volume of the solid a t the melting point, V is the molar volume of the liquid, N is Avogadro’s number, and IC = V / Vs. This report is one of a series of studies applying this theory to various common and uncommon liquids, ranging from liquefied gases to fused salts and molten metals,l and is the second of a particular sequence on the halogem2 The Partition Function for Fluorine.-Fluorine has a normal entropy of fusion (2.28 e.u.) and has a first-order solid state transition at about 8’ below its melting p ~ i n t . ~This , ~ indicates that fluorine probably rotates (1) H. Eyring, T. Ree, and oo..workers in a series of articles in Proc. Natl. Acad. Sci. U. S.,44, 683 (1958), to the present. (2) T. R. Thomson, H. Eyring, and T. Ree, ibid., 46, 336 (1960).
