Indian Journal of ChemistryVol. 24A, November 1985, pp. 927-931

Kinetics & Mechanism of Silver(I) Catalyzed Oxidation of PhosphorusAcid with Peroxodiphosphate in Acetate Buffers

BHARATI GUPTA, A K GUPTA, K S GUPTA & Y K GUPTA*Department of Chemistry, University of Rajasthan, Jaipur

Received 28 January 1985; revised and accepted 26 June 1985

Oxidation of phosphite with peroxodiphosphate has been carried out in acetate buffers in the presence of silver(I). Theorder in peroxodiphosphate, phosphite and silver(l) is found to be one in each case and the third order rate constant (k3) at pH4.70, 1= 1.0mol dm -3 and 65Q is (9.7 ±O.5) dm" mol :? s -I. Hydrogen-ion dependence is complicated. Values of k3 calculatedat different pH values are similar to experimental values. Silver(I) catalysis operates through complex formation withperoxodiphosphate though complex formation with Ag(II) or Ag(III) cannot be ruled out.

It is now well established !.2.3 that oxidations withperoxodiphosphate (PDP) in aqueous perchloric acidsolution occur via acid-catalyzed hydrolytic pathswhich are rate-determining. In less acidic solutions,e.g. in acetate buffers there is no hydrolysis of PDP,but oxidations are very slow. However, silver(I)4.5serves as a suitable catalyst. Although there issufficient evidence for the existence of Ag(I)/ Ag(II) orAg(I)/Ag(III) redox couples in siIver(I) catalyzedoxidations" with peroxydisulphate (PDS), there is noevidence for such a mechanism in oxidations 7 ofarsenic(III) and antimony(III) with PDP. It is thereforeobvious that some more systems, such as the titleinvestigation should be studied to establish themechanism by which siIver(I) catalysis operates in PDPoxidations. Phosphorus acid has been chosen for fourreasons: (i) the system would be less complicated sincethe products of reduction of PDP and of oxidation ofphosphite would be the same; (ii) no complexing ofsilver(I) and phosphite is reported; (iii) in case Ag(II) isformed as an intermediate, details of the reaction" ofAg(II) and H3P03 are available; and (iv) the reactionmay throw light on the role of active form 9 of H3P03,if any.

Materials and MethodsTetrapotassium peroxodiphosphate, a gift sample

from FMC Corporation, USA, was used as such.Potassium phosphate and potassium fluoride presentas impurities in PDP sample had no effect on thekinetics of reaction. It was standardized iodometri-cally I 0 and was found to be 92.7% pure. All otherchemicals were of either BDH (Anala R) or E Merck(GR) quality. Doubly distilled conductivity water wasused for preparing all solutions. Sodiummonohydrogenphosphite (Na2HP03. 5H20) was aBDH (AnalaR) product.

Acetate buffers were employed as the reaction mediaand sodium nitrate was employed to adjust or vary theionic strength. Acetate ion had no effect on the rateand hence pH was changed by varying theconcentration of acetic acid in the acetate-buffers. ThepH of the reaction mixture did not vary much (within±0.01 unit) at the beginning and the end of thereaction. All pH measurements were made using aECL digital pH meter.

The kinetics were followed iodometrically at [H + ]= 1.0 M as described earlier I I and 65 ± 0.1 "C. Initialrates and pseudo-first order (excess phosphite) rateconstants were obtained as described II. A slowreaction between iodine and phosphorus acid has beenreported 12, but under the acid conditions employedduring the time the iodometric determination of PDPwas carried out no reaction occurred. The results werereproducible within ± 5%. Trace impurities of metal-ions such as copper(II) and iron(III), generally presentin the reagents, had no effect on the rate of reaction.

Results

StoichiometryReaction mixtures in the concentration range (1 to 5)

x 10 -3 mol dm -3 were left at 65° for 3 to 4 hr andexcess PDP was determined iodometrically whileexcess phosphite' was determined cerimetrically. Thereaction occurred in accordance with Eq. (1) and nooxygen was detected.

H2P20~ - + H3P03 +H20-+ H3P04 + 2H2P04- ... (1)

Dependence of rate on PDP, phosphite and silver(I)The concentration of PDP was varied in the range

(OJ to 2.0) X 10 -3 mol dm -3 at fixed concentrations ofother reactants. From the initial rates determined by

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INDIAN J. CHEM., VOL. 24A, NOVEMBER 1985

the plane mirror method 13, the order in PD wasfound to be one. Subsequently pseudo-first order plotswere made and the pseudo-first order rate constantwas found to be (3.83 ± 0.04) x 10 -4S -I at 65°, pH=4.70 and 1= 1.0 mol dm -3.

Concentration of phosphite was varied in the range(0.5 to 5.0) x 10-2 mol dm -3 and the plot of pseudo-first order rate constant versus [phosphite] was linearpassing through the origin with a slope of(2.01 ± 0.04)x 10 -2 dm ' mol-I s -I. Such a value obtained fromthe [PDP] variation was 1.92 ± 0.02 x 10 -2 dm 'mol-I s -I . The concentration of silver(I) was varied inthe range (0.6 to 2.0) x 10 -3 mol dm -3 and the order insilver(I) was found to be one. All these results are givenin Table 1 and the empirical rate law at constant pH isgiven by Eq. (2)

- d[PDP]ldt = k3[PDP]T[phosphiteh[Ag(I)]T ... (2)

where suffix T denotes total concentration of theconcerned species. The values of k , were 9.6,10 and 9.6drn" mol '? s -I from the PDP, phosphite and Ag(1)dependences respectively. The average value of k3from Table 1 was found to be (9.7 ±0.5) dm" mol"?S-I at pH =4.70, temp. =65° and 1=1.0 mol dm-3.

The values of k3 (dm" mol-2 s -I) at 55° andpH valuesof 2.85, 3.64, 4.14 and 4.95 were determined in thesame manner and found to be 2.1, 2.8, 3.4 and 5.1respectively.

Hydrogen ion and acetate ion dependencesThe pH of the system was varied from 2.32 to 5.0

with the help of acetate buffers and the reaction wasstudied at 65° and 55°. The rates decreased, attained aminimum and then increased (Fig. O. The reactionbeyond pH 5 was not followed because of theappearance of turbidity. Acetate ion concentrationwas varied in the range 0.2 to 3.0 mol dm -3 by addingsodium acetate to the system at pH = 4.69 and 1= 3.0mol dm -3, but there was no-effect on the rate.

Effect of added salts on the rateThis effect was studied by varying the concentration

of NaN03 at pH values of 5.65,4.70, 3.55 and 2.77.Concentrations of LiN03 and Mg(N03}z were variedat pH =4.70. The rate decreased and became limitingwith increase in [salt]. The results are given in Table 2.

DiscussionPhosphorus acid is dibasic and its dissociation

constants were determined by the usual pH-metrictitrations at 25°,35° and 45° and 1= 1.0 mol dm -3, andthe values at 65° were obtained by extrapolation of thelinear plot of log Kd versus liT. The dissociationconstants at 25° are knownI4,15. These were found tobe 5.25 x 10 -3 and 7.9 x 10 -8 at 65° and 1= 1.0 mol

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Table l-Pseudo-first Order Rate Constants (ko) andDerived Third Order Rate Constants (k3) in Oxidation of

Phosphite with Peroxodiphosphate in Acetate Buffers

[pH =4.70; 1=1.0 mol dm -3; temp. =65°C]

W[PDP](mol dm -3)

0.36250.6250.7251.201.451.7251.7251.7251.7251.7251.7251.7251.7251.7251.7251.7251.7251.7251.7251.725

102[phosphite] 103[Ag(I)] 104ko k3(mol dm -3) (mol dm -3) (s -1) (dm6mol-'s -1)

2.0 2.0 3.83 9.62.0 2.0 4.03 10.12.0 2.0 3.83 9.62.0 2.0 3.90 9.72.0 2.0 3.92 9.82.0 2.0 3.83 9.61.0 2.0 2.30 11.51.2 2.0 2.70 11.21.5 2.0 3.15 10.51.8 2.0 3.65 10.12.0 2.0 3.83 9.62.5 2.0 5.00 10.03.0 2.0 5.85 9.72.0 0.6 1.06 9.02.0 0.8 1.32 8.32.0 1.0 I.72 8.62.0 1.4 2.50 8.92.0 1.6 3.07 9.62.0 1.8 3.45 9.82.0 2.0 3.83 9.6

Av.9.7±0.5

z-'.~ 2'5o..•

·0- 2·0

4·5

3·5

3{)

1·5

1·0

05

o 3{)

pH

Fig. I-Plot of Kobs versus pH ([PDP] = 1.725 x 10-3; [phosphite]

= 2.0 x 10-'; [Ag(1)] = 2.0 x 10-3; 1= 1.0; temp. = 0, 65 ; 0, 55°;concentrations in mol dm -3)

GUPTA et al.: KINETICS OF OXIDATION OF PHOSPHORUS ACID

Table 2-First-order Rate Constants (ko) of PDP-Phosphite Reaction in Presence of NaN03, LiN03 and Mg(N03h([PDP] = I.725 x iO -3 mol dm -3; [phosphite] = 2.0 x iO -2 mol dm -3 [Ag(I)] = 2.0 x 10-3 mol dm -3; temp. = 65°C)

pH =2.77[NaN03]/mol dm -3 0.0 0.1 0.2 0.4 0.6 0.8 1.0104ko/S-1 10.2 6.4 4.72 3.0 115 115 115

pH =3.55[NaN03]/mol dm-3 0.0 0.05 0.1 0.2 0.4 0.5 0.6 0.8 1.0 1.20I04ko/S -1 3.83 3.4 2.3 2.01 1.50 1.45 1.40 1.40 1.40 1.40

pH =4.70[NaN03]/mol dm :" 0.0 0.05 0.1 0.2 0.4 0.5 0.6 0.8 1.0104ko/S-1 12.6 10.0 9.2 5.37 4.0 3.90 3.85 3.85 3.85

pH=5.65[NaN03]/mol dm -3 00 0.05 0.1 0.2 0.4 0.5 0.6 0.8 1.0104ko/S-1 14.6 12.0 10.8 7.3 6.3 5.8 4.45 4.45 4.45

pH =4.70[Mg(N03h]/mol dm -3 0.0 0.025 0.075 0.1 0.15 0.2 0.4 0.5 0.6104ko/S-1 13 5.0 3.85 3.3 2.\. 1.8 1.70 1.20 115

pH=4.70[LiN03]/mol dm -3 00 0.05 0.10 0.15 0.20 0.40 0.50 0.60104ko/S-1 12.9 10.0 8.1 6.0 4.8 4.5 4.0 4.0

dm -3. Thus, in the pH range employed presentlyphosphite would exist as H3P03 and HZP03-. ForPDP, the proto lytic equilibriaI6

•I7 (3-6) are possible.

KlH4PZ08¢H3PZ08-+H+ ... (3)

KZH3PZ08- ¢H2P20§ - + H+

K3H2PZO§ - ¢HP20~ - + H+

K4HP20~ - ¢P20~ - + H+

... (4)

... (5)

... (6)

Different workers'P?" 7 have reported different valuesfor K, and Kz but all these values happen to be largerthan 0.3. The values of K3 and K4 are reported 15 to be(6.6 ± 0.3) x 10 -6 and (2.1 ± 0.1) x 10 -8 respectively atI =0 and temp. =25°. We have determined these valuesat 65° and 1= 1.0 mol dm -3 and found them to be (1.0± 0.2) x 10-5 and (7.2 ±0.8) x 10-8 respectively. Thusthe predominent species ofPDP in thepH range of2.32to 5.0 would be H2PZO§ - and HPzO~ -.

Complex formation between Ag + and CH3COO - isreported l ", but the formation constant is small andmost of Ag(I) may exist as Ag ". There is no evidencefor the existence of Ag(I)/ Ag(II) or Ag(I)/ Ag(O) redoxcouple in the present investigation because of the ratedependence on [PDP] or [phosphite]. We believe thatAg + may be involved in complex formation with PDP(see Eqs 7 and 8). Although there is no kinetic and/orspectrophotometric evidence for complex formation,

such a possibility does exist in view of the formation ofweak complexes+" with Na+, K+, u' and Mg+".

x,HzPzO§ - + Ag +¢HzPz08Ag - ... (7)

K~HPzO~ - + Ag + ¢HP208AgZ - ... (8)

With the above species present in the system followingreactions (9-12) are possible.

klHZPZ08Ag - + H3P03 -> Products ... (9)

kzH2PZ08Ag - + HZP03- -> Products ... (10)

k3HPZ08AgZ - + H3P03 -> Products ... (11)

k4HPZ08AgZ - + HZP03- -> Products ... (12)

The species H3P03 and H2P03- are related throughequilibrium (13)

KdH3P03¢H2P03-+H+ ... (13)

Reactions (9) to (13) would lead to the rate law (14).

-d[PDP]/dt =kIKc[Ag +][H2P20§ -][H3P03]+k2KcCAg +][H2P20§ -][H2P03-]

+k3K~ [Ag +][HPzO~ -][H3P03]

+k4K~[Ag +][HP20~-] [H2P03-]

... (14)

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Or

INDIAN 1. CHEM., VOL. 24A, NOVEMBER 1985

{[Ag(I)] [PD P] [phosphite](k IKoCH +] 2

+ k2KcKd + k3K~K3)[H +] +k4K~KdK3}d[POP]ldt = ------------

Or

k- [Ag(I)][phosphite](A[H +2] + B[H +] + C) (IS)

0- ([H +] + K3X[H +] + Kd) ...

OrA[H+]2+B[H+]+C

k3 = ([H +] + K3X[H +] +KJ .... (16)

In Eqs (IS) and (16) A, Band C are constants involvingthe third-order rate constants and other constants.Rate law (15) has already been verified at constant pHof 4.70. Equation (16) can be verified in the followingway. Figure I shows the minimum at pH = 3.35. In thissituation [H +] is atleast 10 times K3, and x, is about10 times [H+] and hence rate law (16) can beapproximately reduced to (17)

k3 = A [H+]~in + B[+H+]min + Cs, x [H Jmin

A +] B C= Kd[H min+ Kd + Kd[H+]min

... (17)

... (18)

Condition of minimum would yield

Or

OrC=2.12x 10-7 A ... (19)

Equation (20) can be readily obtained from Eqs (16)and (19).

ki[H+]+K3)([H+]+KJ -A[H+][H+] -

2.12x1O-7 B+ + +[H ] ... (20)

The plot of left hand side ofEq. (20) versus [H+] + 2.12x 10 -7/[H +] in the pH range 2.32 to 5.0 is linear with

930

non-zero intercept (Fig. 2). From this plot, values of A,Band C were found to be 2.2 x iO-\ 5 x iO -7 and 4.7x 10 -II respectively at 65°. From these values ofconstants A, Band C, Kd = 5.25 x 10 -3 and K3 = 1.0x 10 -5. The values of ko have been calculated makinguse of Eq. (15). Some of these values are given inTable 3 along with the experimental values. Theagreement in the two values is satisfactory.

It has been observed that concentrated solutions ofPOP and AgN03 yield dark brown solution orprecipitate which oxidizes water+': This brownsolution could be a complex of higher valent silvereither Ag(II) or Ag(III) with POP. If a concentratedsolution of phosphite is added to this brown solution,the former immediately reacts with it. The intensity of

70

60..:;::::

50r:.:;+'"~

40F.:;+"~ 30".<>0

""•....Q20

0

10

0 5

o

10 15

103([H+] + 2'12x 107)[H+]

Fig.2-Hydrogen ion dependence in the reaction of POP andphosphite at 65° ([POP] = 1.725 x 10 -3; [phosphite] =2.0 x 10 -2;

[AgO)] =2.0 x 10 -3; 1= 1.0; concentrations in mol dm -3)

Table 3-0bserved and Calculated" First order RateConstants at Different pH Values of POP-Phosphite

Reaction in Acetate Buffers at 65°

([POP] = I. 725 x 10 -3 mol dm -3; [phosphite] = 2.0 x 10 -2 moldm -3; [Ag(I)] =2.0 x 103 mol dm -3; 1= 1.0 mol dm -3)

2.44 2.51 2.58 2.78 2.90 3.181.53 1.39 1.34 l.l5 l.l0 1.011.47 1.43 1.39 1.28 1.24 l.l93.34 3.40 3.45 3.51 3.66 3.71 4.100.96 l.l0 1.21 1.34 1.53 1.72 2.111.20 1.24 1.27 1.29 1.36 1.68 1.844.40 4.59 4.73 4.92 5.00

2.6 3.10 3.6 4.0 4.432.55 3.19 3.74 4.58 4.86

pH104ko/s -I (obs)104ko/s -I(calc)pHI04ko/s -I (obs)104ko/s -I (calc)pH104ko/s -I (obs)104ko/s -I (calc)

"Calculated from Eq.(I5) using values of Kd=5.25 x 10-3.

K3=1.0x 10-5; A=2.2x 10-4; B=5.0x 10-7; and C=4.7x 10-4•

GUPTA et al.: KINETICS OF OXIDATION OF PHOSPHORUS ACID

the colour increases with the increase in pH. Althoughthere is no experimental evidence for the existence ofhigher valent silver, its formation cannot be ruled out.The present results therefore do not lead to a betterunderstanding of the mechanism.

The effect of added NaN03, LiN03 and Mg(N03his not simply that of variation of ionic strength. Sincethe rate decreases and becomes limiting for largeconcentrations of these salts, the cations seem to formcomplexes or ion pairs with POP. This indirectly showsthat perhaps Ag + -POP complex is reactive, though itsconcentration may be small since Ag + is too small Incomparison to NaN03 employed to adjust the ionicstrength. If the cations, Na +, Li + and Mg2 + arerepresented by Mn+, the complexation with POP (sayHP20§ -) can be represented by Eq.(21).

KMn+ + HP20§ -~MHP208 -3 ... (21)

[POPJrree is given by Eq. (22)

[poph[POP]Cree= I +K[Mn+] ... (22)

A plot of (ko) -I versus [Mn +] at constant (pH islinear with a non-zero intercept (Fig. 3) and from thisvalues of K were found to be (5.0 ± 0.7), (8.3 ± 1.0) and(43.0 ± 3) dm ' mol-I for Na +, Li 1- and Mg2 +

respectively at pH =4.70. These are gross values sinceboth the species, H2P20§ - participatein complex formation. The reported 16 values forthese formation constants are 10.5, 8.0 and 58 forthe above cations in the same order. The value ofK for Na -t- seems to be independent of pH. The value ofk3 from the intercept is found to be 32 dm" mol "? s-\for all the three cations at pH = 4.70. The identicalintercept for all the three cations supports complexformation between POP and the cations. However, thevalue is quite different than the value of9. 7 dm" mol "?

s -\ from Table I at the same pH. As a matter of factthe value 9.7 is obtained at 1= 1.0 mol dm -3, whereasthe value 32 is for 1=0. The values of k3 (dm" mol "?

s -I) found from the results of NaN03 by the aboveprocedure at different pH values are 25 (PH 2.77), 9.6(pH 3.55) and 31 (PH 4.70) and these are in the sameorder as those given in Table 3 at 1= 1.0 mol drn -3.

Fig. 3-Plot of kOb' versus pH ([PDP] = 1.725x 10-3; [phosphite]=2.0 x 10-2; [Ag(I)] =2.0 x 10-3; pH =4.70; Salt = 0, NaN03; D,

Mg(N03h; 1'1, LiN03; concentrations in mol dm -3)

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(1976) 1695.2 Kapoor S & Gupta Y K, J chern Soc Dalton, (1976) 473.3 Kapoor S & Gupta Y K, J inorg nucl Chern, 39 (1977) 1019.4 Creaser I I & Edwards J 0, Topics Phosphorus Chemistry, 7

(1972) 395.5 Anderson M, Edwards J 0, Green A A & Wisewell M D, Inorg

Chern Acta, 3 (1969) 855.6 House D A, Chern Rev, 62 (1962) 185.7 Gupta Bharati, Gupta K S & Gupta Y K, J chern Soc Dalton,

(1984) 1873.8 Viste A, Holm D A, Wang P L & Veith G D. Inorg Chern. 10

(1971) 631.9 Jenkins W A & Yost D M, J inorg nucl Chern. II (1959) 297.

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1845.12 Mitchell A D. J chern Soc. 123 (1923) 2241.13 Latshaw M. J Am chern Soc. 47 (1925) 793.14 Espenson J H & Dustin D F. Inorg Chern. 8 (1969) 1760.15 Griffith R 0 & Mckeown A, Trans Faraday Soc. 36 (1940) 766.16 Crutchfield M M & Edwards J O. J Am chem Soc. 82(1966) 3533.17 Venturini M. Indelli A & Raspi G. J electroanal Chern interfacial

Electrochem, 33 (1971) 99.18 Mac Dougall F H & Peterson S. J phys Colloid Chern. 51 (1947)

1346.

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