Malhotra, H. C.

Thareja, (Miss) S. K.

English

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Indian .TournaI of ChemistryVol. 14A, April 1976, pp. 226 -230Kinetics of Degradation of TetraphosphatesH. C. MALHOTRA & (Miss) S. K. THAREJ AChemistry Department, Delhi University, Delhi 110007Received 14 April 1975; accepted 8 May 1975The degradation of tetraphosphates between pH 2 and 10 and at 50°±0·05°, 60°±0·05°,65°±0·05° and 700±0·05° and 11 = 11\11, is first order in [tetraphosphate]. The H+ ions catalyse andcontrol the equilibria between the various terraphosphate species. The overall rate constants(k) can be resolved into the individual rate constants using the values of dissociation constantsobtained under conditions of the kinetic experiments. The activation parameters for the overallreaction, as also for the stepwise reactions, have been calculated.THE kinetics of pyrophosphate and triphos-phate have been investigated thoroughlyby several workers-:". However, no compre-hensive study seems to have been done on thedegradation of the tetraphosphate. Earlier studies+?on the kinetics of degradation of the tetraphosphatecovered rather limited ranges of PH and temperature.The significant observations recorded during thesestudies were a first order dependence of the rateon [tetraphosphate] and a decrease in rate withincreasing pH. No effort was made to estimatethe concentrations of various tetraphosphate specieswith a view to analysing and interpreting the kineticdata in terms of the degradation of various tetra-phosphate species present in the solution. Theresults of such a study are recorded in this paper.In the present study concentrations of differentspecies were calculated from their dissociationconstants which were obtained under the conditionsof the kinetic experiments. The degradation oftetraphosphate at [L = 1m was carried out at pH2, 3, 4, 5, 6, 7, 8, 9 and 10 and temperatures 50°,60°, 65° and 70° maintained within ± 0·05°.Materials and MethodsAs pure tetraphosphate could not be obtainedin sufficiently large quantities, a phosphate mixturecontaining 40% of tetraphosphate was used. Itwas obtained by heating an alkaline (PH 12.0)solution of sodium tetrametaphosphatc (NaPOa)4'4H20 at 65'5° for 1 hr. The resultant solutionwas analysed for tetraphosphate (P, 40-45 %),.tetrametaphosphate (P, 25-30%), triphosphate (P,20-25%), pyrophosphate (P, 5-7%) and orthophos-phate (P, 1-2%) concentrations.NaOH, HCI, ammonium molybdate and NH40Hused were of AR grade. ZnS04 (99·5% pure)required for pyrophosphate estimation was of May &Baker grade. EDT A disodium salt and the indicatoreriochrome black-T were of E. Merck quality.Acetone and gl. acetic acid used were of BDH grade.The presence of tetrametaphosphate, orthophos-phate, pyrophosphate and triphosphate, however,did not interfere with the degradation of tetra-phosphate, since the degradations of the phosphateswere independent of each other. This was confirmed226by carrying out the degradation of triphosphatein the absence and presence of sodium pyrophosphateat pH 5·0, temperature 65° ± 0·05° and [L = 1M.The reaction rate (6'70x 10-4 min-I) in both thecases was found to be the same as reported bySmith".Sodium tetrametaphosphate - It was obtained bythe low temperature hydration of phosphorus pento-xide" followed by neutralization of the resultanttetrametaphosphoric acid with Na2COa. The crys-tallization of the sodium salt was effected by addingNaCl. It analysed for tetrametaphosphate (P,98-99%), orthophosphate (P, 0·5-1·0%), pyrophos-phate (P, 0·0%) and triphosphate (P, 0·5-1·0°/0).Kinetic measurements - The reaction mixturecontaining sodium tetraphosphate and adjustedto the desired PH value by adding NaOH/HCIwas placed in a 250 ml pyrex measuring flask andsuspended in a thermostat. Aliquots (10 ml each)of the reaction mixture were taken out at diff renttime intervals and analysed for orthophosp,ate,pyrophosphate and triphosphate concentrationsrEstimation of various phosphates present in! themixture - Orthophosphate was estimated initiallyand then at different intervals of time by colori-metric method due to Bernhart and Wreath".A Colemann spectrophotometer was used for thispurpose. The amount of orthophosphate was readfrom a standard linear plot of optical density versus[orthophosphate].Pyrophosphate and triphosphate were estimatedsimultaneously by Bell's method-". To 10 ml ofthe reaction mixture (PH 3·8) was added 10 mlof the ZnS04 solution (5 g of ZnS04 dissolved in100 ml distilled water and pH adjusted to 3,80),which resulted in lowering of pH. The PH of thesolution was again adjusted to 3·8 by adding standardNaOH. The amount of NaOH (x) used is equi-valent to the concentrations of pyrophosphateand triphosphate present in the mixture. Alsoat this stage pyrophosphate present was completelyprecipitated as zinc pyrophosphate. The solutionwas filtered and the precipitate washed with aceticacid (PH, 3·8) solution till the filtrate became freefrom SO~- ions. The precipitate was dissolvedin 2N aq. ammonia and a measured excess of EtoT AMALHOTRA & THAREJA: KINETIcs OF DEGRADATIoN OF TETRAPHOSPHATESsolution added to it. The excess EDTA was thentitrated against standard ZnS04 using eriochromeblack T as indicator. The EDT A needed for zincobtained from zinc pyrophosphate correspondedto the concentration of pyrophosphate. The titra-tion equivalent of EDTA used was subtracted fromx to get the amount of NaOH equivalent to theamount of triphosphate present in the mixture.The amount of tetraphosphate was determined asfollows: Ten ml aliquot of the reaction mixturewas taken at different time intervals and the sampleanalysed for orthophosphate, pyrophosphate andtriphosphate concentrations. In order to get the[tetraphosphate] initially present, the reaction mix-ture (10 ml) was refluxed on a steam-bath for 10-12hr to convert all the tetraphosphate completelyinto mixture of orthophosphate, pyrophosphateand triphosphate and the total amount of ortho-phosphate, pyrophosphate and triphosphate esti-mated. From this the amount of orthophosphate,pyrophosphate and triphosphate present initiallywas subtracted, and the difference correspondedto the amount of tetraphosphate present initially.However, the amount of tetraphosphate presentat various stages of the reaction was calculatedas follows:If sum of the total P present as orthophosphate,pyrophosphate and triphosphate initially = A gatoms of P Ilitre. Sum of the total P present asorthophosphate, pyrophosphate and triphosphateat time t = B g atoms of Pjlitre, and sum of thetotal P present as orthophosphate, pyrophosphateand triphosphate after refluxing = C g atoms ofPjlitre. Then initial [tetraphosphate] =(C -A) gatoms of Pjlitre and [tetraphosphate] at time t =(C- B) g atoms of P jlitre.The presence of tetrametaphosphate in the system,however, did not interfere with the estimations ofortho-, pyro-, tri- and tetra-phosphates at anystage of the reactions which were carried out inthe pH range 2-10 since at these pH values tetra-metaphosphate is quite stable'.Results and DiscussionThe results of the kinetic studies are given inTable 1. The degradation rate (k) of tetraphosphateshowed a first order dependence on [tetraphosphateJ.A linear dependence of log (aja-x) on time, furthersupports this point. The activation energy (Ea)and the frequency factor (A) calculated from thelinear plots of log k versus liT for the overall re-action are given in Table 2.The data in Table 1 show that kj[H+] valuesat any given temperature, rapidly increase withincreasing pH. The fact that the relation betweenthe [H+] and pH is not a simple one is illustratedin Fig. 1. An increase in the rate of hydrolysiswith decreasing pH (Table 1) may be either due toan increase in the fraction of more reactive speciesat a lower pH value or to a catalytic effect of H+ions on the hydrolysis of one or more of the species,or due to both of these factors.The amounts of various species, as fractions (Fi) ofthe total [tetraphosphate] present in the solution,were calculated from the values of dissociationTABLE 1 - AVERAGE FIRST ORDERRATE CONSTANT (k) AND THE VALUES OFk/[H+j AT DIFFERENT TEMPERATURES [ft = l'OM]Initial pH k x 10' k/[H+][P.ots] (min-I) (litre mole'? min-I)Mxl0·TEMP.= 50° ±0'05°1·253 2·0 2·34 2'34xl0-21'264 3·0 1'82 1'82 x 10-11'286 4·0 1·45 1'451'212 5·0 1'15 11·501'264 6·0 0'89 8'90 x 1011'251 7-0 0-72 7'20 x 10·1·270 8-0 0-55 5-50 x 1031'221 9-0 0·44 4-40 x 10'1-246 10-0 0·35 3-50 x 105TEMP_= 60o±0-05°1-296 2·0 8-71 8-71 x 10-21-304 3-0 6·76 6-76 x 10-11-312 4-0 5-25 5-251'204 5·0 4-06 40'601-216 6-0 3-13 313-001-251 7-0 2-43 2-43 x 1031-298 8-0 1-91 1-91 x 10'1-210 9-0 1-45 1-45 x 105\-267 10-0 1-12 1-12x10·TEMP_= 65° ± 0-05°1-259 2-0 20-89 20-89 x 10-21·246 3-0 15-85 15-85 x10-11-267 4-0 12·16 12-161·22 5·0 9-23 92·301'216 6·0 7-00 700-001-263 7·0 5·37 5·37 x 1031·210 8-0 4-07 4-07 x 10'1·202 9-0 3-09 3-09 x 1051·259 10-0 2·40 2·40xl0·TEMP.= 700±0-05°1-211 2-0 30-20 30-20 x 10-21'304 3'0 22-91 22·91 x 10-11·296 4-0 17·38 17'381'261 5-0 13·18 131'801'322 6'0 10'23 10-23xl0·1'242 7'0 7-41 7-41 xl031'205 8'0 5'89 5-89 x 10'1-211 9·0 4·47 4-47 x 1051'206 10·0 3-47 3·47xl0·TABLE 2 - ACTIVATION ENERGY (Ea) AND THEFREQUENCY FACTOR (A) FOR THE OVERALL REACTIONPH Ea log A*(kcal/mole) (mirr '}2·0 27'14 14-763·0 27-29 14-744'0 27-46 14-685·0 27-10 14-416·0 27-07 14-297·0 25-03 12-79S-O 25-84 13-259-0 24-93 12-5110·0 25'90 13-05*A, corresponds to a pseudo first order reaction. i.e. [water]is taken as constant,227iNDiAN j. CHEM., vot, 14A, APRIL 1976constants-! of tetraphosphoric acid using Eqs. (1-7)F _ H6P4013H PoOlS - 6~ HnP4013n=O1= ( tc, KIK2 KIK2K3 KIK2K3K41+[H+]+[Rf]2+ [H+]3-+ [H+]4KIK2K3K4K5+KIK2K3K4K5K6)+ [H+]5 [H+]6... (1)H5P40isFH.P,O:~ = 6~ HnP4013n=O1... (2)1.. (3)1... (4)1HP40~36~ HnP4013n=O12281= ( [H+]6 _+ [H+]5KIK2K3K4K5K6 K2K3K4K5K6[H+J4 [H+]3 [H-f]2 [H+] )+ + +--+--+1K3K4K5K6 K4K5K6 K5K6 K6... (7)The plots of log Pi versus pH at 70°C and !1.= 1·0Mare shown in Fig. 2. Similar plots were obtainedat other temperatures also. Dissociation constantsused in the calculations were obtained under condi-tions of the kinetic experiments.Calculation of the individual rate constants - Therate constants characteristic of the various specieswere calculated using Eqs. (8) and (9).Rate = kl[H6P4013]+k2[H5P40iii] +k3[H4P40~ii]+k4[H3P40jii]+k5[H2P40i3] +k6[HP40~3J+k7[P40~3] +k{[H+] [H6P40d+ k~[H-f][H5P40}:iJ+k~[H+J[H4P40iiiJ+ k~[H+][H3P40i:i]+k' 5[H+J[H2P40tii]+k~[H+][HP40~3J+k;[H+][P40~3] ... (8)where ki is the rate constant for the uncatalysedprocess and ki refers to the same process catalysedby H+ ions. Equation (8) may be written as Eq. (9).Rate = (kl+Klk;)[H6P4013J+(k2+K2k3)[H5P40iil]+ (k3+ K3k~)[H4P40iii]+ (k4+K4k~)X [H3P40iiiJ+(k5+K5k~)[H2P40t:iJ+ (k6+K6k;)]HP40fi] +k7[P40~ii]+k:CH6P4013][H+] .. (9)8'6·0--I.:E-:t9 4'0xoX2·0pHFig. 1 - Plot of k against PH at 60°MALHOTRA & THAREJA: KINETICS OF DEGRADATION OF TETRAPHOSPHATESou,Cl 6·0og·oi2.o~""'&'--:~""'&'_.!:!~--L_...L'-""_....L.--,_..J........Io 8-0 10-0pHFig. 2 - Plots of log Ft versus PH at 70° {L = p.Oig}The fraction of the tetraphosphate species existingas p 40~3 is negligible below pH 7 where as abovepH 2·0 the fractions of H6P4013 and H5P40~3 canalso be neglected. In the pH region 2'0-7'0, thefractions of the species H4P40ia, HaP40ra' H2P40faand HP40~a are significant. Thus the first two andlast two terms in Eq. (9) can be deleted. Thevalues of (ka+Kak~), (k4+K4k5)' (k5+K5k~) and(k6+K6k;) were calculated by substituting in Eq.(9) the fraction of each species at four differentpH values and then solving the four simultaneousequations thus obtained.Calculation of k6 and k7- Since at PH 7·0, thesignificant species are H2P40ta, HP40ri andP40~3' The 1st, 2nd, 3rd, 4th and last term inEq. (9) can be neglected .. Thus knowing the valuesof 5th and 6th term, k7 was calculated. The rateconstant k; is of little importance as the I-J+ ionswould not be present in a significant amount alongwith P40~3' The value of K6 being very small,the product k;K6 can be neglected in comparisonto k6 i.e. k6+K6k; may be taken equal to k6. Thevalues of the coefficients of H4P40iii, HaP40~3'H2P40t:;, HP40ri, P40~3 calculated as aboveat different temperatures are given in Table 3.Calculation of ka, k~, k4' k~, k5• k~ and k~- Theover all rate constants (Table 1) between pH 2·0and 7·0 were used for the determination of theseconstants. The amounts of the significant specieswhich are present in this pH range and [Hi'J weresubstituted in Eq. (8) and by successive eliminationthe values of the above individual rate constantswere calculated at 50°, 60°, 65° and 70° except k~whose value was approximate due to non-availabilityof an accurate value of dissociation constant K2•The individual rate constants are given in Table 4.TABLE 3 - OVERALL RATE CONSTANTOF THEVARIOUS SPECIESCoefficien t Overall rate constant X 104 at50° 60° 65° 70°k3+K3k• 5·51 14-82 26·52 44-89k'I+K4kfi 4·43 11'95 24·40 42'5k5+K5k~ 1'46 4'22 9'27 13-91k.+K.k; 0'81 2-40 4'08 6·10k7 0·40 1·19 2·28 3'25TABLE 4 - VALUES OF THE INDIVIDUAL RATE CONSTANTSOF THE VARIOUS SPECIESReaction k X 10'(min-I)50° 60° 65° 70°".(a) H4P40~3+H.O -+ product 2-91 6·31 13'34 20'90k,(b) H3P40~ii+H.O -+ product 2·31 5·52 9'89 17'08k,(c) H2P.Oti+H.O -+ product 1-40 4-17 9'23 13'50(d) HP.Or3+H20k,-+ product 0'81 2·40 4'08 6·10k,(e) P40~3+H.O -+ product 0·40 1·19 2'28 3'25k X 104(litre mole'? min-I)------------------50° 60° 65° 70°,,;(f) H.P.,Oh+H30+-+ product 2·11 4-17 6'85 9·11X 10-4 X 10-4 X 10-' X 10-'k~(g) H3P40l:;+H30+--+ product 7·16 22·91 33·11 54·96X 10-3 X 10-3 X 10-3 X 10-3k;(h) H.P40t3+HaO+--+ product 4·53 13·44 28'96 48·43X 10-' X 10-' X 10-2 xl0-'k'(i) 5 • 59'85 87'80 116'9 150'8HP.OI;+H30+ -+ productTABLE 5 - COMPARISONOF OVERALLRATE CONSTANTSpHCalc. ReportedTEMP. = 65°2'555·359-8017·098·792·3318'0(a)8·30(a)2'50(a)TEMP. = 60°4·07'011·04'362·901'20(a) Ref. 4, (b) Ref. 7.4'60(b)2'0(b)0'88(b)Employing the individual rate constants, theoverall rate constants at 65° and pH 2·55, 5·35and 9·80, and at 60° and p. 4, 7 and 11 werecalculated. The calculated values (Table 5) com-pared well with those reported by Crowther andWestmann" and Griffith and Buxton",229INDIAN J. CHEM., VOL. 14A, APRIL 1976TABLE 6 - ACTIVATIONENERGY, FREQUENCYFACTORANDENTROPY OF ACTIVATIONReaction" Ea Log A /),.S*(kcaljmole) (e.u.)(a) 17-10 8·13 -21,62(b) 19·43 9'25 -16·50(c) 22-14 9'82 -13-89(d) 18·14 8'15 -21,53(e) 18·72 8·18 -21,39(f) 16'62 7·59 -24,08(g) 19·63 10'60 -10'31(h) 18'33 9·43 -15'67(i) 9·75 8·29 -20'84*The reactions (a), (b), (c), (d), etc. correspond to thosegiven in Table 4.Energy and entropy of activation - The activationenergy and the frequency factor (A) for each reactionwere calculated from the linear plots of log ki orlog k; versus liT where i = 3, 4, 5, 6 and 7. These230parameters and the entropy of activation are givenin Table 6.AcknowledgementOne of the authors (S.K.T.) is thankful to theCSIR, New Delhi, for the award of a researchfellowship.References1. Muss, J., Z. physik. Chem., A159 (1932), 263.2. MITRA, R. P., MALHOTRA,H. C. & JAIN, D. V. S., Trans.Faraday Soc., 62 (1966), 173.3. MITRA, R. P. & THUKRAL, B. R., Indian J. Chem., 8(1970), 350.4. CROWTHER,J. P. & WESTMANN,A. E. R., Can. J. Chem.,34 (1956), 969.5. SMITH, M. J., Can. J. Chem., 73 (1959), 1115.6. OTANI, S., MIURA, M. & DOl, T., Kogyo Kagaku Zasshi,66 (1963), 593.7. GRIFFITH, E. J. & BUXTON, R. L., J. Am. chem. Soc.,89 (1967), 2884.8. BELL, R. N., Ind. Engng Chem., 44 (1952), 568.9. BERNHART, D. N. & \VREATH, A. R., Analyt. Chem.,27 (1955), 44U.10. BELL, R. N., Ind. Engng Chem., 19 (1947), 97.11. MALHOTRA,H. C. & THAREJA, S. K., Indian J. Chem.,14 (1976), 223.

Kinetics of Degradation of Tetraphosphates

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Kinetics of Degradation of Tetraphosphates

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