ROBERT11. HEALYA N D ~ I . \ R Y L. KILPATRICK [CONTRIBCTIOS FROM
THE
DEPARTMENT OF CHEMISTRY O F ILLINOIS
Vol. 77
ISSTITUTE O F T E C H N O L O G Y ]
A Kinetic Study of the Hydrolysis of Trimetaphosphates't' HY r)
5011
2000
Fig. :3.-The effect of the container material on the liiiearity of the plot for the reaction in 0.00693 .If HCI a t 49.89)": A , polyethylene; B, glass; C, the initial slope of curve 13.
HYDROLYSIS OF TRIMETrlPHOSPHATES : KINETICS
Oct. 20, 1955
except as noted below, hut a t 50 and to a lesser extent at 60" there was curvature in the plot of log ( A m - A ) us. time when the reaction vessel was glass and the acid concentration as low as 0.007 .If (cf. curve B of Fig. 3 ) . One difference between the two hydrolyses is t h a t a t the acid concentrations involved the reaction of trimeta- is CQ. 10 times as fast as that of pyrophosphate, so that there is more opportunity for side reactions like adsorption to make themselves felt in the case of pyrophosphate. A number of tests to determine the effect of surface were made by carrying out the reaction a t 70" in 0.01 M , HC1 under various conditions. When the glass surface was increased by a factor of 5 by insertion of pieces Ff rod with fire-polished ends, curvature appeared in the log ( A - 2 )vs. time plot, and the initial slope was about 3 times as large as in the absence of the pieces of rod. LVhen a run was carried out in a 1000-ml. Pyrex flask, and care was taken t o remove the aliquots from the center of the solution, the value of k was the same, within the experimental error, as obtained using 100i d . Pyrex flasks, or 250-ml. polyethylene bottles, and the plots were linear in all cases. (For the technique used when a polyethylene bottle served as reaction vessel, see Campbell and K i l p a t r i ~ k ) . When ~ the polyethylene surface was increased several-fold by insertion of strips of the material, there was no effect upon k . Since there mas no detectable effect of excess polyethylene surface a t 70", the reaction in 0.007 ,lif HCI was remeasured at 50" using a polyethylene container; the data obtained are shown as curve A of Fig. 3. I t will be seen that within the accuracy of the measurements there is no curvature, and t h a t the slope of the line agrees with the initial slope of curve B. Attempts t o eliminate the curvature found with the glass vessel by increasing [P309],to 2 X M ,by addition of inactive salt, were unsuccessful.
The Kinetic Results
In Solutions of Strong Acids.-In
Table I1 are collected the results of experiments carried out a t 69.40" with samples of Na3P*303prepared over a period of several years, and containing various amounts of hydrolysis products, The amount of hydrolysis products in the sample may be estimated roughly from the data in the second column, which give the per cent. of the total activity found TABLE I1 KISETICEXPERIMEETS IN HCl SOLUTIOS AT 69 40' Sample
KO.
m0
activity in Ba PPt.C
M
0,00462 ,00462 ,00462 ,00462 ,00472 .00472 00506 ,00693 ,00943 ,00943 ,00943 ,00943 00943 00943 ,00943 ,01062 ,01084 . 0 1500 .02000
[Pa091
X
4 x 4 x 4 x 1x 2 x 2 x 2 x 1x 2 x
10-5 10-5 10-6 10-5 10-5 10-5
fi/[H-I (mole/l.)l -1 min. -
1.50 1.53 1.52 16a 1.52 16a 1.45 23 1.63 24 10-6 1.47 20 10-6 1.64 16b 10-5 1 .31f 18a 5 x 10-6 1.46 19 5 x 10-8 1.50 19 8 x 10-6 1.54 20 8 x 10-6 1.50 22 24 3 x 10-5 1.48 5 x 10-5 1.47' 20 2 x 10-4 14 1.61 4 x 10-6 1.61 17 9 x 10-6 1.4v 20 9 x 10-5 1.57 17 Av 1 .;i3 f 0 . 0 5 Under the conditions of experiment 2 of Table I . After purification; initial value, 60%. e After purification; initial value, 75%. Omitted from average. Polyethylene vessel used. 15 15
5.2 5.2 8 .iP 8.0" 8 .0 20 7.8 5.3d 10" 30 30 7.8 25 20 7.8 7.1 8.0 7.8 8.0
kH =
HC1,
5261
in the barium precipitate when the sample was tested under the conditions of experiment 2 of Table I. The fourth column gives the initial stoichiometric molarity of trimetaphosphate, and the last column gives the second-order velocity coefficient k H = k/[H+] where [H+] has been taken equal to the concentration of acid. It will be seen that k H is constant, within the experimental error, over the range of acid concentration employed. In the later part of the work k H was used as a criterion of acceptability of each preparation of Na3P*aOs; thus sample 18, which gave a low k H , was found to contain "hexameta-" (3.GyOof the total activity coming down with BaClz a t pH 2)8a,10 and was discarded. The results obtained a t 69.40' in acid-salt mixtures are given in Table 111. Experiments 1-4 of Table I11 show that the rate of reaction is about the same in perchlorate solutions as in chloride. Experiments 6 , 7 and 8 show that k H increases as [H+] increases when the ionic strength is held constant by the addition of (n-Pr)rNC104. Experiment 6 and experiment 13, and experiment 5 and experiments 11 and 12 (interpolated) show that a t M H C l = 0.00472, the hydrolysis is slower in the presence of Na+ than in the presence of (n-Pr)4N+. Experiments without added salt were also carried out a t 59.95 and 49.89' a t MHC~ = 0.00693, 0.01084 and 0.02000, respectively, with [P309]i to 3 X 10-j M . The velocranging from 4 X ity coefficients found were combined with the corresponding coefficients from Table I1 to obtain the parameters of the Arrhenius equation shown in Table V. In Solutions of Strong Bases.-The results obtained in NaOH solution a t 69.40" are given in Table IV, where the last column contains the second-order velocity constant k O H = k/[OH-1, [OH-] being taken equal to the concentration of base. For the runs without added salt log k O H was plotted vs. ~ ~ N ~ and o Hfrom , the plot k o H was estimated to be 0.3 X a t M K a o H = 0, and 0.5 X lo-* at M N ~ O= H 0.001. Experiments 3-7 show that, a t constant [Na+] and constant p , C1and OH- have about the same effect on k o H . On the other hand, when the ionic strength is increased by the use of anions of higher valence, k o H decreases (cf. experiments 9-11). Experiments 12 and 13 are the last of a series of runs carried out to determine the effect of divalent cations. In the earlier experiments with alkaline earth chlorides there was a decrease in the activity of the solution with time, probably owing to precipitation of the salts of hydrolysis products, and in the later experiments lower concentrations of both base and chloride were employed. There was no decrease in the activity of the solution when aliquots were removed as the reaction proceeded in experiments 12 and 13; the curvature in the log ( A , - '4) us. time plots is probably to be attributed to uptake of CO,. Experiments also were carried out in ( E - P ~ ) ~ N O H solution over the range 0.05-0.17 AI'. The values of k o H obtained lay below those in NaOH solution, the difference appearing to increase with concentration of base. However, since different lots of the base gave somewhat different results, numerical
Kom:KT M. HEALYAND M,mu L. KILPATRICK
536%
KINETIC
TABLE I11 EXPERIMENTS I S ACID-SALT MIXTURES
.4cid,
M
Acid
SdCl SaCIOa NaC1 sac104 ( n-Pr)rNC1O., ( n-Pr)dSC104 ( n-Pr)4XC104 (n-Pr)4SC10, CaCI? sac1 sac1 SaCl
sac1 sac1 sac1 sac1
IiINETIC
U.300 17.50
69.40'
[PaOoI,
I x 1 x 3 x :3 x 3 x 3 x 3 x 3 x 3 x 4 x 1x 5 x 3 x 5 x (iX 5 x
0.0151 ,0151
. 0400
0100 0200 . 0400 ,0356 0263 1 . 0 3 x lo-' 0075 0151 0300 0400 ,0494 ,0498
,0935
TABLE I\' EXPERIMENTS IN SaOH
S O L V T I O S AT
Salt, .I I
Salt
0 0100 0489 1000 0300 1250 1250
.M
Salt
H C1 0 00462 HC104 00474 HC1 00472 HClOI 00472 H C1 00472 HC1 .0047% HC1 00943 HCI , 0 1886 HCI ,00943 HC1 ,00472 HCI ,00462 HCl . 00172 HCI , 0047% HC1 00462 HCI .Oil470 HC1 00462 Pol)-ethylene vesael u s e d
KaOII, .M
AT
Salt,
[PJOUll
4 x 10-5
0 0700
sac1
S'lC1
0950
KCI 0784 KISOi 039% K1Fe(CS)6 0262 BaClJ 5 0 x 10-5 CaCIL 1 0 x lo-' Calculdted from initial ilope Polyethj lene vessel used 0196 0196 0196 00 10 0010
values of koH are not reported. Replacement of Na+ by (n-Pr)lN' in (n-Pr)&OH-(n-Pr)4NClNaCl mixtures caused a decrease in k o ~ Three experiments in XaOH solution were carried out a t 59.95", and three a t 49.89". The values of . 1 1 ~ employed ~0~ were 0.0489, 0.1250 and 0.1730, respectively, and [P309],ranged from 8 X l o w 6to 2 X 10-i -11. The results are summarized in Table V. The Water Reaction.-Assuming that there is an uncatalyzed reaction of trimetaphosphate with the solvent, one can write for the first-order velocity coefficient, in a very dilute solution of NaOH
+ k~[H*l
k = ko f k o ~ [ o H - ]
On substituting k o ~= 3 X and kH = 1 . 5 (mole/l.)-l min.-' and K , = 2 x one calculates that a t 69.40" the ininimuni rate should be found a t [H+] = 2 X 10-8 Jl,arid that in 1 X lo-" ill NaOH solution O.lyc of the trimetaphosphate should hydrolyze i n 10 days in the absence of a water reaction. Two-hundred arid fifty 1111. o f solution 4.5 X Jl in NajP*j09was brought by addition of dilute caustic to /IH 9.3, as measured with a Beck-
x x x x ri x 3 x x x 1 x 1 x 1 x 4 x 2 1 :3 3
ii X
P
0 . 020 020 ,045 . 04.5 ,023 045 ,045 045
10-5
10-6 10-5 10-5 10-5 10-5 10-5
10-5 10-j
,010
,012 . 020 03.5 ,043 . 0,55 055 098
10-6
10-j 10-6 10-5 10-6
10-5 10-6
69.40" P
10-4
0 010 ,049
10-5
. 100
lo-"
100 125 12,5 1E5 175 098 . 137 ,177 001
10-5 10-5 10-5 10-5 10-5 10-5 10-5 10-6
. ou1
man pH meter, a t room temperature. It was then kept a t 69.40" for 17 days, samples being removed a t intervals for determination of pH, and for analysis. By the end of the period th_e pH had fallen to 8.7, and from the log (A, - A) us. time plot k was estimated to be somewhat less than 4 x min.-l. In a second experiment a solution initially 1 . 3 X IO-6 X in NajP*jOy, 0.1 -If in NaC1, and 0.01 31 in Na2HP04 was kept for 8 days a t 69.40"; here k was estimated to be less than 3 x 10-6 min.-'. Thus in acid solution, a t [Naf] 0.1 31,any uncatalyzed reaction with the solvent would contribute less than 1.5% of the specific rate ( r j . experiment 16 of Table 111), and in alkaline solutio11 less than 2cc(cf. experiment 4 of Table I V ) . Discussion Any scheme proposed for the reaction must be in agreement with the following observations : (1) In solutions of HCl, without added salt, the second-order constant kH exhibits 1 1 0 electrolyte effect. ( 2 ) 011the other hand, k~ decreases when the ionic strength is increased by addition of (n-Pr)?NCIO? or NaC104or NaCl, a t constant [ H + ] .
HYDROLYSIS OF TRIMETAPHOSPHATES : KINETICS
Oct. 20, 1955
5263
kd' (3) When the ionic strength is maintained conP30g3- + H30+ +Products stant by addition of (n-Pr)4NC104, k H increases with increase in [H+]. for which the second-order velocity coeficient is (4)At a given acid concentration and ionic found to be strength, k H is higher in the presence of (n-Pr)dN+ kH = (k3 kr'K3 k3'[H+l l/(h [H+l 1 ( 2 ) than in the presence of Na+. (5) I n solutions of NaOH, the second-order I t is assumed, in deriving (2))that K1 and Kz are so large, and [H+] so small, that the reactions of HZconstant koH increases with increase in M N a O H . (6) On the other hand, koH decreases when the P309- and H3P309 may be neglected. I n the presionic strength is increased by the presence of poly- ence of Na+ hydrolysis might also take place via the valent anions, the cation concentration and MNaOH reaction k'Na remaining constant. NaP30g2HsO + + Products (7) In (n-Pr)4NOH solution koH is smaller than in NaOH solution, and in (~-Pr)4NOH-(n-pr)~-If (2) applies, i t follows that in acid solution a t NCI-NaC1 mixtures replacement of Na+ by (n- constant p , in the absence of Na+, k H will increase kq'K3). And with [H+] provided K3'K3> (k3 Pr)4N+ causes a decrease in koH. when ( ~ z P r ) ~ N is f replaced by Xa* a t constant (8) Very small amounts of calcium (or barium) chloride cause a great increase in the rate of hy- [H+]. and ,u, it can be shown that k H will decrease drolysis in basic solution; in acid solution, they provided k ' N a < ( k H ) N a = o, the second-order constant for the sodium-free solution. cause a small decrease in rate. Turning to the question as to why k H exhibits no (9) The water reaction is negligible under the electrolyte effect in acid solution, in the absence of conditions of the present experiments. salt, let us examine (2) further. With increase in CL The kinetic results in acid solution cannot be ac- K3 would increase, in dilute solution, and k3' and kq' counted for on the basis of a single reaction between would decrease; the change in k3 would be expected &os3-and H30+, since a reaction between ions of to be small.14 Moreover, since k4' = (k4')ofifa/fi,and opposite sign is characterized by a negative primary K B = (K&/Cfif3/fd, where (kr')o and (K3h are the kinetic salt effect,14 and a t low ionic strengths one limiting values of kd' and K3, respectively, and the would expect the effects of HCl, NaCl and (?z-Pr)4- f's are the activity coefficients of ions of valence NC104 on k H to be about the same. Similarly, the shown by the subscript, k4'K3 should be nearly kinetic results in alkaline solution cannot be ac- constant. Both numerator and denominator in counted for on the basis of a single reaction between (2) would increase with increase in MHC~, and the P 3 0 g 3 - and OH-. The great increase in rate in the observed constancy of k H might thus be due to a presence of Ca++ or Ba++, in alkaline solution; the balancing of the increase in [HP30gZ-] against the difference between the effects of (n-Pr)N+ and Na+; various electrolyte effects. On the other hand, the decrease in k O H with increase in p observed in with increase in [H+] the hydrolysis of HzP309the presence of polyvalent anions-all argue against might become a factor, so that the existence of a single reaction between P3Og3and OH-. Instead, i t appears that several trimetaphosphate species are participating in the measured reaction. Let us assume that there is no formation of (n- An argument in favor of the participation of HZPr)4NP3092--,15 but that there is, at the tempera- P309- is to be found in experiments 6, 7 and 8 of tures of the experiments, formation of HP30g2-, Table 111. If (2) applies NaP30g2-, CaP309-, etc., as reported by Davies ( d k ~ / b [ H " ] ) j=~ (k3'K - (ha klfK3)}/(K3 [ H + ] ) ' and co-workers for 25") and that these ions, as well so the slope of the curve obtained on plotting k H vs. as P 3 0 g 3 - - , are possible reactants. From the experi[H +] should decrease with increasing +I. Davies ments on the water reaction, however, i t can be con- and Monk found (K3)O to be 0,009 a[H t 25". If K3 cluded that the uncatalyzed reactions between P3is taken as (K3)0/(fif3/f2) = 0.009/0.25 = 0.036 a t 0 9 3 - and H20, and between NaP30g2- and H 2 0 , p = 0.05, a t 70", the slope should decrease by 4570 are negligible here; the same is probably true of as [H+] increases from 0.005 to 0.02 M ; actually, the uncatalyzed reactions of the complexes formed k H for the highest [H+] lies well above the line by the other metal cations. drawn through the points for the two lower ones. Let us denote by Kj the jth dissociation constant It seems probable, therefore, that H2P309- did parof H3P309, and to the reaction between H3P30g ticipate in the hydrolysis in the acid solutions used. and HzO assign the velocity coefficient k l , to that Turning to the hydrolysis in alkaline solution, between H3P309 and H30+, the coefficient k l ' , and and assigning to the reaction between OH- and so on. Then in dilute acid solution, in the absence P 3 0 g 3 - the velocity coefficient k4") and to the reacof complexing metal ions, hydrolysis might take tions between OH- and the complex ions NaP3place via the reactions Og2-, CaP30g-, etc., the velocity coefficients k''Na, k"ca,etc., one obtains for the second-order velocity ka HP302- + H20 +Products coefficient the expressions below k3 I n ( ? Z - P ~ ) ~ N solution OH HPsOg2HoO e Products
+
+
+
+
+
+
+
+
koa =
(14) 1. N. Bronsted. Z .b k .v s i k . Chem ., 102.. 164 (1922) (1.5) J. R. \-an a'nzrr and D . A Campanella. THISJ I I I . R N A I , , 72, 065
(lsao).
+
ii
k4"
(4)
I n NaOH solution, or NaOH solution containing sodiuin salt
+ ~ " Y , [ S ~ ~ ]+)INa+]) / { K N(5) ~
several trimetaphosphate species stand in order of charge: MP3O9- > M'P3092- > P30g3-. Simiwhere A N a = [I\;a+][P3093-]/[KaP30s2-]. In NaOH containing a salt of a metal other than larly, Topleyll attributed to decrease in the negative field of the anion the tenfold increase observed sodium in the hydrolysis of potassium polymetaphosphate, OH = 1 kq"KyaK~f k"v&v [ l e d L { f k ' ' ~ K ~ a [ k]/u f] in dilute NasCOs solution a t loo", upon the addi(6) mole of MgS04 per liter; in contion of 5 X where D = K N ~ K L Kra[M] ~ KM[[N~+], and trast, MgS04 had no effect on the rate of hydrolysis in dilute NaH2P04 solution. And similarly, Van K M is the dissociation constant of the new complex. .it a given p , replacement of S a + by (n-Pr)(N+ Wazer, Griffith and McCullough17 attributed the causes a decrease in KOH, so k"hTv, > k4". At con- increase in rate of hydrolysis of pyro- and triphosstant [?;a+] and constant [ K + ] K, O H decreases with phates upon replacement of (CH3)qN+by S a + , a t increasing ,u (cf. experiments 9-11 of Table IV); pH 2 4, to the formation of complexes with Na+. Since the hydrolysis of trimetaphosphate in either this is to be expected from (6) if k R N a > k4" and HCI or NaOH solution is composite, the frequency k " K > k4", since factors and energies of activation obtained from 3lP4OU3 I/Ip1c)91 k~ and k o (cf. ~ Table V) are composite. The value
