NOTES
1761
Kinetics of the Ortho-Pyro Interconversion The aldehyde signal of isomer I is found to be split owing to spin coupling with the 5-hydrogen (J'CHO-S= in 100% Phosphoric Acid 1.05 c.P.s.); any coupling to the 4-hydrogen could no longer be observed. The smaller aldehyde signal by Ronald A,. Munson assigned to isomer I1 is also found to be split into a doublet. That this splitting is due to spin coupling General Electric Research Laboratory, Schenectady, New Y O T ~ with the 4-proton ( J I ' C ~ O= - ~ 0.85 c.P.s.) was estab(Received December 7,1964) lished through the collapse of this doublet into a singlet when a second strong radiofrequency field was applied Crystalline phosphoric acid is believed to consist at the position of the signal from the Phydrogen (the exclusively of orthophosphoric acid. Upon fusion, signals from the Phydrogen are expected to occur at a small portion of the orthophosphoric acid is converted about the same field in both I and 11; the signal from to pyrophosphoric acid and water producing a deisomer I1 is, however, obscured by the much stronger signal from isomer I). It is estimated that J'cHo-~ ki and J " c ~ o are-less ~ than 0.2 C.P.S. 2HsP04 HZ207 Hz0 (1) kP Under the assumption that J'c~o-4 and J I ' C ~ O - ~ crease in specific electrical conductivity (u). This are zero, we may write the following relations for the conductivity decrease has been found to be directly averaged spin coupling constants above the temperaproportional to the pyrophosphate concentmtion.4 ture at which the rotation of the aldehyde group is At 38O, 5.2 mole % orthophosphoric acid is converted.s "frozen in": J c ~ 0 - 5= PI X 1.05 and Jc~0-4 = The rate expression for eq. 1 written in terms of the (1 - P I ) X 0.85 c.P.s., where PI is the fractional mole fraction pyrophosphate (z) is population of isomer I. The temperature dependence of the equilibrium constant K = PI/(^ - PI) was dx - = kl(1 - 242 - h X 2 determined from the temperature variation of J c ~ o - 4 dt and J c ~ 0 - 5between -40 and $50" and from a plot of In K os. 1/T a value of 1.2 i 0.2 kcal./mole for the which, when integrated and expressed for near-equienthalpy difference AHo(= HI" - H I I " )was obtained. librium conditions, yields From the apparent coalescence temperature, -63", In [ u - urn[= constant - 2 d a t (3) for the aldehyde signal an approximate value for the free energy of activation, AF* % 11.0 kcal./mole16can be The preparation of crystalline orthophosphoric acid calculated. This value is somewhat higher than the has been des~ribed.~The conductivity of the phosAF* values recently reported by Anet and &mad7 for phoric acid was measured following fusion in a thin, three benzaldehyde derivatives. sealable Pyrex conductivity cell of standard design If the above-mentioned interpretation of the lowwhich had been placed in a silicone oil constant-tempertemperature spectrum of 2-furanaldehyde is correct, the ature bath. The high viscosity of the phosphoric observed stereospecific, long-range aldehyde couplings acid and its heat of fusion slowed the attainment of in the rotational isomers I and I1 do not follow the rule thermal equilibrium so that the uncertainty in t = of coupling via the "straightest zigzag path" proposed 0 did not allow the initial hyperbolic tangent relaby Banwell and Sheppard.8 tionship expected from (2) to be useful in interpretaThe difference of 0.15 p.p.m. in proton shift for the tion of the data. 3-hydrogen between the two isomers indicates that care Values of the product k~kzdetermined from the slope must be exercised when conclusions regarding r-elecof plots similar to Figure 1 are tabulated in Table I. tron densities are drawn from shift data on aromatic An attempt was made to determine the value of kl/k2 aldehydes. by a n.m.r. Palresonance investigation,6using a 12-Me.
+
(6) The value of AF* is calculated from the theory of absolute reaction rates and actually is an average value of AF*I +11 and AF*II-+I (the subscripts refer to the rotational isomers). These two quantities differ by AFO at -63' (or about 0.6 kcal./mole). As the AF* value reported may be in error by some &0.3 kcal./mole, no attempt has, however, been made to divide up AF*. (7) F. A. L. Anet and N. Ahmad, J. Am. Chem. Sac., 86,119 (1964). (8) C. N. Banwell and N. Sheppard, Discussions Faraday SOC.,34, 115 (1962).
(1) A. Simon and G. Schulze, 2. anorg. allgem. Ohm., 242, 316 (1939). (2) 5. Fuberg, Acta C h a . Scand., 9, 1557 (1955). (3) J. P.Smith, W. E. Brown, and J. R. Lehr, J. Am. C h a . Sac., 77, 2728 (1955). (4) R. A. Munson, to be published. (6) R. A. Munson, J. Phys. C h a . , 68, 3374 (1964). (6) C. M.Huggins, J. B. Bush, Jr., and R. A. Munson, unpublished
study.
Volume 60, Number 6 May 1966
NOTES
1762
Table I Temp.,
OC.
40 4.5
80 100.5
kikP
6.11 X 1.57 x 6.06 x 10-4 7.41 x 10-3
kdki
ki
8.79 f 0.4 X 9.5 0.5 x 10-4 1.6 i 0 . 4 X 2 . 1 f 0 . 8 x 10-3
2.31 i 0.04 X 10-6 3.87 f 0.1 X 10-6 9.85 i 1 . 2 x 10-4 3 . 9 i 0 . 7 x 10-3
ki
2.64 f 0.05 4.05 i 0.1 0.615 f 0.07 1 . 9 f 0.4
x x
10-2 10-2
a kl and are given in units of reciprocal mole fraction reciprocal minutes. The wtimated error in the values of kland k, at 40 and 45' is determined principally by the accuracy with which b/h is known. At the higher temperatures the error limits are determined Approach to equilibrium from the pyrophosphate-rich side a t 40"; from pure orthoby the uncertainty in the estimation of AH'. phosphoric acid a t the other temperatures.
'
-1.5
I-
TIYE (MINUTES)
Figure 1. The approach to pyrophosphateorthophosphate equilibrium at 80.0'.
A F O , and ASo have been found in concentrated aqueous solutions of NaH2P04.' A reported slow heat evolution* in molten phosphoric acid was probably caused by the hydrolysis of pyrophosphate formed at a higher temperature. Good Arrhenius plots were obtained from the rate constants although it might be mentioned that molten phosphoric acid is a supercooled liquid a t 40'. The forward reaction, kl, has an activation energy of 20 f 1 kcal./mole, and the activation energy for k2is 17 kcal./mole. The rate of hydrolysis of pyrophosphate in aqueous solution increases with decreasing ~ H , ~ - -and l l it appears that all the pyrophosphate species undergo hydrolysis with the possible exception of P207-*anion. In strong acid solutions there is good evidence for both a direct water reaction and a hydrogen ion catalyzed hydrolysis.10 The activation energy of the over-all hydrolysis decreases continuously with decreasing pH10J2from about 30 kcal./mole a t high pH to 21 kcal./ mole at pH 1. In anhydrous phosphoric acid the hydrolysis may be expected to proceed exclusively by means of the acid-catalyzed path. The value of 17 kcal./mole which we find for this hydrolysis is consistent with the identifhation of the lower activation energy for pyrophosphate hydrolysis with the acidcatalyzed reaction and the assignmen.t of the higher activation energy of 30 kcal./mole to that of a direct water reaction.
probe, of the pyro to ortho signal ratio as a function of temperature. Unfortunately, the quality of the signal decreased sharply above room temperature, but the results did suggest a possible moderate increase in the pyrophosphate concentration as the temperature was raised. A sample of phosphoric acid when melted at 45' undergoes a total conductivity decrease of approximately 9.2%. The same sample when equiAcknowledgment. The author is indebted to Mr. librated a t 80' and then rapidly cooled to 40' shows a M. E. Lazarus for laboratory assistance. conductivity increase of 3.4%. After a small correction for the greater change in conductivity per mole of (7) C. D. Schmulbach, J. R. Van Wazer, and R. R. Irani, J. Am. solute at lower temperat~re,~ we estimate the ratio Chem. SOC.,81, 6347 (1960). of pyrophosphate concentration at 80' to that a t 40' (8) E. P.Egan, Jr., and Z. T. Wakefield, J. Phys. Chem., 61, 1500 (1957). t o be (9.6 3.4)/9.6 = 1.35 f 0.15, which is equi(9) J. P. Crowther and A. E. R. Westman, Can. J . Chem., 32, 42 valent to a N ofor eq. 1of +3.3 1 kcal./mole. (1954). at 38°.6 The values k1/k2is known to be 8.45 X (10) D.0. Campbell and M. L. Kilpatrick, J. Am. Chem. Soe., '76, 893 (1954). of k& of Table I are obtained from this value and the (11) J. D. McGilvery and J. P. Crowther, Can. J. Chem., 32, 174 estimated heat of reaction 1. This leads to AFo = (1954). 1.9 i 0.2 kcal./mole and ASo = +4 e.u. in the tem(12) J. R. Van Wazer, E. J. Griflith, and J. E'. McCullough, J. Am. perature ra,nge 0 to 100'. Similar values of AHo, C h . Soc., 74, 4977 (1952).
+
The Journal of Physical Chemistry
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