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385
Calculation of the Ostwald Solubility Coefficient for Hydrogen Atoms
and the Absolute Rate Constants of Their Addition to Propylene
by M. Szwarc Department of Chemistry, State University College of Forestry at Syracuse University, Syracuse, New York (Received November 8 , 1963)
The Ostwald solubility coefficient for H atoms in butane at 77OK. was calculated from the data of Klein and Scheer. The result3 show that the heat of solution of H atoms is about 0.1 kcal./mole, i . e . , the polarizability of H is higher than that of He or H, and slightly lower than that of argon. The absolute rate constant of H atom addition was calculated to be 1 X 10a cc./mole. see., Le., it seems to be only slightly higher than the value proposed by Klein and Scheer.
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In an elegant paper, Klein, et aLll attempted to determine the absolute rate constant for H atom addition to propylene dissolved in butane a i 77°K. They assumed that the addition of H atoms is much faster than their combination and on this basis they found k a d , j . [HI = 2.5 >C set.-' and (k,dda))”*[H] = 8 >< 10-8 mole’” em.-‘/z sec.-l. The derivation of the absolute rate (constant was then based on an arbitrary assumption, namely that the Ostwald solubility codficient of H atoms in butane is unity at 77°K. We shall show now that this assumption, which turned out to be nearly correct, is unnecessary and further information may be derived from Klein and Scheer’s data. I t is essential to prove that the basic assumption of the relatively slow combination of H atoms is correct. This is shown by Klein and Scheer in their following paperz where the absence of the ’reaction C3HaD D + C3HeD2 was demonstrated in the system in which the reaction C3H6 D -+ C,H613 did occur. On this basis, we may write the inequality
+
kadd
+
[propylene]
3
~ o k[HI ,
where k, denotes the bimolecular recombination COW stant of H atctms in butane, the coeficient 10 indicating that no more than 10% of the atoms recombine. The recombination is diffusion-controlled and hence k,lB = 4rpN
where 9 is the diffusion constant of H atoms, p their collision radiw, and Ai the Avogadro number. Taking
the reasonable value p = 0.5 A., one finds k,/D -= 3.8 X l o f 6and this in conjunction with the findings of leads to k r / k a d d = Klein, et aL,l Le., k a d d / 9 = 3.8.106. Substituting this value into the above inequality and knowing the concentration of propylene to be mole/cc. we find [HI 2.6 X mole/ cc.; k a d d 3 108 cc./mole see.; D 3 1 x 10-3 cm.8,’ sec.; and k , 3 3.8 X 1013cc./mole sec. It is improbable that either 9 or IC, would be much greater than their limit and hence the lower limits give the approximate values of these constants. This scheme is, of course, self-consistent, giving the rate of addition 10 times greater than the rate of H recombination. The concentration of H atoms in the gas phase is calculated on the basis of Langmuir’s equation3 to be 2 X lO-’O niole/cc. Therefore, the Ostwald solubility coefficient of H atoms at 77’K. is only slightly larger than unity. The entropy change for this proeess may be taken to be the same as for the transfer of He from the gas phase into the equal concentration of He atoms in liquid butane. The latter may be calculated from the data of Gross, et a1.,4 and gives As -= 1.5 e.u. Hence, the heat of solution of H atoms m
> rate of addition.
Acknowledgment. We wish to thank the Office of Ordnance Research, Durham, for financial support of this work through Grant DA-ORD-31-12461-G72. leading to the rate of D uptake = ( l e , ~ ~ [ ~ l e f i n ] d ) ) ~ ' ~ , Co. We may now calculate the concentration Go of D ( 5 ) S.Peter and M. Weinert. Z . physik. Chem., 5 , 114 (1956). atoms in the highest layer of the liquid propane. Hav(6) T. T. Kassal and M.Sswarc, J . Phys. Chem., 6 8 , 381 (1964) ing the values for the concentration of propylene and (7) R. Klein and M D. Scheer, ibid., 65, 375 (1961). the rate of D atom uptake and accepting the above (8) T. T. Kassel, Ph.D. Thesis, Syracuse University, 1963. D(d2CX/dX2) =
T h e Journal of Physical Chemistrg
kadd
[Olefin]CX
