8078 J. Phys. Chem. A, Vol. 106, No. 35, 2002
Taub et al.
magnesium. In keeping with the observed kinetics, this chan-
neling effect becomes more extensive as chloride concentration
increases, but the effect of chloride levels off when the surface
becomes sufficiently porous that the rate-determining process
is availability of reactive magnesium lattice sites. If an acidic
solution is used, such as HCl or even CuCl2, which hydrolyzes
extensively lowering the pH to 2, the precipitate does not form
and the oxide/hydroxide layer is rapidly removed, so the
magnesium surface is readily available for further reaction.
Accordingly, reaction 10 is faster when copper(II) solutions are
used. Moreover, the phenomenological rate of dihydrogen
formation will depend on the total availability of unreacted
magnesium sites, which will generally increase with increasing
surface area. Consequently, the reaction rate normalized for the
same mass of magnesium is slowest when the Mg(Fe) is shaped
as a plate or cylinder and fastest when left as small particles (I.
A. Taub et al., unpublished data).
The nonhomogeneous distribution of the transient precursor
and resultant electron entities in the vicinity of the interface
between magnesium and solution will change with time, because
reactions involving these entities occur on a time scale
comparable to diffusion away from the sites of their formation.
Thermodynamic values obtained from measurements on equili-
brated homogeneous systems should be applied cautiously, if
at all, to individual steps in such mechanisms. Nevertheless, it
is worthwhile considering the free energy change of reaction 2,
the mechanism’s rate-determining step. Using available ther-
modynamic data leads to an unfavorable free energy change
for this reaction. The reverse of reaction 2 involves a sequence
of two elementary steps. If we assume the reverse steps are
rapid, possibly diffusion controlled, and apply the steady-state
concept to [Mg+], we can calculate the rate constant of the
forward step from the mass action law. This rate constant should
be equal to the observed rate constant, k, defined above. With
K2 ) 3.15 × 10-18 M2, and the third-order reverse rate constant
approximately equal to 1 × 1015 M-2 s-1, we calculate a forward
rate constant approximately 3 × 10-3 s-1, consistent with k
(Figure 3).
to suppress H2 formation, while otherwise controlling the overall
rate of reaction of iron-activated magnesium with water by
adjusting [Cl-] or pH. The model developed herein provides a
better understanding of the many roles played by magnesium
in technology, especially with regard to corrosion, and the
formulation of chemical heaters and underwater H2-generators.
Acknowledgment. We thank Donald Pickard for his interest
in and support of this project, and Edward W. Ross for his help
in developing mathematically sound techniques for the extraction
of reliable rate data from calorimetric measurements.
References and Notes
(1) Raynor, G. V. The Physical Metallurgy of Magnesium and Its
Alloys; Pergamon Press: New York, 1959.
(2) Cotton, F. A.; Wilkinson, G. AdVanced Inorganic Chemistry, 5th
ed.; John Wiley & Sons: New York, 1988.
(3) Perrault, G. G. In Encyclopedia of Electrochemistry of the Elements;
Bard, A. J., Ed.; Marcel Dekker: New York and Basel, 1978; Vol. VIII,
pp 263-319.
(4) Topper, H. H. Educ. Chem. 1978, 15, 134.
(5) Folomeev, A. I. Zh. Prikl. Khim. 1986, 59, 267-270.
(6) Kuhn, W. E.; Friedman, I. L.; Summers, W.; Szegvari, A. In ASM
Handbook Vol. 7: Powder Metallurgy; ASM International: Materials Park,
OH, 1984; pp 56-70.
(7) Kustin, K.; Ross, E. W. J. Chem. Educ. 1993, 70, 454-459.
(8) Feigl, F.; Anger, V.; Oesper, R. E. Spot Tests in Inorganic Analysis,
Sixth English Edition; Elsevier Publishing Company: Amsterdam, 1972.
(9) Makar, G. L.; Kruger, L. Int Mater ReV 1993, 38, 138-153.
(10) Weisz, P. B.; Goodwin, R. B. J. Catal. 1966, 6, 227-236.
(11) Jordan, P. C. Chemical Kinetics and Transport; Plenum Press: New
York, 1979.
(12) Ross, A. B.; Mallard, W. G.; Helman, W. P.; Buxton, G. V.; Huie,
R. E.; Neta, P. NDRL-NIST Solution Kinetics Database:-Ver. 3.0; Notre
Dame Radiation Laboratory, Notre Dame, IN, and National Institute of
Standards and Technology, Gaithersburg, MD 1998.
(13) Hunt, J. W. In AdVances in Radiation Chemistry; Burton, M.,
Magee, J. L., Eds.; John Wiley: New York, 1976; Vol. V, pp 185-315.
(14) Jonah, C. D.; Miller, J. R.; Matheson, M. S. J. Phys. Chem. 1977,
81, 1618-1622.
(15) Balkas, T. I.; Fendler, J. H.; Schuler, R. H. J. Phys. Chem. 1970,
74, 4497-4505.
(16) Pimblott, S. M.; LaVerne, J. A. J. Phys. Chem. A 1998, 102, 2967-
2975.
(17) MATLAB; The MathWorks, Inc., 24 Prime Park Way, Natick, MA
01760, 508 647 7000.
(18) Tomashov, N. D. Theory of Corrosion and Protection of Metals;
The MacMillan Company: New York, 1966.
(19) Dupla`tre, G.; Jonah, C. D. Radiat. Phys. Chem. 1985, 24, 557-
565.
(20) Steen, H. B. J. Phys. Chem. 1970, 74, 4059-4061.
(21) Hughes, G.; Roach, R. J. Chem. Commun. 1965, 600-601.
(22) Walker, D. C. Can. J. Chem. 1966, 44, 2226-2229.
(23) Walker, D. C. Can. J. Chem. 1967, 45, 807-811.
(24) Sternberg, H. W.; Markby, R. E.; Wender, I.; Mohilner, D. M. J.
Am. Chem. Soc. 1967, 89, 186-187.
The e-s and H• that survive reaction near the magnesium-
solution interface and become homogeneously distributed
throughout the solution then undergo competitive kinetic
reactions that further influence the nature and amount of final
products, including H2. The relative amounts of e-s and H• that
appear in the bulk solution, however, will be significantly
affected by the reactivity and concentration of scavengers. These
concepts were considered in developing a chemical heater based
on the Mg(Fe) reaction with water in which 70% more heat is
generated while suppressing 80% of the H2 yield.33
(25) Gillis, H. A.; Quickenden, T. I. Can. J. Chem. 2001, 79, 80-93.
(26) Gauduel, Y.; Pommeret, S.; Migus, A.; Antonelli, A. J. Phys. Chem.
1989, 93, 3880-3882.
Conclusions
(27) Pe´pin, C.; Goulet, T.; Houdet, D.; Jay-Gerin, G.-P. J. Phys. Chem.
A 1997, 101, 4351-4360.
These studies on the kinetics of the reaction between iron-
activated magnesium particles and water demonstrate that short-
lived, partially, and fully solvated electrons (e-p and es-) are
precursors of dihydrogen, and that they and hydrogen atoms
(H•) formed from them can be scavenged, resulting in suppressed
(28) Goulet, T.; Pe´pin, C.; Houdet, T.; Jay-Gerin, G.-P. Radiat. Phys.
Chem. 1999, 54, 441-448.
(29) Kimura, Y.; Alfano, J. C.; Walhout, P. K.; Barbara, P. F. J. Phys.
Chem. 1994, 98, 3450-3458.
(30) Pastina, B.; LaVerne, J. A.; Pimblott, S. M. J. Phys. Chem. A 1999,
103, 5841-5846.
H2 yields. In the absence of scavengers, e- and H• each react
(31) La Verne, J. A.; Pimblott, S. M. J. Phys. Chem. A 2000, 104, 9820-
s
9822.
bimolecularly to give dihydrogen. Consequently, it is possible
and practical to choose solutes with suitable solubilities and
with appropriate rate constants for reaction with e-p , es-, or H•
(32) Konovalov, V. V.; Raitsimring, A. M.; Tsvetkov, Yu. D. Radiat.
Phys. Chem. 1988, 32, 623-632.
(33) Taub, I. A.; Kustin, K. U.S. Patent 5,517,981, May 21, 1996.