KINETICS OF THE DISSOLUTION OF DILUTE SODIUM AMALGAM * BY ROBERT LIVINGSTON
Bronsted and Kane' have recently demonstrated that the rate of dissolution of sodium from a dilute amalgam into a solution of a weak acid is given by the following equation d(ZNa) - k(ZNa) *(A) I dt where (ZNa) is the stoichiometric concentration of sodium in the amalgam and (A) is the concentration of the acid in the aqueous (or benzene) layer. I n interpretation of these results, they advance the following mechanism.
A
+ e -+ B + H (slow)*
2H + Hz (relatively rapid) Na+ -+ Naf (relatively rapid) (metal) (dissolved)
4B-K 6B-K 3B-K
While this mechanism affords an explanation of the proportionality of the rate to the concentration of the acid, it does not offer a direct explanation of the dependence of the rate upon the square root of the sodium concentration. It is well known that sodium and mercury form the compound NaHg,. Evidence for the stability of this compound may be obtained (I) from the sharpness of the corresponding maximum in the melting-point curve: ( 2 ) from the high heat of solution of sodium in mercury: and (3) from the large difference of electrical potential between sodium and sodium amalgama6 It seems probable therefore that the following equilibrium (which may take place in steps) is an important factor in determining the rate of dissolution. NaHgz FI Na+
+ 8 + Hgz (rapid reversible)
2
The rate of reaction 4B-K is V4B
-X
= k4B - K
(A)
(e)
3
But applying the mass action law to reaction z 4
* Contribution
from the School of Chemistry, University of Minnesota. Bronsted and Kane: J. Am. Chem. SOC.,53, 3624 (1931). 2 A and B represent a conjugate acid and base respectively. See Bronsted: Rec. Trav. chim., 42, 718 (1923). 3 Inter. Crit. Tables, 2, 436. 4 Inter. Crit. Tables, 5, 202. 6 Inter. Crit. Tables, 6, 332. 1
2 IO0
ROBERT LIVINGSTON
Since the greater part of the sodium exists as the compound, equation 4 may be written approximately as(€3) = K1 (zNa)* 4a The combination of equations 3 and 4a leads directly to the empirical equation I . I t should be mentioned that no mechanism which postulates the existence of appreciable concentrations of the ion NaHg+zneed be considered, since such a compound, between the mercury molecule and the sodium ion (with its rare gas structure) would undoubtedly be relatively unstable. In other amalgams where there is less tendency toward compound formation, the rapid reversible step may be
+
Me $ Me+ 8 5 This reversible step would be consistent with an empirical equation similar to equation I , if the metal were largely non-ionized; but if it existed chiefly as ions and electrons, the rate of dissolution would be directly proportional to the stoichiometric concentration of the metal. This suggests a possible explanation of the results of Fraenkel and Heinz6 on the rate of dissolution of alkaline earth amalgams. Summary A mechanism is presented for the dissolution of sodium from dilute amalgams. 6 Fraenkel and Heine: Z. anorg. Chem., 137, 39 (1924). While this paper was in proof two articles have appeared which discuss the results of Bronsted and Kane ( I ) . C.V. King and M.M. Braverman( J. Am. Chsm. Soc. 54,1744( 1932)) have studied the rate of dissolution of solid metals in acid sohtions oontsinin: depolarizers, and hay-e concluded that f hs rates are entirelydeterm'ned by diffusionspeed. L.P. Hammett and A.E. Lorch (J.Am. Chem. Soc. 54,2128(1932)) advance the theory that the square root law is to be attributed to a phenomenon related to over vo!tsge. Needles3 to s l y , the mechanism discLssed hera is a s'gnificant explanation only if the measured rates were not influenced by the speed of diffusion. (cf.Ref. I , pp. 3634-5).
