5524
References and Notes E. W. Garbisch. J. Org. Chem., 30,2109 (1965). M. Gaudry and A. Marquet, Bull. SOC.Chim. Fr., 4169 (1969);Tefrahedron,
versity of Newcastle upon Tyne, Taylor and Francis, London, 1968,p 323; (b) L. S.Guss and I. M. Kolthoff, J. Am. Chem. SOC.,62,1494 (1940). (13)The apparent acidity constant in methanol containing small amounts of water is defined by the following equation
26, 5611 (1970).
K, = [SH+][B]/[BH+]
M.Bettahar and M. Charpentier, Chem. Commun., 629 (1970). For the mechanism of enol ether formation, see A. Kankaanpera, P. Saiornaa, P. Juhala, R. Aaltonen, and M. Mattsen, J. Am. chem. Soc.,95,3618
(1973). For the mechanism of ketone-ketal interconversion, see (a) E. H. Cordes, Prog. Phys. Org. Chem., 4,1 (1967);(b) E. H. Cordes and H. G. Bull, Chern. Rev., 74,581 (1974):(c) T. S.Davis, P. D. Feil, D. G. Kubler, and D. J. Wells, J. Org. Chem., 40, 1478 (1975). Although step a is composite, with intermediate formation of the conjugated acid of hemiketal. it is not necessary for this purpose to distinguish the two
CHBH
+
CHI-C-CH, OH b' k.a
= [CH30H2+] (Ka)m
+ [H30+]. On the other hand, in pure meth-
= [CH~OHZ'I [BI/[BH+]
Equation 7 is directly deduced from these two equations, taking into account the [CH30H2+] expression:12b [CH30H2+] = [SH+]([HzO]/([H20]
t 0.23))
(14)Equation 9 assumes that proton elimination (rate constant, k ~ , is ) the
I!+
OH
where [SH'] anol:
I
CH,--C+H,
I
-
rate-determiningstep of enol ether formation. This has been demonstrated for the following r e a ~ t i o n : ~
ka'J
CH,-C-CH3
I!
+HOCH,
+ H20
+
OCH3
k, = k,'kk'/(k-,'
+
+ C2HsOH
+
elementary steps a' and a". The rate constants k, and k-a can be expressed in the following form:
k-, = k-,'k-,''/(k-,'
RCH~CH(OC~HS)OC~H~ RCH=CH(OCzHs)
For acetone, the sum of the rate constants of ketone-ketal interconversion ( k ~ k ~for) [HBr] = M is about 0.05M-l s-l (Table I), that is, a factor Of 5 X lo3 higher than k., for the same acidity (Table Ii).Thus, kE,/ k-.[HzO] is lower that lo-$; kEt [Ill is negligible compared to the other rates of formation and destruction of Ion 11. (15)A.M. WentheandE. H. Cordes, J. Am. Chem. SOC.,87,3173(1965): see also ref 5b. (16)Given eq 10,eq 15 is deduced from the following equation
t k.") t k,")
Since the equilibrium hemiketal concentration is very low (
