JOURNAL O F T H E AMERICAN CHEMICAL SOCIETY Regislered i n U.5'. Palenl Ofice.
@
C o P v i g h l , 1964, by the American Chemical Sociely
VOLUME86, NUMBER10
MAY
20, 1964
PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION FROM
THE ESSO
RESEARCHAND ENGINEERING CO., P R O C E S S RESEARCH DIVISION,LINDEN,N. J . ]
The Cage Effect in Solution and Gas Phase with Application to the Determination of Rate Constants BY RICHARD K. LYON RECEIVED J U N E18, 1963 T h e hitherto not generally recognized gas phase cage effect has been demonstrated. The Samuel-Magee model' permits calculation of the recombination rate constant of methyl radicals from the observed efficiencies of t h e gas phase cage effect. The rate constant thus calculated agrees well with t h a t measured by Gomer and Kistiakowsky.z The application of this theory t o investigations of the cage effect in solution gives generally satisfactory agreement. I t is concluded t h a t the model provides a general method for obtaining rate constants from measurements of the efficiency of the cage effect.
Introduction and Definitions The fact t h a t radicals can react with each other very rapidly and t h a t they are necessarily created and destroyed in pairs produces two well known effects in solution chemistry : the diffusion controlled reaction and its obverse, the cage e f f e ~ t . ~The , ~ rate of the reaction A B + AB is given by
+
d[AB]/dt = JkR[A][B]dV/b'
=
~ R [ A ] [ B ](1)
where [ A ] [ B ]is read as the product of the local concentrations of A and B averaged over the entire volume of the solution. If A and B are formed from the same molecule (for example, by the reaction ANNB + A B Nz) then [A][B] >> [AI X [Bl for newly formed radical pairs. But [AI[B]
