ðÞenergy conversion efficiency ¼’DGDb
Ephoton: ð 1 ÞHowever, the reasonability of this calculation has been scarcely
discussed so far.
IV. KineticsA. FIRST-ORDERKINETICS
It is well known that first-order kinetics is commonly observed for
reactions occurring in homogeneous phases, that is, reactions in
homogeneoussolutionsoringasphase.Ideally,rateofamonomolec-
ular reaction obeys first-order rate expression which is explained by
that the proportion (number) of molecules that have kinetic energy
larger than the activation energy is determined only by the temper-
ature of reaction and actual number of molecules with energy for
activation is proportional to the concentration (or pressure) of
molecules. For thesereactions,kineticdata areanalyzedbyplotting
the logarithm of concentration of a substrate or a product against
time of the reaction( 17 ) to obtain a linear line, and absolute value
of the slope of the line is a rate constant,k(Fig. 6). The rate (r) of
consumption of a substrate (A) is shown by the following equation.
r¼dA½
dt¼k½A: ð 2 ÞOn the other hand, kinetics of reactions occurring on a solid
surface, that is, catalysis or photocatalysis, must be significantly
different. There may be two representative extreme cases. One is
so-called a diffusion controlled process, in which surface reactions
and the following detachment process occur very rapidly to give a
negligible surface concentration of adsorbed molecules, and the
overall rate coincides with the rate of adsorption of substrate
molecules. In this case, the overall rate is proportional to concen-
tration of the substrate in a solution or gas phase (bulk), that is,
first-order kinetics is observed( 18 ). The other extreme case is so-
called surface-reaction limited, in which surface adsorption is kept
in equilibrium during the reaction and the overall rate coincides
with the rate of reaction occurring on the surface, that is, reaction
of e–and hþwith surface-adsorbed substrate ( 19 ). Under these
conditions, the overall rate is not proportional to concentration of
the substrate in the bulk unless the adsorption isotherm obeys a
Henry-type equation, in which the amount of adsorption is propor-
tional to concentration in the bulk ( 20 ). In the former case, the rate
406 B. OHTANI