Does a Photochemical Reaction Have a Reaction Order?

Abstract

Among chemical reactions in the gas phase or in solution that require no external agent such as light or ionizing radiation to bring them about, the concept of reaction order is well understood as the index of the concentration of the reactant that leads to a parameter proportional to the reaction rate. Where the reaction is occasioned by light absorption and is a straightforward conversion of one species into another, the progress of the reaction is controlled simply by the rate of light absorption by the molecules of reactant. However, one can cite circumstances in which the log of the concentration of the reacting species will fall linearly with time and there is then a temptation to describe the photochemical process as being a first-order reaction. The propriety of so doing deserves comment.If one considers a simple photochemical reaction system in which the reactant molecule A absorbs at the wavelength of the exiting light whereas the product molecule B does not, assuming that a parallel and uniform beam of light makes normal incidence on a rectangular cell, it is possible to produce a simple expression for the rate of light absorption. If there are Q quanta per second entering the cell, of path length l, then the number of quanta per second absorbed within the cell is given by Q (1 -10 -εcl ), where ε is the molar decadic absorption coefficient of A at the wavelength of irradiation and c denotes the concentration of A. Consequently the number of moles of A caused to react in unit time will be φQ(1 -10 -εcl )/N A , where φ is the quantum yield for the photochemical interconversion of A to B and N A is Two extreme situations are readily identified. One occurs when εcl > 2, so that well in excess of 99% of the light entering the cell is absorbed within it. Thus the number of moles of A reacting in unit time is essentially φQ/ N A , which is independent of the concentration of A. That is, provided that the concentration of A is much greater than (ε l) ᎑1 , the rate of the photochemical conversion is constant. Consequently, the amount of A in the cell will now decrease linearly, and if the cell contents are well stirred, the concentration of A will fall off in that manner.The other extreme is when εcl << 1, and only a small fraction of the light entering the cell is absorbed within it. In this case the factor (1 -10 ᎑εcl ) is well approximated by 2.303 εcl, so that the number of moles of A reacting in unit time is given by 2.303 φQεcl /N A , which is directly proportional to the concentration of A. Consequently, the amount of A in the cell will decrease exponentially.This shows that, as a consequence of these differences in experimental conditions, this photochemical conversion may fit either of two regimes. In the first, the amount of A in the cell decreases as it would for a reaction of zero order; but in the second, it falls as for a firstorder reaction. Since the manner of the decrease of the reactant concentration is so totally a function of the reaction conditions, it makes no sense to speak of a reaction...

Time‐Dependent Differential and Integral Quantum Yields for Wavelength‐Dependent [4+4] Photocycloadditions

“…For the (apparent) reaction order to be zero, c A needs to be in a range in which ( k 2 + k 3 ) c A ≫ k −1 meaning that the k −1 term, corresponding to the monomolecular de‐excitation events, becomes negligible in comparison to term for the bimolecular events ( k 2 + k 3 ). Additionally, within the term, Equation (4), ϵ Lc A has to be sufficiently large so that small changes in do not lead to significant changes in the fraction of light absorbed, thus appearing to be independent of concentration . Under such conditions Equation (5) reduces to Equation reflecting zero‐order kinetics: …”

“…The case of an apparent reaction order of two is possible under conditions in which ϵ c A L is again small enough, so that is proportional to , while ( k 2 + k 3 ) c A ≪ k −1 making ( k 2 + k 3 ) c A negligible. This allows the simplification of Equation (5) to Equation : …”

“…Additionally,w ithin the J A term, Equation (4), eLc A has to be sufficiently large so that small changes in c A do not lead to significant changes in the fractiono fl ight absorbed, thus appearing to be independento fc oncentration. [32] Unders uch conditions Equation (5) reduces to Equation (6) reflectingzero-order kinetics: The case of an apparent reaction order of one can be achieved under two circumstances. If the eLc A term in J A ,E quation (4), is still large and thus J A appearsi ndependent of c A , [32] and simultaneously (k 2 + k 3 )c A !…”

“…[32] Unders uch conditions Equation (5) reduces to Equation (6) reflectingzero-order kinetics: The case of an apparent reaction order of one can be achieved under two circumstances. If the eLc A term in J A ,E quation (4), is still large and thus J A appearsi ndependent of c A , [32] and simultaneously (k 2 + k 3 )c A ! k À1 ,m aking (k 2 + k 3 )c A negligible Equation (5) reduces to Equation (7):…”

Photochemical Reactivity of 1,6-Methano[10]annulene

“…This obviously implies that at least two photoproducts are generated under continuous irradiation. The absorption spectrum at the end time, where the structured profile overlaps a high rising background absorption, is reported in the inset of , it is possible to extract the time dependence of the 1a and nph concentrations, 38 respectively, in the pulsed experiment. For instance, at t = 320 min, ∼92% of the initial amount of 1a has reacted.…”