Research: Science & Education
Does a Photochemical Reaction Have a Reaction Order? S. R. Logan Department of Chemistry, University of Ulster at Coleraine, N. Ireland, BT52 1SA, UK 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) /NA, where φ is the quantum yield for the photochemical interconversion of A to B and N A is Avogadro’s constant. An equation equivalent to the above expression is to be found in Levine (1) as eq 21.82. In general, the topic of photochemical kinetics is not treated in physical chemistry texts.
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/ NA, 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
