The author replies to Toby.
Light absorption in photochemistry can be described by standard kinetic concepts, without inconsistencies or anomalies (1). Considering the absorbing molecular species A and the photons γ as reactants, the primary absorption step is a bimolecular elementary reaction with total order two (order one relative to A and γ, respectively), see eq 1 in ref 1. In a typical photochemical reaction mechanism, many elementary steps are relevant, but under certain assumptions such as the quasi stationary-state condition for the photoexcited A*, the rate of product formation follows also a second order law (order one relative to A and γ, respectively), see eq 5 in ref 1. If the concentrations [A] or [γ] do not change much in a particular experiment, the apparent order may be “pseudo-first order” or “pseudo-zero order”, but the true order is still two (1). One must distinguish between apparent orders, which depend on experimental conditions and may vary, and true orders.Conceptual difficulties may further arise from the following: A standard photolysis experiment is not like a conventional kinetic experiment, where reactant concentrations are uniform; rather a beam of photons collides with a sample of absorbing molecules A and is scattered elastically or inelastically, much as in a molecular beam scattering experiment (1). Along the beam path, [γ] and [A] are both changing; they are tied to each other by coupled rate equations, for example eqs 1 to 3 in ref 1. To obtain an averaged rate of product formation for the entire photolysis cell, one has to integrate the local rate equations over the cell/beam dimensions (2). Since [A] is often approximately uniform due to diffusion or convection, and since absorbed photons are replaced by a constant light source in a standard experiment, one may define an averaged concentration [A], an averaged absorbed light intensity Ia, and then define an averaged rate law with these quantities; this is the approach developed in ref 2 and referred to by Toby in his letter. One easily runs into difficulties, however, considering reaction orders of the averaged rate law: Ia is intrinsically dependent on [A] (the more A is abundant, the more photons will be absorbed) and also dependent on the cell/beam geometry, and thus a “constant” incorporating the averaged [γ] or Ia is not really a constant. This is essentially the anomaly quoted by Toby (2).
It appears to us more appealing to treat a conventional photolysis experiment like a molecular beam scattering experiment with γ and A as reactants, and to consider the underlying, fundamental local rate equations, which clearly have a defined reaction order, and not averaged quantities, which are interdependent and also depend on the physical dimensions of the setup used. These rate equations can also be applied for example to light absorption in an optical cavity which corresponds more to a conventional kinetic experiment with uniform concentrations (1). In conclusion, we still hold that a photochemical reaction has a meaningful kinetic order.
Concerning the overall net reaction, A + γ = P is a summary of the reaction mechanism under conditions, where quenching is negligible, as pointed out by Toby; in the interest of simplicity, less important reactions have been ignored in this summary. For a more thorough discussion of the (time-dependent) stoichiometry of complex reactions, we refer to the pertinent literature, ref 3–5; this does not affect the discussion of reaction orders. Literature Cited- Hippler, M. J. Chem. Educ. 2003, 80, 1074.
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- Toby, S.; Tobias, I. J. Chem. Educ. 2003, 80, 520.
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