Chemical Education Today
Letters with equals signs. If we want the overall stoichiometry of the species in the system under consideration, it is
Does a Photochemical Reaction Have a Kinetic Order? In the article “Photochemical Kinetics: Reaction Orders and Analogies with Molecular Beam Scattering and Cavity Ring-Down Experiments” (1), Hippler asserted that if a photochemical reaction is initiated by (1)
A*
A + hν
then the system can be assigned a kinetic order. An order is associated with a rate constant and is simply related to a concentration term. As pointed out by Shaw and Toby some time ago (2) there are anomalies associated with the characterization of eq 1 in terms of a rate constant. These are resolved by writing for the rate of reaction 1 d − [ A ] = Ia dt where Ia is the absorbed intensity. Ia represents an intensity averaged over a photolysis cell of length L with units of quanta (or einsteins) per volume–time. Using the Beer–Lambert law and taking the absorption coefficient (molar or particle) as ε gives the instantaneous rate as d [ A ] = I 0 1 − e − ε [ A] L dt As Logan has pointed out (3), when the light absorption is high the rate is proportional to I0 which corresponds to zero order in reactant concentration. At low light absorption the rate is proportional to [A] which is first order. Since the order depends on the magnitude of [A], the concept of reaction order for a photochemical reaction is of little use. If we include the secondary reactions −
A* A*
P
(2)
A
(3)
then assuming a steady state in [A*] we have −
d k2 [ A ] = Ia dt k2 + k3
= Φ Ia
where Φ is the overall quantum yield. The overall rate, like the primary rate, still lacks a meaningful order that is independent of [A]. Further, Hippler writes for the overall reaction of steps 1, 2, and 3 A + hν = P The equals sign implies that every quantum absorbed results in a molecule of product, which is clearly not true if reaction 3 is appreciable. As has been pointed out (4), overall reactions cannot generally be obtained by replacing arrows
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[ A ] 0 − [ A]
= [P ]
assuming no product is initially present. Literature Cited 1. 2. 3. 4.
Hippler, M. J. Chem. Educ. 2003, 80, 1074. Shaw, H.; Toby, S. J. Chem. Educ. 1966, 43, 408. Logan, S. R. J. Chem. Educ. 1997, 74, 1303. Toby, S. J. Chem. Educ. 2000, 77, 188. Sidney Toby Department of Chemistry Rutgers University Piscataway, NJ 08854
[email protected] The author replies: 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,
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Chemical Education Today
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.
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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 (timedependent) stoichiometry of complex reactions, we refer to the pertinent literature, ref 3–5; this does not affect the discussion of reaction orders. Literature Cited 1. 2. 3. 4. 5.
Hippler, M. J. Chem. Educ. 2003, 80, 1074. Shaw, H.; Toby, S. J. Chem. Educ. 1966, 43, 408. Toby, S. J. Chem. Educ. 2000, 77, 188. Lee, J. Y. J. Chem. Educ. 2001, 78, 1283. Toby, S.; Tobias, I. J. Chem. Educ. 2003, 80, 520. Michael Hippler Physical Chemistry ETH Zürich CH-8093 Zürich, Switzerland
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