Quantum Yield and Rate of Direct Photolysis

First-Order Rate Constant for Quantification of Direct Photolysis 

In Section 15.2 we defined a reaction quantum yield, Oir(A), describing the total number of compound molecules (e.g., moles compound) transformed by a chemical reaction per total number of photons (e.g., einsteins) absorbed by a given system resulting from the presence of the compound (Eq. 15-9). In Eq. 15-18, we denoted the rate of light absorption of wavelength A by the pollutant per unit volume (e.g., einstein per liter per second) as 7a(A). It is now easy to see that the product of these two entities describes the number of compound molecules transformed per unit volume per time [e.g., (mol compound i) per liter per second]. This is also equal to the concentration change per unit time in a given system, or the rate of transformation of the pollutant  

If we assume that the quantum yield is independent of wavelength, we simply multiply the total specific light absorption rate of the compound in a well-mixed water body by Oir to obtain k.  

Similarly, the near-surface first-order rate constant k° for direct photolysis is given by  

As indicated by Eq. 15-36, to estimate the rate of direct photolysis of a pollutant in a given system, one needs to know the k3 value as well as the reaction quantum yield for the compound considered. As we have extensively discussed, k3 values may be estimated with the help of spreadsheet calculations or computer programs. However, 

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Once the actinic fluxes, quantum yields, and absorption cross sections have been summarized as in Table 3.19, the individual products < .,v(A)wavelength interval can be calculated and summed to give kp. Note that the individual reaction channels (9a) and (9b) are calculated separately and then added to get the total photolysis rate constant for the photolysis of acetaldehyde. However, the rate constants for the individual channels are also useful in that (9a) produces free radicals that will participate directly in the NO to N02 conversion and hence in the formation of 03, etc., while (9b) produces relatively unreactive stable products. 

First-Order Rate Constant for Quantification of Direct Photolysis Illustrative Example 15.3 Estimating the Photolysis Half-Life of a Weak Organic Acid in the Well-Mixed Epilimnion of a Lake Determination of Quantum Yields and Chemical Actinometry Advanced... 

Table 12.1 summarizes some data on direct photolysis rates and quantum yields for some organic contaminants. Rates of direct photochemical reactions of aqueous species, S, as measured in thin-layer samples, correspond to rates that would occur in the top few centimeters of a water column. Corrections have to be considered for mixed water columns at greater depths (see Zahriou, 1973, and Haag and Hoign, 1986). 

Direct photolysis often is kinetically simple and easily modeled, especially if the absorption spectrum of the compound and its quantum yield of disappearance are known. The average photoreaction rate in direct photolysis can be expressed as... 

Any mechanism which involves isoenergetic, radiationless internal conversion from C, P, or T to a high vibrational level of the ground state would be expected to show a large deuterium isotope effect on the rate of internal conversion. In the direct photolysis of perdeuterio and perhydrostilbene, Saltiel<8a) found no isotope effect on the photostationary state or upon the quantum yields of cis-to-trans and trans-to-cis conversion. 

The quantum yield for isomerization in the direct photolysis was found to be d> = 0.94. The reaction could also be sensitized with acetophenone ( = 1.02) and quenched with piperylene, indicating a reactive triplet species with a rate constant kr of 3 x 10l°sec-1. With a 3-(p-methoxyphenyl) derivative two products were obtained<81) ... 

In Table 15.7 the reaction quantum yields are given for some selected organic pollutants. As can be seen, reaction quantum yields vary over many orders of magnitude, with some compounds exhibiting very small Oir values. However, since the reaction rate is dependent on both ka and Oir (Eq. 15-34), a low reaction quantum yield does not necessarily mean that direct photolysis is not important for that compound. For example, the near-surface direct photolytic half-life of 4-nitrophenolate (Oir = 8.1 x 10 6) at 40°N latitude is estimated to be in the order of only a few hours, similar to the half-life of the neutral 4-nitrophenol, which exhibits a Oir more than 10 times larger (Lemaire et al., 1985). The reason for the similar half-lives is the much higher rate of light absorption of 4-nitrophenolate as compared to the neutral species, 4-nitrophenol (compare uv/vis spectra in Fig. 15.5 and Illustrative Example 15.3). As a second example, comparison of the near-surface photolytic half-lives (summer, 40°N... 

So far the methods described for measuring excited state lifetime, and hence reactivity, have been indirect methods that rely on a comparison with some standard le.g. actinometer quantum yield or quenching rate constant) that has already been measured. A direct method for measuring the lifetime of short-lived species produced photochemically is flash photolysis. This is a very important technique in photochemistry, though only the basic ideas as they apply to mechanistic studies are outlined here. In flash photolysis a high concentration of a short-lived species (electronically excited state or... 

The transformation of various substituted phenols has been studied in the presence of nitrite under irradiation dihydroxybenzenes [78,79,113], nitrophenols [109], phenylphenols [114], Obviously, the observed transformation intermediates vary according to the reaction rate of each substrate and intermediate with the various reactive species formed during irradiation and according to the absorption spectrum and direct photolysis quantum yield of each compound. 

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