ss

hv

0

hν

0

2

3

0

0

(4)

hv

0

a

–PA

–PA

–CO 2

–CO 2

2

8

2

0

a

(5)

a

0

0

hv

0

a

(6)

ss

(7)

(8)

7

oxo–C 7

DMTA

8

oxo–C 8

product

0

product

product

0

The steady state concentration of excited state pyruvic acid, [PA*], can be inferred by balancing out its measured initial rate of production with an upper limit set by the measured loss of PA,[PA], against the loss of PA* by thermal processes in reaction R2 and from its bimolecular reaction with ground state PA by reaction R3 ( Scheme 1 ). For practical purposes, there is no difference if the (indistinguishable) photoinduced bimolecular process represents a hydrogen atom transfer, an electron transfer, or PCET. Thus, from[PA][PA*] +[PA*] [PA], it is possible to obtain at variable [PA]Figure S8 ( Supporting Information ) shows that the photolytic rate in eq 4 [PA], depends linearly on the photon absorption by aqueous PA solution () with a slope of ∼2. Indeed, Figure S8 indicates that Φ≈ 2 or that each PA* produced per photon absorbed consumes an additional molecule of PA in a highly efficient bimolecular process. The Φshould not be confused with the photodecarboxylation quantum yield of aqueous PA, Φ= 0.78. (21) While Φaccounts for ∼50% of the evolution of CO(g) from the primary decomposition of Xper photon absorbed, the secondary decarboxylation of the oxo-Cproduct must contribute the other ∼28% of this gas. Thus, the missing ∼22% of produced Kradical must recombine to produce DMTA, which does not emit CO(g). For experiments with [PA]≥ 4 mM,is given by (2) only varies with [PA], because the incident photon rate,= 1.14 × 10M s, the molar absorptivity of PA (ε = 11.3 Mcm), (28) and the optical path length of the NMR tube (= 0.424 cm) are constants. Therefore, by substituting[PA]≈ 2in eq 3 Assuming this simplified reaction scheme, for each photolyzed molecule of PA generating the stoichiometric amount of ketyl and acetyl radicals, PA +→ K+ Y, provides a means to solve the steady state concentration of ketyl radicals, [Kin the system. Thus, balancing out the measured initial rate of PA loss to the initial rate of generation of product consuming K(observed from the channels R6 + R8 + R9 in Scheme 1 ) indicates thatThe initial rate of generation of product and loss of PA are presented in Figure S9 ( Supporting Information ) for a ≤ 20% conversion. By substituting [PA*] from eq 6 in eq 7 , and reordering, it is apparent thatThus, the sum of the corresponding photochemical quantum yields for the oxo-Cproduct (Φ), 2,3-dimethyltartaric acid (Φ), and the oxo-Cproduct (Φ), ∑Φ, depends on [PA]as described by the hyperbola in eq 8 . The ∑Φis calculated from the initial formation rates divided by the absorbed photon rate from eq 5 Figure 7 shows the sum of the quantum yields for the three products ∑Φvs [PA]for the interval 5–100 mM measured using neutral density filters that reduce the total photon flux to 10.64%.