Oxygen Measurement via Phosphorescence: Reaction of Sodium Dithionite with Dissolved Oxygen

A homemade instrument for the measurement of oxygen concentration in aqueous solutions measures the decay rate of the phosphorescence of a Pd-porphyrin complex (phosphor) dissolved in the solution, which is flashed every 0.1 s with 630 nm light. The concentration of O2 is a linear function of the decay rate. The instrument is used to study the reaction of dithionite (S2O42-) with O2 at 25 degrees C and 37 degrees C. It is found that the ratio of dithionite to oxygen consumed in the reaction is 1.2 +/- 0.2 at 25 degrees C and 1.7 +/- 0.1 at 37 degrees C, suggesting a temperature-dependent stoichiometry. At both temperatures, the initial rate of O2 consumption, -d[O2]/dt, is found to be 1/2 order in S2O42- and first order in O2. This finding is consistent with a previously proposed mechanism: S2O42- <--> 2SO2- comes to a rapid equilibrium, and SO2- reacts with O2 in the rate-determining step.


Introduction
Measurement of O 2 concentration based on the quenching of the phosphorescence of Pd (II)-meso-tetra-(4-sulfonatophenyl)-tetrabenzoporphyrin (Pd phosphor) was introduced by Wilson and his co-workers. [1][2][3][4] This method allows accurate and sensitive determination of [O 2 ] in biological systems. 1 Using a homemade instrument, we recently used this method to monitor cellular respiration (mitochondrial O 2 consumption) under various conditions. [5][6][7] The instrument records and analyzes the phosphorescence profile (emitted light intensity vs time) of the Pd phosphor, which is excited with a flash of 630 nm light. [1][2][3][4] Since O 2 quenches the phosphorescence of this probe, the decay constant of emitted light depends linearly on [O 2 ]. 5,6 The stoichiometry and kinetics of the reaction of dithionite with dissolved oxygen is studied here using this instrument, which we briefly describe below, as well as the analysis of experimental results. We then report our measurements of stoichiometry and rate constants for the reaction of sodium dithionite (Na 2 S 2 O 4 ) with dissolved O 2 .
Sodium dithionite (Na 2 S 2 O 4 ), also known as sodium hydrosulfite or hyposulfite, has been reported to decompose in aqueous solutions. Under aerobic conditions, dithionite ion S 2 O 4 2reduces O 2 to the -2 oxidation state rapidly, 8 producing bisulfate and/or bisulfite. The overall reaction is written as: (implying equal amounts of bisulfite and bisulfate are produced, as first reported). 9,10 Two reactions are actually possible: The ratio between bisulfite and bisulfate depends on the relative contributions of reactions 2 and 3. The initial steps of the reaction may involve eqs 4 and 5: with eq 5 being followed by a series of further reactions. 9 Raman spectroscopy 11 and X-ray 12 studies on S 2 O 4 2suggested a planar D 2h structure, which has one S-S bond in the center and two S-O bonds with different lengths in each halfanion. This is consistent with eq 4, which shows dissociation of S 2 O 4 2into two units of SO 2 -. In addition, a mechanism for eq 5, which explained the equal amounts of bisulfate and bisulfate, was proposed by Rinker et al. The first step in eq 5 was with several other radicals involved in subsequent steps. 9 Nonetheless, there is no evidence for or against this mechanism.
Depending on which step is rate-determining in eqs 4 and 5, different kinetic schemes result. Some authors 10 reported zeroorder with O 2 , implying the forward reaction in eq 4 is ratedetermining; this also predicts the reaction to be first-order with respect to S 2 O 4 2-. Other researchers 9 claimed that the equilibrium in eq 4 is very rapid, and thus, eq 5 is the rate-controlling step; this predicts first-order kinetics with respect to O 2 and 1/2-order with respect to S 2 O 4 2-. However, the rate-controlling step, like the ratio of bisulfate and bisulfite in the final products, may depend on temperature and relative amounts of S 2 O 4 2and O 2 .
Only a few studies 13 of the reaction of S 2 O 4 2with O 2 in solutions have been reported lately, and they do not address the mechanism. Most investigations monitored changes in the spectroscopic absorbance of S 2 O 4 2-(λ max ) 315 nm). Here, we investigate the stoichiometry and kinetics of this reaction by tracking O 2 consumption using our O 2 analyzer. The results suggest the stoichiometry for the overall reaction is temperaturesensitive. The kinetics is shown to be 1/2-order with respect to S 2 O 4 2and first-order with respect to O 2 , showing that eq 5 is the rate-limiting step.  [1][2][3][4] The probe was excited by light pulses (10 per s) that peaked at 625 nm (OTL630A-5-10-66-E, Opto Technology, Inc., Wheeling, IL). Duration of a pulse was 50-100 µs. Emitted phosphorescence was isolated by a filter centered at 800 nm and passed through a Hamamatsu photomultiplier tube (# 928). Five microseconds after each flash, the resulting phosphorescence was digitized at 1 MHz by the ultrahigh-speed PCI-DAS4020/12 analog input board (Measurement Computing Corporation, Norton, MA). DASYlab (Measurement Computing Corporation, Norton, MA) was used for data acquisition.

Experimental
Samples (final volume, 1.0 mL with dH 2 O) containing 2 µM Pd-phosphor and 0.5% bovine fat-free albumin were placed in 1 mL glass vials. Serum albumin binds the Pd-phosphor molecules and protects them from external chemical disturbance, such as changes in pH. The vials were sealed and placed in the instrument for O 2 measurement. Mixing was accomplished with the aid of parylene-coated stirring bars.

Data Analysis.
A typical phosphorescence intensity profile, for air-saturated dH 2 O to which 200 µΜ S 2 O 4 2has been added, is shown in Figure 1. Dithionite reacts rapidly with dissolved O 2 and, as shown below, 200 µΜ S 2 O 4 2removes more than half of the O 2 in air-saturated water. The data were analyzed by a computing program (C ++ language, Table 1) that calculated the phosphorescence lifetime (τ) and decay constant (1/τ), from which [O 2 ] can be determined using eq 7 where the values of 1/τ 0 (10087 ( 156 s -1 ) and k q (96.1 ( 1.2 µΜ -1 s -1 ) were established by calibration. 5 In the phosphorescence profile shown in Figure 1, the flash goes on at t ) t 0 ∼ 0.078548 s, stays on with a constant intensity until t ) t 1 ∼ 0.078626 s, and then goes off, so that the flash duration is ∼78 µs. Since phosphorescence is a first-order process, the phosphorescence intensity (I) is proportional to the number of phosphor molecules in the excited state. This population decays with time and is pumped by the flash at a constant rate k′. Thus, I ) 0 for t < t 0 , and which integrates to where c is the maximum intensity (at t 1 ); that is, The value of c is proportional to τ only if t 1t 0 . τ. There are several ways of obtaining τ from an intensity profile like the one in Figure 2, and we compare them here.
From direct reading of the experimental intensities (solid dots), one finds t 0 ) 0.0785482 s, t 1 ) 0.0786263 s, maximum intensity c ) 3.00293 arbitrary units, and total area under the curve, ) 0.0003028 arbitrary units × s (by numerical integration). If these data followed the theoretical equation exactly, the ratio of the area to the height c would be so that exp[(t 0t 1 )/τ] ) 1 -0.77457 and τ ) 5.24 × 10 -5 s. This method for extracting τ has the advantage of using all of the experimental data and does not necessitate determining k′ separately. The disadvantages include involving calculations in which accuracy is lost because (c/A)(t 1t 0 ) is often close to 1 and requiring an arbitrary choice of where to truncate the area integration. An alternative is to fit the experimental data to the theoretical form using nonlinear least-squares. The best fit (dashed curve in Figure 2 ) 0.0786150 s, maximum height c ) 2.84994 arbitrary units, and peak area ) 0.0002714 arbitrary units × s (from integration of eqs 8 and 9 to t f ∞). Then A/c ) 9.523 × 10 -5 s, so that exp[(t 0t 1 )/τ] ) 1 -0.90309 and τ ) 3.68 × 10 -5 s. The fitting process is much more tedious than direct measurement, and the quality of the fit (see Figure 2) is only fair, so that the value of τ is inaccurate. Fortunately, a simpler and more accurate method is available: after locating the position of the maximum, one fits the decreasing part of the profile to an exponential function. The fit, shown as a solid gray line in Figure 1, gives τ ) 4.71 × 10 -5 s, reasonably close to what is obtained by direct analysis of all the data. The exponential fit is more reliable; although it uses less of the data, it requires determination of only one parameter, the decay rate (1/τ). This method is easily implemented in the computer program, and we therefore use the exponential fit to determine the value of τ.
Furthermore, we will always be comparing τ values after calibration. The sampling was done at 307 200 Hz. Since the lamp flashes every 0.1 s, the duration of the flash is 78 µs, and the decay time τ is about 40 µs; the useful data from each flash involves fewer than 100 points, and >99.8% of the readings are zero and of no interest. The analysis program removes all zero or zero-like readings by setting a data-dropping threshold (e.g., 0.05), producing a sawtooth intensity-versus-time plot, composed of a number of profiles like that of Figure 1. It is necessary to find the maximum in each profile and fit the points after the maximum to an exponential. The Microsoft Visual C ++ program (Table 1) combines these tasks by screening the data stream for maxima with intensities greater than 0.05, noting the time of each maximum (t 1 ) and keeping only data declining from the peak but above the data-dropping threshold within 0.1 s. This produces 10 decay curves per second, each of which is fit to an exponential function.
The possibility that the phosphor is affected by the dithionite or its oxidation products 14 was also investigated, by measuring the glucose oxidase-catalyzed oxidation of glucose at 25°C and 37°C ( Figure 2). The overall reaction of glucose (C 6  At 25°C (Figure 2A), the slope without dithionite (circles) was -86.065 ( 4.479 (r 2 > 0.99) and with dithionite (squares) -87.581 ( 4.778 (r 2 > 0.99). At 37°C (Figure 2B), the slope without dithionite (circles) was -134.72 ( 16.19 (r 2 > 0.95) and with dithionite (squares) -132.13 ( 3.99 (r 2 > 0.99). Thus, the effect of dithionite and its oxidation products on the Pdphosphor at 25°C and 37°C was negligible. The curves in the presence of dithionite were lower because of less dissolved O 2 in these solutions. Figures 3 and 4 show representative plots of the reciprocal of the measured decay constant τ (+ signs) obtained in successive measurements at 25°C ( Figure  3) and 37°C (Figure 4). Each plot corresponds to an experiment in which dithionite was added to air-saturated water at the concentration shown in the plot label. Here, 1/τ is plotted versus elapsed time. Since, according to eq 7, 1/τ is a linear function > 500 µΜ, the value of 1/τ a corresponds to total depletion of O 2 ; that is 1/τ a ) 1/τ 0 . From the values of 1/τ b and 1/τ a , we obtain information about the stoichiometry of the overall reaction (see below). From the shape of the experimental curve, we obtain information about the kinetics and rate constant of the reaction. It can be seen, for instance, that the drop in 1/τ is rapid and mostly linear, suggesting a reaction which is zero-order in O 2 . However, in many plots, one can also note a tail or roundingoff in the experimental data as 1/τ approaches 1/τ 0 , suggesting either that the plots are actually curved or that the ratedetermining step is no longer zero-order when [O 2 ] drops below a certain level.

Experimental Results.
The solid lines in Figures 3 and 4 are fits of the experimental data to the four-parameter function with the values of the parameters C and t b found by minimizing the sum of the square deviations of eq 10 from experimentally measured 1/τ, 1/τ b and 1/τ a having been previously determined. One obtains a first-order rate constant for oxygen depletion by multiplying -d(1/τ)/dt by τ/k q , where k q ) 96.1 µΜ -1 s -1 . Further, one obtains the initial rate (or zero-order rate constant) from the value of -d(1/τ)/dt at t ) t b : We have also fitted (not shown) the experimental data to the four-parameter function, glucose ) 1/τ a t > t a From eq 12, the zero-order rate constant or reaction rate is The fit to eq 10 is somewhat better than the fit to eq 12 because eq 10 takes into account the curvature in the plots as 1/τ approaches 1/τ a .  Figure 5A, where each error bar is the standard deviation for one determination of 1/τ a . Figure  5B,  , 1/τ a should equal 1/τ 0 , since all of the oxygen has been reduced. The broken line in Figure 5A is the best fit of all 22 data points to the 3-parameter function where R + δ ) γ. Τhis best fit has R ) 28 844 s -1 , ) -54.0 s -1 µΜ -1 , δ ) 312.3 µΜ, and γ )  This result is consistent with eq 1 but suggests that s may be slightly greater than 1.

Stoichiometry of the Reaction of S 2 O 4 2with O 2 . At
A similar analysis was made of the 28 data sets from measurements at 37°C with dithionite concentrations below 1.0 mM. The values of 1/τ a are plotted versus [S 2 O 4 2-] in Figure  5B, where each error bar is the standard deviation for one determination of 1/τ a . The dashed line in Figure 5B is the best fit to eq 14, using all 28 values of 1/τ a . In this case, R ) 41745 s -1 , ) -80.4 s -1 µΜ -1 , δ ) 384.2 µΜ, and γ ) 10823 s -1 . Since [O 2 ] 0 ) 225.4 µΜ, s ) 1.705 ( 0.134 (error from linear fit). This result is significantly different from what is implied by eq 1 and shows that eq 2 occurs more often than eq 3 at the higher temperature.

Kinetics of the Reaction of S 2 O 4 2with O 2 .
In these experiments, S 2 O 4 2was added to a sample of air-saturated dH 2 O containing Pd phosphor without interrupting the measurement of τ, and the measured values of 1/τ, which depends linearly on [O 2 ], were plotted versus t. The data sets studied resemble those in Figures 3 and 4. The plots for 25°C ( Figure  3A,B) show a mostly linear decrease in 1/τ from t ) t b to t ) t a ; that is, the decrease is initially linear and deviates from linearity for 1/τ below about 15 000 s -1 ; according to eq 7, this corresponds to [O 2 ] < 40 µΜ. In the plots for 37°C ( Figure  4A,B), the decrease is much faster, corresponding to faster rates at the higher temperature. Where . The rapid decrease in 1/τ when S2O4 2is added corresponds to its reaction with O2. The solid lines are best fits to a horizontal line followed by a decreasing exponential. ]/dt to follow zero-order kinetics "over at least 80% reaction" when S 2 O 4 2was present in excess. It is also possible that the decrease is exponential, since an exponential is linear close to the origin. In order to establish the order with respect to S 2 O 4 2and to calculate rate constants, we compare the initial rates of reaction r for different [S 2 O 4 2-]. These are calculated according to eq 11 or eq 13. Since the initial rate should be proportional to Values of r determined from experiments at 25°C are given in Table 2, and values determined at 37°C are given in Table  3. Equations 10 and 11, the exponential fitting functions, were used to obtain these values. There was much more scatter in the initial reaction rates at higher T, because of insufficient time resolution in the values of 1/τ. In fact, little information is available when the value of 1/τ drops from 1/τ b at time t to a value indistinguishable from 1/τ 0 ([O 2 ] ∼ 0) at t + ∆t where ∆t is the time between measurements. Since the standard deviation in 1/τ is ∼10 3 s -1 and 1/τ b -1/τ 0 is ∼3 × 10 4 s -1 , this means or, with ∆t ) 0.07 s, C > 49 s -1 . Thus, values of r are of doubtful validity when All the values of r in Tables 2 and 3 were used in the fitting; removing those greater than 1.5 × 10 4 µM s -1 changes the results only slightly.
To find the order of the reaction with respect to S 2 O 4 2-, we perform a linear regression of ln(r) versus ln[S 2 O 4 2-], shown in Figure 6. For the 25°C data, the slope is 0.59 ( 0.07, showing clearly that the reaction is 1/2-order with respect to S 2 O 4 2-. This is expected if eq 4 is the rate-determining step. For 37°C, the slope is 0.49 ( 0.09 (Figure 6), showing that 30 e -C∆t < 1 r > 3 × 10 4 C/k q ) 1.5 × 10 4 µM s -1 the rate-determining step is 1/2-order at the higher temperature as well. We have also calculated r values using eqs 12 and 13, corresponding to fits to a three-line function. Although the values of r are much higher than those in Tables 2 and 3, the slope of a plot of ln(r) versus ln[S 2 O 4 2-] is still ∼0.5.

Rate Constants.
In summary, the initial rate of the oxygen-consumption reaction, in µΜ s -1 , is found to be equal to at 25°C and at 37°C, where [S 2 O 4 2-] is in µM. Assuming the reaction is first order in O 2 (see below) and using initial concentrations of O 2 of 267 µΜ at 25°C and 225 µΜ at 37°C, we calculate that the rate constants are 66.7 M -1/2 s -1 at 25°C and 872 M -1/2 s -1 at 37°C. The temperature dependence of the rate constant corresponds to an activation energy of which should be related to the dissociation energy of S 2 O 4 2into 2SO 2 2-. The S-S single-bond energy is 425 kJ/mol; 15 therefore, the S-S bond in dithionite is highly destabilized.
Assuming eqs 4 and 5 are the only reactions contributing to oxygen consumption (note that in the scheme of Rinker et al., 9 O 2 enters as a reactant in a later step as well), we may write the rate equations as follows. Letting k 1 and k -1 be the forward and reverse rate constants for reaction 4 and letting k 2 be therate constant for reaction 5, we find the steady-state equation for the reactive intermediate •SO 2is According to Creutz & Sutin 10 k 1 ∼ 2.5 s -1 at pH 8, 25°C; k -1 ∼ 1.8 × 10 9 M -1 s -1 at pH 6.5, 25°C; k 2 > 10 8 M -1 s -1 25°C . If, in our experiments, the second term in eq 17 were much smaller than the third, we would have and This predicts the order of the reaction with respect to S 2 O 4 2incorrectly. Apparently, the second term in eq 17 is larger than

Conclusions
From the above results, it can be seen that our instrument can be conveniently utilized to monitor rapid chemical reactions, by measuring the phosphorescence decay rate, 1/τ. Since 1/τ is linearly dependent on [O 2 ], measurement of 1/τ gives [O 2 ]. [1][2][3][4][18][19][20][21][22][23] The tail of each phosphorescence decay profile was fit to an exponential function to measure [O 2 ]. Presently, phosphorescence profiles are obtained every 0.1 s (flash rate), making it feasible to monitor chemical reactions in which the oxygen concentration changes substantially in a few hundred mil-liseconds. Reactions 100 times faster could be tracked if the flash rate were increased to 1000 Hz.
We applied our O 2 analyzer to investigate the reaction of S 2 O 4 2with O 2 , which apparently begins with the reactions of eqs 4 and 5. The stoichiometry study shows 1.2:1.0 (S 2 O 4 2-/ O 2 ) at 25°C (consistent with the results of other workers) and 1.6:1.0 at 37°C. The variation may be due to different temperature dependences of the rates of the reaction steps which follow eq 5. The relative rates of these steps determine the overall stoichiometry and, equivalently, the relative amounts of bisulfate and bisulfate produced. The reaction of SO 2with O 2 very probably produces SO 2 and O 2 -, and SO 2 in aqueous solution already yields HSO 3 -. Subsequent reactions involve further oxidations by O 2 and O 2 -.
The kinetics study shows that at both temperatures the oxygen depletion -d[O 2 ]/dt is 1 / 2 -order in [S 2 O 4 2-] and first-order in [O 2 ]. This supports the suggestion of previous workers that conversion between S 2 O 4 2and SO 2 -(eq 4) reaches equilibrium rapidly, so that reaction 5 is rate-determining and is the main contributor to the depletion of oxygen.