Acceleration Mechanism of Chemical Reaction by Freezing: The

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J. Phys. Chem. 1996, 100, 13874-13884

Acceleration Mechanism of Chemical Reaction by Freezing: The Reaction of Nitrous Acid with Dissolved Oxygen Norimichi Takenaka,*,† Akihiro Ueda,† Tohru Daimon,† Hiroshi Bandow,† Takaaki Dohmaru,‡ and Yasuaki Maeda† Department of Applied Materials Science, College of Engineering, Osaka Prefecture UniVersity, 1-1 Gakuen-cho, Sakai 593, Japan, and Research Institute for AdVanced Science and Technology, Osaka Prefecture UniVersity, 1-1 Gakuen-cho, Sakai 593, Japan ReceiVed: September 1, 1995; In Final Form: March 15, 1996X

The oxidation of nitrite by dissolved oxygen to form nitrate is known to be accelerated ca. 105 times by the freezing of the aqueous solution.1 Here we report a detailed study on the acceleration mechanism of the above-mentioned oxidation. The reaction was studied at pH values between 3.0 and 5.6 at various freezing rates, by different freezing methods, and with and without additional salts. The effect of freezing which induced concentration (freeze concentration) of reactants into the unfrozen bulk solution was too small to explain the acceleration factor of ca. 105. Nitrate formations were completely prevented by addition of salts, such as NaCl and KCl, which make the freezing potential of ice negative, while the reaction was not affected by addition of salts, such as Na2SO4 and NH4Cl, which make the freezing potential of ice positive. When a sample solution was frozen in such a way as to form a single crystal of ice, most nitrite was exclusively liberated from the ice to the gas phase. This observation suggests the importance of ice in the polycrystalline form to retain nitrite during freezing. When freezing begins, grains of crystalline ice begin to grow. The solutes are rejected from the ice and concentrated in the interfacial water layer by assistance of the electrostatic force generated by the freezing potential. At a certain stage of freezing, the water layer is completely confined by the walls of some ice grains. Protons move from the ice phase to the unfrozen solution surrounded by the ice walls to neutralize the electric potential generated, and thus the pH of the unfrozen solution decreases. As a result, the reactant species, HNO2, increased more in the unfrozen solution. After this stage, the concentrations of the reactants in the unfrozen solution abruptly increase resulting in the acceleration of the rate of formation of nitrate. On the basis of the above mechanism, the concentration factor for nitrite was calculated as 2.4 × 103. The validity of this mechanism is further discussed.

Introduction Chemical reactions in the liquid phase are generally slowed at lower temperatures. At still lower temperatures, they are inhibited because migration of molecules is heavily suppressed in the solid phase. On the other hand, some reactions are known to be accelerated in partially frozen aqueous solution.2-13 Fennema11 reviewed the factors important for the acceleration, that is, (I) a freeze concentration effect, (II) a possible catalytic effect of ice crystals, (III) greater proton mobility in ice than in water, (IV) a favorable substrate-catalyst orientation caused by freezing, and (V) a greater dielectric constant for water than for ice. Furthermore, he11 reported that the freeze concentration in an unfrozen bulk solution can account for almost all acceleration phenomena and that one or more of the other four factors II-V may also be involved. Bronshteyn and Chernov described the acceleration effect of a reaction in a partially frozen solution.14 Inequality between the distributions for solute anions and cations in ice and in solution produces an electric potential between the solution and the growing ice, which is called a “freezing potential”. Anions or cations accumulate in the water contiguous to the interface due to the electrostatic force generated. The potential is then neutralized by highly mobile OH- or H3O+ ions, and the pH of the solution is varied. Most of the reactions accelerated in the freezing process which have been reported so far are explained in the terms of freeze † ‡ X

Department of Applied Materials Science. Research Institute for Advanced Science and Technology. Abstract published in AdVance ACS Abstracts, July 1, 1996.

S0022-3654(95)02580-9 CCC: $12.00

concentration and hydrolysis accelerated by accumulated OHor H3O+. Recently Finnegan and Pitter reported that sulfate and H2 were produced by the reaction of SO2 with H2O in a frozen fog and that the reaction proceeded by an electric potential produced by the ion separation.15 However, there are many ambiguous points in the electrochemical reactions by freezing that they reported. Acceleration factors, that is, the ratio of rate constants in the freezing process to those in solution, have also been investigated in the literature cited above.2-13 The acceleration factors reported are several to several tens, when it is assumed that the reaction mechanism in the freezing process is the same as that in solution. A few reactions have been reported so far to be accelerated several thousand times. Recently, Takenaka et al. found that the reaction of nitrite with dissolved oxygen to form nitrate was extremely accelerated during freezing in aqueous solution.1 The rates in the freezing process were several hundreds to several hundred thousands times faster than those in solution at 25 °C (the factors depend on initial conditions). In aqueous solution, the reaction of nitrite with dissolved oxygen is very slow. The rate equation is given by Damschen and Martin:16

-d[O2]/dt ) 36[HNO2]2[O2] (mol dm-3 s-1), pH 1-4 (1) This reaction in solution becomes faster at higher temperatures.17 However, the rate of nitrate formation was extremely accelerated by freezing as shown in Figure 1. The rate equation for the freezing process is reported as follows:1 © 1996 American Chemical Society

Acceleration of Reaction by Freezing

Figure 1. Time profile of the reaction of nitrite with dissolved oxygen in the freezing process and in solution at room temperature: (b) nitrite and (O), nitrate concentrations in the freezing process with the coolant at -21 °C and (4) nitrate concentration in solution at 25 °C. [nitrite]0 ) 100 µmol dm-3. For the freezing process, [O2]0 ) 440 µmol dm-3 and for the solution [O2]0 ) 240 µmol dm-3.

d[NO3-]/dt ) 0.4[nitrite][O2] (mol dm-3 s-1), pH 3-5.6 (2) In the freezing process, the concentrations of HNO2 and NO2are hardly determined because the reactants are concentrated and the pH of the sample varies due to the freezing potential as mentioned above. Equation 2 is an experimental one, and nitrite is represented as initial concentrations of HNO2 plus NO2-. In the freezing system, the reaction takes place only in acidic solution.1 The reactants are reported to be HNO2, which is a weak acid (Ka ) 5.9 × 10-4 at 25 °C18), and dissolved oxygen.1,17 Nitrate (or nitric acid) is one of the most important species which cause acid rain. Formation paths to nitrate are mainly a reaction of NO2 with OH radicals in the gas phase in the daytime and dissolution of N2O5 into water at night.19 On the other hand, the formation of nitrate in the aqueous phase is not completely understood and is not regarded to be an important process of nitrate formation in rain.20 Concentrations of nitrite are reported to be a few parts per billion per volume in the gas phase,21,22 sub µmol dm-3 to a few µmol dm-3 in rain23,24 and as high as several hundred µmol dm-3 in fog.25,26 If the nitrite oxidation by freezing takes place in water droplets in the environment, especially in a cumulonimbus, or in the formation of hailstone, freezing rain, or ice pellets, the role of nitrate formation in the condensation phase cannot be disregarded. Furthermore, although freezing of water is a common physical process in most regions in the world, chemical changes by freezing have not been considered in the environmental science. Chemical reactions are generally accelerated at higher temperature, and hence, preparation rates of unstable substances have limitations. If the reactions can be accelerated by freezing, the unstable substances could be efficiently prepared and stored simultaneously with preparation. In this connection, clarification of the acceleration mechanism of chemical reactions by freezing is very important for understanding environmental chemistry as well as for developing a new technique for the formation of chemicals. We report here the acceleration mechanism of the reaction of nitrite with dissolved oxygen during the freezing process. Experimental Section Reagents and Analytical Methods. Weak acidic solutions of nitrite were frozen by various freezing methods at various temperatures (-0.2 to -196 °C), and changes in the concentra-

J. Phys. Chem., Vol. 100, No. 32, 1996 13875 tions of reactants and products were investigated after the samples were completely thawed. The samples were completely or partially frozen depending on the purpose. Frozen samples were thawed in a hot water bath, and then concentrations of the reactants and products were analyzed. All results were obtained from separate experiments; in other words, the sample which had been once frozen was not used again even in one course of time profile experiments. Reagent grade chemicals were obtained from Wako Pure Chemicals, Inc. and used without further purification. NaNO2 was dried at 120 °C for several hours. We prepared aqueous nitrite solutions by dissolving NaNO2 in Milli-Q water (resistivity > 18.2 MΩ cm). The concentration of dissolved oxygen was adjusted by bubbling the desired concentration of an O2/ N2 gas mixture and by adjusting the temperature of the sample solution. Sulfuric acid, hydrochloric acid, or formic acid was used for adjusting the pH of the solutions just before freezing. Concentrations of nitrite and nitrate as well as other anions, such as Cl-, SO42-, HCOO-, and CH3COO-, were determined by ion chromatography (Yokogawa Analytical Systems, Inc., IC7000 Series Ion Chromatographic Analyzer: column type, ICS-A23; eluent solution, 1 mmol dm-3 NaHCO3 and 2.5 mmol dm-3 Na2CO3 mixture; flow rate, 1 cm3 min-1). Na+ and K+ were measured by flame photometry. Concentrations of NH4+ were measured by an indophenol method,27 and the pH was measured with a pH meter (COS Ltd. CP-1 pH meter with a glass electrode), which was calibrated with pH 7 and 4 buffer solutions. Dissolved oxygen was analyzed by a gas chromatograph with an electron-captured detector (Hewlett Packard 5890A Gas Chromatograph), and the detailed method was described in the literature.28 Freezing Methods. A polypropylene syringe was mainly used as a reaction vessel, and a glass bottle and a stainless steel bottle were also used when necessary. It should be noted that the material of the reaction vessel did not affect the reaction during freezing. The volume of the coolant was about 20 dm3, and the temperature was controlled within (0.5 °C unless otherwise noted. Since the sample volume was 3-10 cm3, the freezing temperature could be held constant throughout the experimental period. The reaction was investigated by various methods in order to clarify the mechanism of the acceleration of the reaction during the freezing. (1) Normal freezing: An aliquot of the sample solution was drawn into a polypropylene syringe 75 mm long and 15 mm in inner diameter. The inlet of the syringe was sealed with a septum. The syringe was immersed in a coolant. Unless otherwise stated, the samples were frozen by this method. (2) Freezing from the bottom: As shown in Figure 2, an aliquot of the solution was placed into a polypropylene tube (110 mm long and 28 mm in inner diameter with a copper bottom) which was attached to a copper block immersed in a coolant. This method was used when separation of solution, i.e., the unfrozen part, from ice was necessary in the course of the freezing process for analysis. The ions concentrations in both phases were analyzed to determine changes in the extent of partition of ions between ice and the solution. In this method, the freezing rate can be determined as g min-1. A 1 g min-1 freezing rate corresponds to about a 1.6 mm min-1 freezing rate in height. The nitrate formation vs freezing time with this method was in good agreement with that with method 1 when the freezing rate was the same. (3) Freezing under the condition of single-crystal formation: Figure 3 depicts the experimental setup for examining the nitrite oxidation reaction under single-crystal growing conditions. The

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Figure 2. Schematic diagram of an experimental setup for freezing from the bottom: A, thermostat; B, stirring fan; C, cryostat; D, thermocouple; E, controller; F, water/methyl alcohol mixture; G, polypropylene tube (110 mm in height and 28 mm in inner diameter); H, sample solution; I, copper plate; J, copper block.

Takenaka et al. order to investigate the evaporation of solutes from the surface of the sample in the single-crystal experiments, a flushed gas, N2, was introduced to the sample tube, and the effluent gas was passed through an alkaline solution during freezing and thawing. A concentration change of solutes in the liquid phase by evaporation of water vapor was corrected by a weight change. Evaporation of HNO2 from solution could be ignored in the present experimental conditions. (4) Freezing at a temperature higher than -12 °C: At a temperature higher than -12 °C, the sample was often supercooled. The rapid freezing of a supercooled sample affects the reproducibility of the results. Hence, 5 cm3 of the sample was drawn into a glass tube, and the bottom of the tube was brought into contact with liquid nitrogen to start freezing the sample. Just after the thin ice layer was formed at the bottom of the tube (about 10 s), the sample tube was transferred into the coolant at the temperature examined. The formation of nitrate by the formation of the thin ice layer was negligibly small (less than 0.3%). In this method, temperature is a very important factor. Hence, the coolant was stirred well by a stir pump, and the direction of the water stream from the pump was adjusted so as to minimize the temperature fluctuation. In this way the temperature could be controlled within (0.1 °C during freezing. (5) Freezing with stirring: the sample solution and a stirring spin bar were placed into a 100 cm3 glass beaker immersed in the coolant on a magnetic stirrer. This method was used in order to determine whether or not the nitrate formation reaction proceeds on the ice surface. Results and Discussion

Figure 3. Schematic diagram of a freezing setup for single ice crystal growing: A, copper tube; B, thermally insulated container; C, sample solution; D, water/methyl alcohol mixture; E, microfeeder; Fi and Fo, warmer water inlet and outlet, respectively; Gi and Go, cold liquid inlet and outlet, respectively; H, ceramic tip; I, alkaline solution; J1J3, silicone rubber stopper. The total length of the tube is 200 mm, and the length of the constricted part is 35 mm. The inner diameter of the upper and the lower part of the tube is 10 mm, and that of the constricted part is 0.1 mm.

sample solution was placed into a glass tube constricted in the middle, and the tube was slowly moved from the upper warm zone (about 5 °C) to the lower cold zone (about -5 or -10 °C) at a constant speed which is regarded as a freezing rate. It is known that if the diameter of a constricted part of a tube is as small as the size of one single crystal of ice and the sample is frozen from the bottom part in the manner mentioned above, the single crystal of ice grows above the constricted part.29 In

The mechanism of how the nitrite oxidation reaction is accelerated in a freezing and thawing process is not well understood. There are a number of physical and chemical steps which could potentially affect the rate of reactions involved in the solution during the freezing and thawing process. The amounts of nitrate formed in a freezing process obtained under various conditions are summarized in Table 1. Reaction in Freezing or Thawing Process or in Ice. The amount of nitrate measured after the sample was completely frozen at -21 °C was not changed from that measured 10 min later (No. 1 in Table 1). This result suggests that the reaction did not proceed in ice. The formation of nitrate was examined with different thawing methods or rates (No. 1 in Table 1). At room temperature, 3 g of completely frozen sample was thawed within ca. 1 h. In a hot water bath (temperature: 50-70 °C), the same amount of the frozen sample was thawed within a few minutes. The reaction in solution was negligibly small even at 90 °C (about 0.6%). With the microwave oven, the frozen sample (3 g) was thawed within several minutes. As shown in Table 1, the amounts of nitrate formed were almost equal among the three thawing methods. In the case of sulfite, it was reported that sulfite was oxidized in a thawing process when the frozen sample of sulfite solution was thawed at room temperature or in a hot water bath but could not be oxidized by thawing with a microwave oven.30 On the other hand, in the case of nitrite, the thawing process did not affect the oxidation of nitrite. The reaction rate in the freezing process was investigated at various freezing rates with the setup shown in Figure 2 and freezing method 2. The rate of formation of nitrate increased linearly with increasing freezing rates as shown in Figure 4. The relation is expressed by the following equation:

Rr ) (1.06 × 10-4) Rf + 2.15 × 10-8, r ) 0.992 at -2 to -196 °C

Acceleration of Reaction by Freezing

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TABLE 1: Summary of Nitrate Formed in Various Experiments resultsa [NO3-]f/[N(III)]0

procedure (1) reaction during freezing-thawing process or in ice reaction in ice reaction during thawing process at room temperature at 60 °C in hot water with microwave oven reaction during freezing process (2) effect of light reaction under visible light reaction in the dark (3) effect of ice surface crushed pure ice added freezing with stirring (4) effect of added acid H2SO4 HCl HCOOH (5) effect of electric difference normal freezing woven metal wire electrode added

0.575 (0 min)c f 0.579 (8 min)

conditionb

[N(III)]0 ) 0.10, pH 4.0 [N(III)]0 ) 0.725, pH 3.0

0.880 0.917 0.938 formation rate increased with increasing freezing rate as shown in Figure 4 0.917 0.934

[N(III)]0 ) 0.725, pH 3.0

0.00 0.001

[N(III)]0 ) 0.85, pH 2.9

0.78 0.793 0.744

[N(III)]0 ) 0.08-0.10, pH 3.0

0.700 0.508

[N(III)]0 ) 0.100, pH 4.0

a Concentrations of nitrate are normalized with initial concentration of nitrite. b Concentrations are in mmol dm-3. c Concentration of nitrate obtained after a given standing time in completely frozen sample indicated in parenthesessthe sample was completely frozen within 12 min and held until 20 min after the sample was immersed in a coolant.

Figure 4. Relationship of reaction rate and freezing rate. [nitrite]0 ) 100 µmol dm-3, [O2]0 ) 250 µmol dm-3, and pH0 ) 4.0.

where Rr is the reaction rate in mol dm-3 s-1, Rf is the freezing rate in g s-1, and r is a correlation coefficient. From the above results, it is concluded that the reaction is accelerated during freezing of aqueous solution. Possibilities of Acceleration of the Reaction by Other Processes. Other processes could also affect the rate of chemical reactions in the freezing process. Nitrous acid is wellknown to be decomposed by sunlight. A photochemical effect on the reaction during freezing was then examined by comparing the reaction in the dark with that under visible light. The result in the dark was the same as that under the room light as shown in Table 1, indicating that visible light irradiation is not responsible for the acceleration in the freezing process. To investigate the catalytic effect of the ice surface, crushed ice prepared with pure water was added to the sample solution at 0 °C and pH 3.0. The crushed ice was melted in a few hours, but no nitrate was obtained. Although this result indicates that the ice surface does not enhance the reaction, the nature of ice surface during freezing (ice growing) can be considered to be different from that of a melting ice surface. Accordingly, the following experiment was carried out to examine the catalytic activity of the growing ice surface. A sample solution of 0.1 mmol dm-3 at pH 3.0 was frozen with stirring in order to increase the collision frequency of the reactants with the growing ice surface. Virtually no nitrate was obtained. These results

are listed in Table 1 and suggest that the acceleration of the reaction effect does not originate by catalytic activity of the ice. Sulfuric acid was mainly used for adjusting the pH of the solution. It is well-known that most species included in a solution are excluded from the ice phase when the aqueous solution is frozen. Sulfuric acid remains a liquid in ice even when the surrounding water is frozen. One possibility of the acceleration by freezing in the present system is an oxidation reaction by sulfuric acid. In another series of experiments, therefore, hydrochloric acid or formic acid, which is known to have no oxidative activity, was used for adjusting the pH instead of sulfuric acid. As shown in Table 1, the rate of formation of nitrate in both cases was almost the same as that in the case of H2SO4. From the above results, the freezing process must be the most important for the acceleration of the reaction. Freeze Concentration of Ions into Unfrozen Bulk Solution by Freezing. When an aqueous solution is frozen, solutes in the solution are excluded from the ice phase. As a result, the solutes are concentrated into the solution. Some reactions are known to be accelerated by this freeze concentration effect.2-13 This effect was also examined in the present reaction. The sample solution was frozen from the bottom using the setup shown in Figure 2. In this experiment, the liquid phase and the ice phase were separated by pouring out the liquid from the reaction tube at a given time of freezing. Then the concentrations of ions in both phases were measured. To obtain reproducible results, the data obtained only when the ice was grown parallel to the bottom plate were used for analysis. Figure 5 shows the time profile of the concentration of ions in solution and ice. All kinds of ions, nitrite, sulfate, and sodium ions, contained in the initial solution were excluded from the ice phase. The concentration of nitrite in the solution increased by 90%): amounts of products by an electrochemical reactions depend on an electric current consumed, but the current obtained in the freezing process is dominated by amounts of ions separated into ice and solution. To achieve high efficiency, the separated ions reacted efficiently without relaxation by another process, such as neutralization of separated ions by counterions. However, Finnegan et al. concluded that electrochemical reactions took place in freezing of fog particles.15 It is not clear whether the freezing potential proceeds electrochemical reactions or not, but there are possibilities that high freezing potential affects chemical reactions. To examine the electric effect of freezing potential, a number of stainless steel wires were placed into the solution. The ratio of volume of stainless steel wires immersed in the solution to that of the sample solution was about 50%. Stainless steel itself did not affect the reaction as mentioned in the experimental section. If the freezing potential generated in freezing causes an electrochemical reaction to proceed, the amounts of nitrate would increase because the circuit is completed by the stainless steel wires. On the other hand, if the effect of the freezing potential is an electrostatic one, the amounts of nitrate would decrease because the electrostatic effect is removed by the wires. As shown in Table 1, addition of the stainless steel wire depresses the oxidation reaction indicating that the acceleration of the reaction by freezing would be due not to an electrochemical reaction but to an electrostatic effect. In order to investigate the electrostatic effect in the freezing process on the reaction, 1.0 mmol dm-3 NaCl, KF, KCl, KI, NH4Cl, Na2SO4, K2SO4, CH3COONH4, or CH3COONa was added to the sample solution. Table 3 shows the amounts of nitrate formed when each salt was added to the solution. The values of the freezing potential reported by Cobb and Gross32 are also listed. From this table, it is found that the formation of nitrite is affected not by the kind of ions but instead by the

Figure 9. Ion separation in freezing from the bottom in the presence of 1.0 mmol dm-3 of NaCl [nitrite]0 ) 130 µmol dm-3, [NaCl]0 ) 1000 µmol dm-3, [O2]0 ) 250 µmol dm-3, and pH0 ) 4.5. The temperature of the coolant was -21 °C. The sample started to freeze within 2 min and was completely frozen at about 25 min. (O), (b) N(III); (4), (2) NO3-; (0), (9) pH. The open symbols indicate concentrations or pH in ice, and the solid ones indicate those in solution.

sign of the freezing potential. Furthermore, it is apparent that the nitrate formation is completely inhibited when the sign of the potential difference of the ice is negative. However, in the case of the positive potential difference, the nitrate formation was not inhibited except in the case of acetate. The results are consistent with the theory proposed by Bronshteyn and Chernov.14 When the charge of the ice phase is positive, nitrite ions excluded from the growing ice crystals into the solution are attracted to the ice surface and are thus concentrated at the freezing interface. Protons in the positively charged ice rapidly move to the solution to neutralize the electric charge and recombine with the concentrated NO2-. Concentrated HNO2 thus formed at the interface and dissolved oxygen are confined in the solution surrounded by ice crystals and could react to yield nitrate. Figure 9 shows the time profile of the ion concentrations in solution and in the ice when 1.0 mmol dm-3 NaCl was added when the sample was frozen by freezing method 2 using the setup shown in Figure 2. It can be seen that nitrite was more concentrated into the solution than that in the case where no additional salts were added as shown in Figure 5. Note that the nitrite in ice when no additional salts were added was oxidized to nitrate. NaCl addition would interfere with the accumulation of nitrite around the interface because the sign of the ice becomes negative. Furthermore, the pH of the solution became higher than the initial pH for the same reason mentioned above, and the equilibrium between HNO2 and NO2- shifted to NO2-. As pointed out in the previous study,1,16 HNO2, not NO2-, is the reactive species for the oxidation reaction with dissolved oxygen. This effect is also one of the causes of interference with the reaction. As for the pH change during freezing, the fact that the final pH is higher in spite of no reaction is due to the chloride ion loss in the freezing process, which is consistent with the results reported by Lodge et al.33 Role of Dissolved Oxygen. In solution, it is reported that nitrite is oxidized by dissolved oxygen.16 To confirm that oxygen is required for the nitrate formation in the freezing process, the effect of dissolved oxygen concentration on the reaction was investigated at high and low nitrite concentration,

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Figure 11. Illustrative elucidation of acceleration mechanism by freezing. Only five single ice crystals are depicted for simplicity. I, single crystal of ice; C, concentrated phase; S, solution confined in the solution surrounded by walls of ice grains; R, concentrated solution in which the reaction is accelerated. See text for descriptions of a-d.

Figure 10. Amounts of nitrate formed at various concentrations of dissolved oxygen at high and low initial nitrite concentration. (b) Amounts of nitrate formed at low initial nitrite concentration. [nitrite]0 ) 100 µmol dm-3 and pH0 ) 4.0. (O) Amounts of nitrate formed at high initial nitrite concentration. [nitrite]0 ) 1 × 104 µmol dm-3 and pH0 ) 4.0.

and the results are shown in Figure 10.

2HNO2 + O2 f 2NO3- + 2H+

(3)

From the reaction 3 one molecule of dissolved oxygen is required for the oxidation of two molecules of nitrite. When the initial nitrite concentration was low, 0.1 mmol dm-3, and enough oxygen existed, amounts of nitrate formed were almost the same at various oxygen concentrations, 0.2-2.0 mmol dm-3. On the other hand, at high concentrations of nitrite, 10 mmol dm-3, amounts of nitrate formed increased linearly with concentration of dissolved oxygen, 0-1.0 mmol dm-3. Furthermore, the reaction rate obeyed first order for oxygen concentration in the freezing process.17 As shown in Figure 10, in the absence of dissolved oxygen nitrate formed was only 0.056 mmol dm-3 in 30 min at 10 mmol dm-3 nitrite and pH 4.0. From the slope of [NO3-] vs [O2] at high nitrite concentration in Figure 10, about 60% of dissolved oxygen was used for the nitrate formation. When pure water was frozen and thawed, about 40% of dissolved oxygen was excluded from the sample. These results gave good agreement. Therefore all of the dissolved oxygen remaining in the sample reacted with nitrite at high nitrite concentration. The formation of small amounts of nitrate was also observed both at higher and lower nitrite concentration samples in the absence of oxygen.

2HNO2 h N2O3 + H2O

(4)

N2O3 h NO2 + NO

(5)

2NO2 h N2O4

(6)

N2O4(2NO2) + H2O h HNO2 + NO3- + H+

(7)

2NO + O2 f 2NO2

(8)

3HNO2 f NO3- + 2NO + H+ + H2O

(9)

Reactions 4-7 are one possible path of nitrate formation in the absence of dissolved oxygen. Pires et al. reported the fast reaction of NO(aq) oxidation by dissolved oxygen in aqueous solution to form nitrite and nitrate (reaction 8).34 The mechanism they proposed is essentially the same as reactions 4-8. The reaction of nitrite with dissolved oxygen in the freezing process is simulated according to the mechanism proposed by

Pires et al.34 The simulated results can explain the experimantal results in the presence of dissolved oxygen. However, in the absence of dissolved oxygen the simulated results were different from the experimental results. The reason for the inconsistency is that one molecule of nitrate and two molecules of nitric oxide are produced through reactions 4-7, which can be expressed in reaction 9, from three molecules of nitrite, while in the experiment two molecules of nitrate were produced from three molecules of nitrite, and one molecule of nitrogen-containing species was lost from the sample. As a result we cannot conclude that the reaction of nitrite by dissolved oxygen takes place according to the mechanism proposed by Pires et al. Oxygen could oxidize nitrite directly or NO which is produced through reaction 8 followed by reactions 6 and 7. Since it is difficult to control or to determine the concentrations of oxygen and nitrite in the unfrozen solution in the freezing process without an understanding of the various phenomena in the freezing process such as the concentration factor of the reactants or the behavior of oxygen, the reaction mechanism of nitrite with dissolved oxygen in the freezing process has not been clarified. There is a possibility that oxygen is also accumulated in the liquid phase during freezing, and, as a consequence, this accumulation of oxygen could also contribute to the acceleration. In relation to the freeze concentration of gaseous species in the solution, scattering of light has been observed from the solidsolution interface during the growing of ice crystals.35-37 Mesquita reported that the scattering of light is caused by fine air bubbles dispersed at the liquid side of the solid-liquid interface.36 It is well-known that the concentration of dissolved oxygen is lower in ice than that in solution.38,36 Oxygen excluded from the ice is also accumulated at the freezing interface as dissolved oxygen. When the concentration of dissolved oxygen exceeds its saturation concentration, fine bubbles are formed at the interface.36 During the reaction, the concentration of dissolved oxygen would be kept at the equilibrium concentration for the freezing temperature by a supply from the fine bubbles. Acceleration Mechanism of the Reaction in the Freezing of Aqueous Solution. On the basis of the above results, we propose the following acceleration mechanism of the reaction in the freezing of aqueous solution. The mechanism is schematically shown in Figure 11. The first step is the accumulation of oxygen and nitrite at the freezing interface of each ice crystal (Figure 11a). When the ice crystal grows, nitrite and oxygen excluded from the ice are concentrated at the freezing interface of each single crystal of ice (Figure 11b). In the second step, as each single crystal of ice grows, concentrated nitrite and oxygen are confined in the solution surrounded by walls of ice grains (Figure 11c). As each single crystal of ice grows further, nitrite and oxygen are much more concentrated because they cannot escape from the solution surrounded by the walls of ice grains (Figure 11d) and are hardly incorporated

13882 J. Phys. Chem., Vol. 100, No. 32, 1996

Takenaka et al.

into the ice crystals. As a result, the concentrations of HNO2 and oxygen become extremely high in the solution surrounded by the walls of ice grains, and the reaction rate becomes much higher. From Figure 8, the freezing rate at lower than -3 °C is considered to be faster than the reaction rate. With the above mechanism, the concentration factor can be calculated from the theory of the depression of the freezing point (a cryoscopic constant is 1.858 K mol-1 kg for H2O). The sum of concentrations of solutes in the unfrozen solution equilibrated at -3 °C is estimated to be about 1.5 mol dm-3. It is known that the concentration of 1.5 mol dm-3 or 3° of freezing point depression, however, is so high that a simple relation of concentration and freezing point depression does not exist.39 Furthermore, because the concentration of each solute or ion in the unfrozen solution is not the same as those mentioned in the section on the freezing potential and the pH is varied in the course of freezing, the accurate concentration of nitrite in the unfrozen solution between ice grains could not be determined. Although the concentration factor cannot be calculated accurately by the theory of freezing depression, the order of the concentration factor can be calculated if it is assumed that the simple relation of concentration and the freezing point depression hold. In the initial solution 0.1 mmol dm-3 NaNO2 and about 0.06 mmol dm-3 H2SO4 were contained, and therefore, the concentration factor is calculated to be about 4 × 103. Hateley et al. estimated that the concentration factor was 11 500 at -12 °C and 40 449 at -20 °C from comparison of rate constants observed and predicted from an Arrehenius plot of the reaction in solution.12 Although there is no evidence that the reactions in freezing (the present system and also the system studied by Hateley et al.) involve the same mechanism as those in solution, according to Hately et al. the concentration factor can be calculated if we assume that the mechanisms of the reaction in freezing and in solution are the same. The initial condition was that the nitrite concentration was 0.10 mmol dm-3, the concentration of dissolved oxygen was 0.253 mmol dm-3, and the pH was 4.0. The rate of nitrate formation obtained from the slope of the time profile at -3 °C was 9.8 × 10-8 mol dm-3 s-1 at 0.085 mmol dm-3 nitrite. At -3 °C, the rate constant of reaction 3, the concentration of dissolved oxygen, and the acid dissociation constant of nitrite extraporated from those in solution are 10.8 mol-2 dm6 s-1,17 0.48 mmol dm-3,40 and 3.2 × 10-4 mol dm-3,18 respectively. The concentrations of HNO2 were calculated as 4.3 × 10-3 mol dm-3 in the freezing process and 2.0 × 10-5 mol dm-3 in the initial solution. The concentration factor is 220. This value, 220, is much smaller than that calculated from the rough estimation of freezing potential depression, 4 × 103. In order to calculate the concentration factor accurately and to clarify that the reaction mechanism of the freezing process is same as that in solution, at -3 °C the reaction in the freezing process was analyzed as follows. First we postulated that all kinds of ions, except protons, included in the sample are included in the same proportion in the unfrozen solution between ice grains. The concentration of nitrite in the unfrozen solution, therefore, is expressed as C0F, where C0 is the initial concentration of nitrite in the bulk solution and F is the concentration factor. As mentioned above, the concentration of dissolved oxygen in the unfrozen solution is constant during the reaction, and the change of nitrite can be expressed as

1/Cu ) k′t + 1/C0F

(10)

where Cu is concentration of nitrite in the unfrozen solution at time t and k′ ) k[O2] when the rate constant of the reaction is

Figure 12. Time profile of nitrite concentration by freezing at -3 °C. [nitrite]0 ) 100 µmol dm-3, [O2]0 ) 250 µmol dm-3, and pH0 ) 4.0. (O) [nitrite]; (b) 1/[nitrite]. Solid line: least-square approximation line; 1/[nitrite] ) -3161 + 752t mol-1 dm3 min-1 and r ) 0.992. Broken line: calculated curve of nitrite concentration by eqs 13 and 14. The function of volume change of the unfrozen solution used in the calculation was fitted to the experimental results, and here we adopted Vt ) a(exp(0.1t) + 1), where a ) 0.1Vu/(exp(0.1tf) - 0.1tf - 1).

k.

Cu ) C0F/(C0Fk′t + 1)

(11)

Amounts of unfrozen solution between ice grains in a unit time increase with growing ice and are represented as V1, V2, V3, ...

V1 + V2 + V3 + ... + Vi ) Vu

(12)

Here Vu indicates the total volume of the unfrozen solution. Then VuF ) V holds, where V indicates the initial volume of sample solution. Numbers of moles of nitrite in the each unfrozen solution are CuV1, CuV2, CuV3, ..., and those in the bulk solution are C0V - C0FV1, C0V - C0FV2, C0V - C0FV3, .... The concentration of nitrite measured at time t until the sample is frozen as a whole can be expressed as

C ) [C0V - C0F(V1 + V2 + V3 + ...) + C0F(V1/(C0k′Ft + 1) + V2/(C0k′F(t - t1) + 1) + V3/(C0k′F(t - t2) + 1) + ...)]/V (13) After the sample is frozen as a whole, the measured concentration is expressed as

C ) C0F[V1/(C0k′Ft + 1) + V2/(C0k′F(t- t1) + 1) + V3/(C0k′F(t - t2) + 1) + ... + Vi/(C0k′F(t - tf) + 1)]/V (14) where tf indicates the time at which the sample is frozen as a whole. If t . tf, C0k′F(t - tj) + 1 becomes almost constant. At this condition the eq 13 becomes

1/C ) k′Ft + 1/C0

(15)

Figure 12 shows time profiles of nitrite concentration and inverse of nitrite concentration at -3 °C. The straight line was obtained in a 1/C vs time plot from several minutes after the sample was frozen as a whole, despite that t was not much bigger than tf. This is probably due to the fact that at the latter stages of freezing most nitrite was incorporated into the unfrozen solution between ice grains since volumes of the unfrozen solution at the latter stages are much greater than those at the first stages. Therefore, the reaction is dominated by the latter stages, and t in the eq 15 is approximately equal to t - tf. The slope of 1/C vs t in Figure 12 was 752.2 mol-1 dm3 min-1. The concentration factor, therefore, was determined as 2.4 × 103 from eq 15

Acceleration of Reaction by Freezing

Figure 13. Time profile of ion separation in freezing with stirring. [nitrite]0 ) 100 µmol dm-3, [O2]0 ) 250 µmol dm-3, and pH0 ) 3.0. The temperature of the coolant was -21 °C. The sample started to freeze at about 2 min and was completely frozen at about 15 min. (O), (b) N(III); (4), (2) NO3-; (0), (9) pH. The open symbols indicate concentrations or pH in ice, and the solid ones indicate those in solution.

with a rate constant of 10.8 mol-2 dm6 s-1 17 and a concentration of dissolved oxygen of 0.48 mmol dm-3 40 at -3 °C. This value is in good agreement with that obtained by rough estimation from the freezing point depression (4 × 103). The calculated concentration factor from the rate of the nitrate formation (220) is smaller than the above value (2.4 × 103). This is probbably due to the fact that only about 15% of nitrite is contained in the unfrozen solution. In the eqs 13 and 14, V1, V2, V3, ... cannot be determined easily. With the concentration factor calculated above, eqs 13 and 14 were fitted to the experimental results with various functions for V1, V2, V3, .... The result is also indicated with a broken line in Figure 12. The calculated curve is in good agreement with the experimental results. The facts that the relation of 1/C vs t was a straight line and that the calculated and experimental curves showed a good relation indicate that the kinetics of the reaction in the freezing process would be the same as that in solution. Explanation of Other Processes Affecting the Reaction in Freezing. Figure 13 shows the time profile of ion concentrations in solution and in ice during freezing with stirring. When the sample solution was frozen with stirring by operating a stirring spin bar until whole sample was frozen, ice was formed from the wall of a sample container. Since no ice particles were included in the solution phase, the solution and the ice could be easily separated. All kinds of ions, nitrite, Na+, and sulfate, were excluded from the ice more than those in the case without stirring as shown in Figure 5. These results could be explained as follows: ions and especially oxygen contained in the unfrozen solution between each ice crystal are released by stirring before being confined in the solution surrounded by walls of ice grains. As a result, no nitrate was formed as shown in Figure 13. The time profile of the pH of the solution in the present system (frozen with stirring) is different from that in Figure 5 (frozen without stirring). With stirring, the pH of the solution decreased from 3.0 to 2.1 but decreased from 3.0 to 2.6 without stirring. This great pH depression under stirring conditions is due to the movement of protons from the ice to the solution to neutralize the electric potential generated in freezing and then their release into the bulk solution. These results also suggest the formation

J. Phys. Chem., Vol. 100, No. 32, 1996 13883 of HNO2 in the unfrozen solution in the solution surrounded by walls of ice grains. In Table 3, the addition of 1.0 mmol dm-3 CH3COONa or CH3COONH4 reduces the amounts of nitrate in spite of the positive freezing potential. Because acetic acid is a weaker acid (Ka ) 1.728 × 10-5 at 25 °C18) than nitrous acid (Ka ) 5.9 × 10-4 at 25 °C18), protons transferred from the ice to the interface would bond with CH3COO- rather than with NO2-. Nitrite anion is not a reactive species in the reaction of nitrite with oxygen; therefore, addition of acetate anion reduces the reactive HNO2 and thus inhibits the nitrate formation. Advantages of Reactions Accelerated by Freezing. Freezing of the solution supplies an effective reaction condition. At an initial concentration of 10 mmol dm-3 nitrite and a pH of 4.0 under 100% bubbling oxygen (1.2 mmol dm-3 dissolved oxygen) at 27 °C, the initial formation rate of nitrate in solution was 3.5 × 10-7 mol dm-3 s-1. The reaction rate rapidly decreased with time, and only 5% nitrite was oxidized to nitrate in an hour. On the other hand, at initial concentrations of 0.1 mmol dm-3 nitrite, which is 100 times lower than the concentration in the above solution system, 0.25 mmol dm-3 dissolved oxygen, pH 4.0, and -21 °C, the rate of nitrate formation was 3.1 × 10-7 mol dm-3 s-1. The formation rate by freezing was almost the same in solution in spite of the 100 times lower nitrite concentration. Further, more than 70% of the nitrite was oxidized to nitrate within 20 min. If a reaction condition, such as initial pH, initial concentrations of reactants, kinds and concentrations of additional salts, and freezing rate, are adjusted for the reactions to be accelerated, many other reactions which are spontaneous in solution could also be accelerated by freezing. The freezing process is very useful to prepare chemicals which are unstable in solution at high temperatures, because the chemicals can be stored in ice simultaneously with formation. Conclusion The freeze concentration effect proposed in the literature2-13 does not show where the reactants are concentrated or how the reactants are concentrated into the unfrozen solution. On the basis of the above results, it is most likely that the reactants are concentrated into the unfrozen solution surrounded by walls of ice grains. The pH of the unfrozen solution must be lowered by the freezing potential. This pH depression supports the acceleration of the reaction of nitrite with dissolved oxygen. Furthermore, the freezing potential would increase the concentration of nitrite ion around ice grains by the electrostatic force. For the acceleration of the reaction the freezing potential would affect the pH depression rather than accumulation of ions. Nitrite ions attracted by the freezing potential are accumulated around the ice grains, HNO2, NO2-, and O2 are confined in the solution surrounded by wall of ice grains, and the pH of the solution decreases by the freezing potential. The mechanism of acceleration of the reaction of nitrite with dissolved oxygen in the freezing process is that thus formed HNO2 is highly concentrated and reacts with dissolved oxygen rapidly. The concentration factor was 2.4 × 103 at -3 °C and expected to be higher than 2.4 × 103 at lower temperature. Furthermore, it is found that the mechanism of the reaction of nitrite with dissolved oxygen in the freezing process is the same as that in solution. Acknowledgment. The authors thank Dr. Y. Furukawa, Institute of Low Temperature Science, Hokkaido University, for fruitful discussion and for teaching us the preparation of a single crystal of ice. This study has been carried out in part

13884 J. Phys. Chem., Vol. 100, No. 32, 1996 under the Visiting Researcher’s Program of Institute for Hydrospheric-Atmospheric Sciences, Nagoya University, and was supported in part by Grant-in-Aid for Scientific Research from the Ministry of Education and Culture, Japan. References and Notes (1) Takenaka, N.; Ueda, A.; Maeda, Y. Nature 1992, 358, 736. (2) Grant, N. H.; Clark, D. E.; Alburn, H. E. J. Am. Chem. Soc. 1961, 83, 4476. (3) Weatherburn, M. W.; Logan, J. E. Clin. Chim. Acta 1964, 9, 581. (4) Butler. A. R.; Bruice, T. C. J. Am. Chem. Soc. 1964, 86, 313. (5) Bruice, T. C.; Butler, A. R. J. Am. Chem. Soc. 1964, 86, 4104. (6) Alburn, H. E.; Grant, N. H. J. Am. Chem. Soc. 1965, 87, 4174. (7) Grant, N. H.; Alburn, H. E. Biochemistry 1965, 4, 1913. (8) Grant, N. H.; Alburn, H. E. Science 1965, 150, 1589. (9) Grant, N. H.; Alburn, H. E. Nature 1966, 212, 194. (10) Grant, N. H.; Alburn, H. E. ArchiV. Biochem. Biophys. 1967, 118, 292. (11) Fennema, O. Water relations of foods; Duckworth, R. G., Eds.; Academic Press: London, 1975; pp 539-556. (12) Hatley, R. H. M.; Franks, F.; Day, H.; Byth, B. Biophys. Chem. 1986, 24, 41. (13) Hatley, R. H. M.; Franks, F.; Day, H. Biophys. Chem. 1986, 24, 187. (14) Bronshteyn, V. L.; Chernov, A. A. J. Cryst. Growth 1991, 112, 129. (15) Finnegan, W. G.; Pitter, R. L.; Young, L. G. Atmos. EnViron. 1991, A25, 2531. (16) Damschen, D. E.; Martin, L. R. Atmos. EnViron. 1983, 17, 2005. (17) Takenaka, N.; Ueda, A.; Maeda, Y. Proc. NIPR Symp. Polar Meteorology Glaciology 1993, 7, 24. (18) Nair, S. K.; Peters, L. K. Atmos. EnViron. 1989, 23, 1399. (19) Calvert, J. G. SO2, NO and NO2 Oxidation Mechanisms: Atmospheric Considerations: Butterworth Publishers: Boston, MA, 1984; Chapter 1.

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