Acceleration and Reaction Mechanism of the N-Nitrosation Reaction

Jun 29, 2017 - Some reactions (e.g., oxidation of nitrite, denitrification of ammonium) are accelerated in freeze-concentrated solution (FCS) compared...
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Acceleration and Reaction Mechanism of the N‑Nitrosation Reaction of Dimethylamine with Nitrite in Ice Kodai Kitada,† Yusuke Suda,‡,§ and Norimichi Takenaka*,†,§ †

Laboratory of Environmental Materials Chemistry, Department of Applied Chemistry, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai-shi, Osaka 599-8531, Japan ‡ Laboratory of Environmental Materials Chemistry, Department of Sustainable System Sciences, Graduate School of Humanities and Sustainable System Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai-shi, Osaka 599-8531, Japan ABSTRACT: Some reactions (e.g., oxidation of nitrite, denitrification of ammonium) are accelerated in freeze-concentrated solution (FCS) compared to those in aqueous solution. Ice is highly intolerant to impurities, and the ice excludes those that would accelerate reactions. Here we show the acceleration of the N-nitrosation reaction of dimethylamine (DMA) with nitrite to produce N-nitrosodimethylamine (NDMA) in FCS. NDMA is a carcinogenic compound, and this reaction is potentially accelerated in frozen fish/meat. The eaction rate of the Nnitrosation reaction becomes fastest at specific pH. This means that it is a third-order reaction. Theoretical pH values of the peak in the third-order reaction are higher than the experimental one. Freeze-concentration of acidic solution causes pH decrement; however, the freeze-concentration alone could not explain the difference of pH values. The theoretical value was obtained under the assumption that no solute took part in ice. However, solutes are incorporated in ice with a small distribution coefficient of solutes into ice. This small incorporation enhanced the decrement of pH values. Using the distribution coefficient of chloride and sodium ion and assuming those of nitrite and DMA to explain the enhancement, we succeeded in estimating the distribution coefficients of nitrite: 2 × 10−3 and DMA: 3 × 10−2.

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during the freezing of aqueous solutions.17,18 FCS becomes higher concentration compared to the initial solution. Ice is highly intolerant to impurities, and consequently, the ice lattice does not contain foreign atoms and contains very few ions, and most of them escape to the FCS. The concentration of solutes in the FCS increases with growth of ice. Finally, the reaction is accelerated in FCSs that include extremely high concentrations of solutes. These phenomena cause the reaction to be accelerated by freezing. The reactivity of reactions in the FCS varies depending on the condition of freezing. Recently, Bogdan et al. revealed that frozen solutions are a complex ice/FCS morphology, and the FCS can be liquid, solid, or glassy by the temperature and the solute molecular structure.19 In addition, we cannot explain all reactions accelerated by freezing solely by the increase concentration of the FCS. Freeze-concentration causes not only an increase in the concentration of the solution.20−24 For example, a change of pH in the FCS is also caused by the freeze-concentration. The pH of the FCS changes for the following two reasons. The pH of the aqueous solution depends on the difference in concentrations of anions and cations and the ion product of water. When the concentration

INTRODUCTION In general, chemical reactions in the liquid phase are slowed at lower temperatures. Therefore, we store foodstuffs in a refrigerator or a freezer to slow down the deterioration process. However, it is not always the case because some reactions in aqueous solution are accelerated by freezing.1−16 For example, denitrification of ammonium nitrite and oxidation of nitrite are reported to be accelerated by freezing. Regardless of these reports, reactions accelerated by freezing are little known. These reactions may play important roles for revealing the chemistry in cold regions and in freezers. Studying reactions accelerated by freezing overturns common sense and gives us new knowledge of chemistry. Although the mechanism of reactions accelerated by freezing has not been fully understood yet, in many cases, a freezeconcentrated solution (FCS) is explained as a reaction field. Takenaka et al. reported the following results about the oxidation of nitrite by dissolved oxygen. This reaction was not accelerated by either addition of ice produced from pure water at 273 K or being frozen with stirring. This reaction was accelerated only when polycrystalline ice was formed from solution. Under dark conditions, this reaction also occurred in ice. Nitrate produced via this reaction was found in the ice phase. From these results, they concluded that this reaction was accelerated in FCS. At the beginning of the ice growth process, a continuous ice framework entangled with a FCS is formed © 2017 American Chemical Society

Received: April 6, 2017 Revised: June 28, 2017 Published: June 29, 2017 5383

DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388

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The Journal of Physical Chemistry A

In this study, we investigate the details of acceleration of the N-nitrosation reaction of DMA with nitrite by freezing of aqueous solution. Furthermore, we determined the reaction order for the N-nitrosation reaction and proposed a new method to determine the partition coefficient of solute to ice.

of aqueous solution changes, the difference in concentrations of anions and cations increases. As a result, the pH increases or decreases depending on the balance of anions and cations. For example, the FCS of an acidic solution becomes more acidic than that of the initial solution, and the FCS of an alkaline solution becomes more alkaline than the initial solution. The second cause of pH change by freezing solution is the difference in distribution coefficients of solutes into the ice lattice of ions.25−27 In the case of freezing of a sodium chloride solution, more chloride ions are taken in ice than sodium ions. Then, ice is charged negatively while the solution is postively charged and electrical charge is generated between the ice and solution. As a result, chloride ions taken in ice lattice withdraw hydronium ions in solution to neutralize this electrical charge. This phenomenon causes an increase of the hydroxide ion in the FCS, and the pH of the FCS increases. The distribution coefficients of various solutes in an ice lattice are reported by Gross et al. However, the measuring method of the distribution coefficient is complicated, and distribution coefficients differ in condition. Due to these problems, a study about the distribution of solute in an ice lattice has not been developed. N-Nitrosation is a reaction of amines with nitrite to form nitrosamines. Nitrosamines are hazardous because they are carcinogenic.28−30 The N-nitrosation reaction proceeds with the same mechanism as denitrification of ammonium nitrite, which is already confirmed to be accelerated by freezing. Amines exist in meat and fish, while nitrites are in vegetables. It is notable that sodium nitrite is added to processed meats that include a lot of amines as a food color additive and inhibitor of the multiplication of Clostridium botulinum.31,32 If N-nitrosation proceeds by freezing, a dangerous amount of nitrosamine may be generated in processed meat. Therefore, studying Nnitrosation by freezing is of practical significance. Nitrosamines are known to be generated via the reaction of nitrite and amines under acidic conditions (reaction 1). R 2NH(aq) + HNO2 (aq) ⇄ R 2NNO(aq) + H 2O

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EXPERIMENTAL SECTION All reagents were obtained from Wako Pure Chemicals, Inc. and used without further purification. Ultrapure water was prepared by Millipore Co. Ltd. Direct-Q 3UV using tap water. The resistivity of the ultrapure water was higher than 18.2 MΩ cm. An aqueous solution that includes both sodium nitrite and DMA was prepared so that nitrite and DMA concentrations were 1.0 mmol dm−3. The pH of the solution was adjusted using hydrochloric acid. The pH was measured with an F-52 Horiba Co. Ltd. pH meter connected with a 9611_10D glass electrode, and the pH meter was calibrated by using a phosphate buffer (pH 6.8) and phthalate buffer (pH 4.0). A volume of 5 mL of 1.0 mmol dm−3 nitrite and DMA solution were put into a 6 mL polypropylene syringe sealed with a silicon stopper and kept in a Sanyo SR-D170NG freezer for 45 h at 258 K. Following 45 h of freezing, the sample was thawed at 20 °C. After the sample became liquid state, the concentration (shown as the final concentration in the Results and Discussion section) of DMA was measured by a Yokogawa Analytical Systems Co., Ltd., IC-7000 ion-chromatographic analyzer, and nitrite and nitrate (generated by oxidation of nitrite) were measured by a Dionex ion chromatography system, ICS-1500. For analysis of the inorganic anions, a Dionex AS-12A column with 9 mM Na2CO3 eluent was used, and for analysis of the cations, a Shodex IC YS-50 column was used with 4 mM methanesulfonic acid as the eluent. For the control experiment, the same solution was kept at 20 °C for the same period of time as the freezing experiments. Although 5 mL of aqueous solution in a 6 mL polypropylene syringe will produce an ice/FCS morphology different from that of the solutions in meat/fish, we employed a 6 mL polypropylene syringe to prevent the reaction vessel from breaking caused by volume expansion triggered by phase change of water and to seal samples in order to remove the influence of air. In addition, dissolved oxygen was not removed for mimicking the environment of foods. GC/MS Agilent 5975 and HPINOWAX 19091N-133 capillary columns were used to detect N-nitrosodimethylamine (NDMA).

(1)

Many researchers have reported that reaction 1 is a secondorder reaction.33,34 R = k[R 2NH][HNO2 ]

(2)

The following are reaction pathways of the second-order reaction: HNO2 + H+ ⇄ H 2NO2+ ⇄ NO+ + H 2O

(3)

R 2NH + NO+ ⇄ R 2NNOH+ ⇄ R 2NNO + H+

(4)

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RESULTS AND DISCUSSION N-Nitrosation in Ice. Figure 1a shows the concentration of nitrite, nitrate, and the sum of them versus pH after 45 h at 258 and 293 K. The result shows that the concentration of nitrate increased at pH < 5 and nitrite decreased at pH < 5 at 258 K (in the freezer). We could conclude that the increase of nitrate at pH < 5 is due to the oxidation of nitrite by dissolved oxygen (reaction 9).

In recent year, Hughes and others proposed a third-order reaction.35−37 R = k[R 2NH 2+][HNO2 ][NO2−]

(5)

Reaction pathways of the third-order reaction are explained below. HNO2 + H+ ⇄ H 2NO2+ ⇄ NO+ + H 2O

(6)

NO2− + NO+ ⇄ N2O3

(7)

2HNO2 + O2 ⇄ 2H+ + 2NO3−

This reaction is known to occur under acidic conditions and accelerate in a FCS. It means that not all of the nitrite decreased by being consumed in the N-nitrosation reaction. Therefore, in order to evaluate whether the N-nitrosation reaction occurred or not, we calculated the sum of concentrations of nitrite and nitrate (“nitrate + nitrite”). Decrement of nitrite + nitrate means that nitrite is consumed

R 2NH 2+ + N2O3 ⇄ R 2NNOH+ + HNO2 ⇄ R 2NNO + H+ + HNO2

(9)

(8)

However, the pathways of the third-order reaction are not widely accepted. 5384

DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388

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h. On the other hand, nitrate + nitrite at 258 K decreased by 45% at around pH 4.6. From the results in Figure 1a, it is clear that some reactions are accelerated in the FCS. Figure 1b describes the pH profiles of the change in DMA concentration at 258 and 293 K. The DMA concentration followed almost the same pattern as that of nitrate + nitrite. The amount of DMA was almost unchanged at 293 K and was decreased by 45% at 258 K at around pH 4.6. Both the nitrate + nitrite and concentration of DMA decreased in the same way. We detected NDMA in the frozen sample, as shown in Figure 2. Therefore, we could conclude that the N-nitrosation reaction proceeded at around pH 4.6 at 258 K. Although we could detect NDMA by GC/MS, we evaluated the N-nitrosation reaction by ion chromatography to prevent further N-nitrosation reaction from proceeding. Reaction Order for N-Nitrosation. We calculated the relative reaction rate of DMA (reacted amount of DMA per 45 h). The results are shown in Figure 3. The vertical axis shows the ratio of the reacted amount of DMA compared to the maximum one at pH 4.6 for 72 h. This figure indicates that the N-nitrosation reaction would occur most efficiently at around pH 4.6. As described earlier, the reaction order of the N-nitrosation reaction has been discussed. In the case of the second-order reaction, the reaction species could be HNO2 or NO2− and (CH3)2NH or (CH3)2NH2+. In addition, the N-nitrosation reaction is pH-dependent. Therefore, in all cases, we calculated the theoretical relative value of the reaction rate of Nnitrosation against pH. The theoretical relative reaction rate can be calculated by the following method. For example, if the reaction species are HNO2 and (CH3)2NH2+, the reaction rate R is shown by the following equation.

Figure 1. pH profiles of N-nitrosation reaction species in a reaction mixture at 258 and 293 K. Initially, the reaction mixture includes 1.0 mmol dm−3 of sodium nitrite and DMA. The final concentrations of nitrite (include nitrate generated by oxidation of nitrite) and DMA are shown in following, individually. (a) Triangles, diamonds, circles, and squares show the final concentrations of nitrate (258 K), nitrite (258 K), the sum of nitrate and nitrite at 258 K, and the sum of nitrate and nitrite at 293 K, respectively. Error bar shows 1 standard deviation (σ) for five samples. (b) Diamonds and triangles show the final concentrations of DMA at 293 and 258 K, respectively. Error bar shows σ for five samples.

R = k[HNO2 ][(CH3)2 NH 2+]

(10)

Here, k is a reaction rate constant. Additionally, acid dissociation constants of nitrite and DMA are shown as KN = [H + ][NO 2 − ]/[HNO 2 − ] and K A = [(CH 3 ) 2 NH][H + ]/ [(CH3)2NH2+], respectively. At 258 K, KN = 10−3.62 is already reported.38 Because we already knew the equilibrium constant of amine (KA = 10−10.73,39) and the enthalpy of dissociation (ΔH = 5.04 × 104,40) at 298 K, we calculated KA at 258 K

by some reactions. Nitrate + nitrite at 293 K (keeping the reaction solution unfrozen) remained almost unchanged for 45

Figure 2. Mass spectrum of NDMA (MW 74.08) detected by GC/MS in the sample of 72 h frozen at 258 K and pH 5.2. The initial concentration of sodium nitrite and DMA was 1.0 mmol dm−3. 5385

DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388

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concluded that the N-nitrosation reaction is not a second-order reaction. In the case of a third-order reaction, we also calculated the relative theoretical value of the pH profiles of the reaction rate of the N-nitrosation reaction. The reaction species of the thirdorder reaction are two molecules of HNO2 or NO2− and one molecule of (CH3)2NH or (CH3)2NH2+. For example, if the reaction species are HNO2, NO2−, and (CH3)2NH, the reaction rate R is shown by the following equation. R = k′[HNO2 ][NO2−][(CH3)2 NH]

(12)

Here, k′ is a reaction rate constant. Then, we assigned the equations for KN, KA, N, and A and could transform eq 12 into the following equation: ⎛ [H+]N ⎞⎛ [H+]KN ⎞⎛ [H+]KA ⎞ R = k′⎜ + ⎟⎜ + ⎟⎜ + ⎟ ⎝ KN + [H ] ⎠⎝ KN + [H ] ⎠⎝ KA + [H ] ⎠

Finally, we could obtain four possible lines in which they show relative reaction rates of {HNO2, HNO2, and (CH3)2NH2+}, {HNO2, NO2−, and (CH3)2NH2+} or {HNO2, HNO2, and (CH3)2NH}, {HNO3, NO2−, and (CH3)2NH} or {NO2−, NO 2 − , and (CH 3 ) 2 NH 2 + }, and {NO 2 − , NO 2 − , and (CH3)2NH}, shown in Figure 3b. The shape of the continuous line conformed to the shape of the plot of experimental values. At last, we can conclude that the N-nitrosation reaction is a third-order reaction whose species are HNO2, NO2−, and (CH3)2NH2+ or HNO2, HNO2, and (CH3)2NH. Here, we cannot distinguish that reaction species are HNO2, NO2−, and (CH3)2NH2+ or HNO2, HNO2, and (CH3)2NH. Reaction rate constants of HNO2, NO2−, and (CH3)2NH2+ or HNO2, HNO2, and (CH3)2NH are different. These reaction rates show a maximum at pH 3.7. Partition Coefficients to Ice. We could conclude that the N-nitrosation reaction is a third-order reaction. However, the theoretical value of the pH at which the maximum reaction rate was 3.7, while the experimental value of that was 4.6. We thought that the pH 4.6 solution was concentrated in the FCS to pH 3.7. When the acidic solution is concentrated, the pH of the concentrated solution becomes lower than that of the initial solution. As a trial, we calculate the theoretical pH in the FCS. First, we consider the electrical balance shown in the following equation:

Figure 3. Relative experimental and theoretical values of the reaction rate of the N-nitrosation reaction against pH at 258 K. Here, R is the reaction amount of DMA per 45 h and Rmax is the maximum reaction amount. (a) In the case of second-order reaction, the solid line, dotted line, and broken line show species {HNO2 and (CH3)2NH2+}, {HNO2 and (CH3)2NH} or {NO2− and (CH3)2NH2+}, and {NO2− and (CH3)2NH}, respectively. Diamond plots show the relative experimental value of the average reaction rate of the N-nitrosation reaction against pH after 45 h in ice at 258 K. (b) In the case of the third-order reaction, the dotted line, solid line, broken line and chain line show species {HNO2, HNO2, and (CH3)2NH2+}, {HNO2, NO2−, and (CH3)2NH2+} or {HNO2, HNO2, and (CH3)2NH}, {HNO3, NO2−, and (CH3)2NH} or {NO2−, NO2−, and (CH3)2NH2+}, and {NO2−, NO2−, and (CH3)2NH}, respectively. Diamond plots show the experimental value of the average reaction rate of the N-nitrosation reaction against pH after 45 h in ice at 258 K.

[H+] + [(CH3)2 NH 2+] + [Na +] = [OH−] + [Cl−] + [NO2−] (14)

Next, we consider the mass balance shown in following equations:

through the Van’t Hoff equation. Then, we obtained K258 K = 10−12.14. Then, we used the sum of HNO2 and NO2− (N = [HNO2] + [NO2−]) and that of (CH3)2NH and (CH3)2NH2+ (A = [(CH3)2NH2+] + [(CH3)2NH]. Then, we assigned equations for KN, KA, N, and A and could transform eq 10 into the following equation: ⎛ [H+]N ⎞⎛ [H+]A ⎞ R = k⎜ + ⎟⎜ + ⎟ ⎝ KN + [H ] ⎠⎝ KA + [H ] ⎠

(13)

(11)

C N = [Na +] = [HNO2 ] + [NO2−]

(15)

CA = [(CH3)2 NH 2+] + [(CH3)2 NH]

(16)

C HCl = [Cl−]

(17)

Here, CN, CA, and CHCl are the initial concentrations of sodium nitrite, DMA, and hydrochloric acid, respectively. By substituting these equations into eq 14, we can obtain the following equation:

On the basis of this calculation method, we can compute the relative theoretical value of the reaction rate of the Nnitrosation reaction against pH. Finally, we obtained three possible lines that show {HNO2 and (CH3)2NH2+}, {HNO2 and (CH3)2NH} or {NO2− and (CH3)2NH2+}, and {NO2− and (CH3)2NH}, shown in Figure 3a. However, there was no line that conformed to plots of experimental values. Therefore, we

[H+] +

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K [H+]CA KNC N + C N − W+ − C HCl − =0 + [H ] + KA [H ] [H+] + KN (18) DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388

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The Journal of Physical Chemistry A Here, KW shows the ion product for water. We can calculate the theoretical pH in aqueous solution by evaluation of [H+] to satisfy eq 18. We assume that all solutes are excluded from ice lattice. However, under this assumption, no matter how the initial solution is concentrated, the reaction solution of pH 4.6 reaches a plateau at pH 4.2 and does not decrease down to pH 3.7. In fact, a little solute is taken in ice. We conclude that incorporation of solutes into ice is the reason why the pH of the FCS did not decrease by 3.7 in the calculation above. Each solute or ion has different distribution coefficients in an ice lattice and is taken in the ice lattice in a different ratio. Therefore, we calculate the pH of the FCS in consideration of distribution coefficients of each solute. The value of the molar depression of freezing point of water is Kf = 1.86 (K kg mol−1). The equation of the freezing point depression is ΔT = Kfm. Here, ΔT and m are the freezing point depression and molality, respectively. According to the equation, for the FCS at −15 °C, the solution would be concentrated about 1800 times. Although decrement of molecules associated with the N-nitrosation reaction in the FCS may cause further freeze-concentration, we discount the effect of this concentration because of the smallness and slowness of concentration change. The ice/ liquid interface at lower temperatures is inherently out of equilibrium, or equilibrium is reached very slowly. Hence, we assume that a sodium ion would be concentrated 1800 times. Takenaka et al. advocate the following equation: ⎛V ⎞ Ct = C0⎜ 0 ⎟ ⎝ Vt ⎠

nitrosation reaction has a peak at a specific pH means that the N-nitrosation reaction is a third-order reaction. On the other hand, the theoretical value of the pH at which the reaction rate shows a maximum is 3.7 at 258 K. This value is lower than the experimental value of that. The FCS from a pH 4.6 solution at 258 K needs to be pH 3.7. Although the concentration of the acidic solution cause a decrease of pH, no matter how the solutes are concentrated in the FCS, the FCS cannot show pH 3.7 under the assumption that all solutes are excluded from ice. In fact, ice takes part in a little solute. Decrement of the pH is supported by the difference of the ratio of each solute taking part in the ice lattice. As a result, from the difference of experimental and theoretical values of the pH, we could obtain a crude value of distribution coefficients of solutes in an ice lattice, nitrite: 2 × 10−3 and DMA: 3 × 10−2. Storing of processed meat/fish in a freezer may potentially be dangerous because N-nitrosation reactions of nitrite and DMA, which are accelerated in frozen solution, produce carcinogenic nitorosamines. However, the experimental condition is different from that of frozen meat/fish. In order to find safe conditions for freezing meat/fish, more studies should be carried out.

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*E-mail: [email protected]. ORCID

Kodai Kitada: 0000-0002-1635-9320

(1 − kX )

Author Contributions §

(19)

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Y.S. and N.T. contributed equally.

Here, Ct and C0 indicate the concentrations in the FCS and initial solution, respectively, Vt and V0 indicate the volumes of the FCS and initial solution, respectively, and kX gives the distribution coefficients (kX = [X]ice/[X]unfrozen solution). At a certain time t, V0/Vt is constant for each solute. Then, we can transform eq 19 into following equation: ⎛ C Y ⎞(1 − kX)/(1 − kY) C X = C0X ⎜ ⎟ ⎝ C0Y ⎠

AUTHOR INFORMATION

Corresponding Author

Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Grant, N. H.; Clark, D. E.; Alburn, H. E. Imidazole-and basecatalyzed hydrolysis of penicillin in frozen systems. J. Am. Chem. Soc. 1961, 83, 4476−4477. (2) Brown, W. D.; Dolev, A. Effect of freezing on autoxidation of oxymyoglobin solutionsa. J. Food Sci. 1963, 28, 211−213. (3) Weatherburn, M. W.; Logan, J. E. The effect of freezing on the potassium ferricyanide-potassium cyanide reagent used in the cyanmethemoglobin procedure for hemoglobin determination. Clin. Chim. Acta 1964, 9, 581−584. (4) Pincock, R. E. Reactions in frozen systems. Acc. Chem. Res. 1969, 2, 97−103. (5) Hatley, R. H.; Franks, F.; Day, H.; Byth, B. Subzero-temperature preservation of reactive fluids in the undercooled state: I. The reduction of potassium ferricyanide by potassium cyanide. Biophys. Chem. 1986, 24, 41−46. (6) Hatley, R. H.; Franks, F.; Day, H. Subzero-temperature preservation of reactive fluids in the undercooled state: II. The effect on the oxidation of ascorbic acid of freeze-concentration and undercooling. Biophys. Chem. 1986, 24, 187−192. (7) Takenaka, N.; Ueda, A.; Maeda, Y. Acceleration of the rate of nitrite oxidation by freezing in aqueous solution. Nature 1992, 358, 736−738. (8) Takenaka, N.; Ueda, A.; Daimon, T.; Bandow, H.; Dohmaru, T.; Maeda, Y. Acceleration mechanism of chemical reaction by freezing: The reaction of nitrous acid with dissolved oxygen. J. Phys. Chem. 1996, 100, 13874−13884. (9) Takenaka, N.; Furuya, S.; Sato, K.; Bandow, H.; Maeda, Y.; Furukawa, Y. Rapid reaction of sulfide with hydrogen peroxide and formation of different final products by freezing compared to those in solution. Int. J. Chem. Kinet. 2003, 35, 198−205.

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Here, C0X and C0Y indicate the initial concentrations of solutes X and Y, respectively. CX and CY indicate concentrations of solutes X and Y in FCS, respectively. kX and kY indicate distribution coefficients of solutes X and Y. We determined the volume of the FCS to be 1/1800 of the volume of the initial solution. If we know the distribution coefficient of solute X or Y, we can calculate that of Y or X, respectively. Now, we can adopt reported values of distribution coefficients of Cl− of 2.7 × 10−3 and Na+ of 2.6 × 10−3.41 To achieve pH 3.7, the distribution coefficients of nitrite and DMA must be 2 × 10−3 and 3 × 10−2, respectively. We could make a prediction of unknown distribution coefficients that are very difficult to obtain. Although these values are nothing but guesses, we can determine distribution coefficients of a solute in the case that distribution coefficients of other solutes are already known. Distribution coefficients have a large impact on pH. A solution under mild conditions changes to hard in the FCS by the distribution of solutes into the ice lattice.

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CONCLUSIONS The results suggest that the N-nitrosation reaction of nitrite and DMA proceeds in ice when the pH of the solution before freezing is around 4.6. The fact that the reaction rate of the N5387

DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388

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DOI: 10.1021/acs.jpca.7b03246 J. Phys. Chem. A 2017, 121, 5383−5388