1461
Znd. Eng. Chem. Res. 1992,31, 1461-1465 Cox, P. R.; Strachan, A. N. Two phase nitration of toluene-I. Chem. Eng. Sci. 1972, 27, 457. Draper, M. R.; Ridd, J. H. Nitration in Aqueous Nitric Acid the Rate Profile and the Limiting Reaction Rates. J. Chem. SOC., Perkin Trans. 2 1981, 94. Field, J. P.; Strachan, A. N. Evidence from the Rate of Homogeneous Nitration of Hexafluoro-m-xylene for Kinetic Control in the Two-Phase Reaction. Ind. Eng. Chem. Prod. Res. Dev. 1982,21, 352.
Hanson, C.; Marsland, J. G.; Wilson, G. The Macrokinetics of Aromatic Nitration. Chem. Znd. 1966, 675. Hanson, C.; Pratt, M. W. T.; Sohrabi, M. Some Aspects of Aromatic Nitration in Aqueous Systems. ACS Symp. Ser. 1976, 22, 225-244.
Moodie, R. B.; Schofield, K.; Taylor, P. G. Electrophilic Aromatic Substitution. Part 21. Rate Constants for Formation of Nitro-
nium Ion in Aqueous Sulphuric, Perchloric, and Methanesulphonic Acids. J. Chem. Soc., Perkin Trans. 2 1979, 133. Perry, R. H.; Chilton, C. H. Chemical Engineers' Handbook; McGraw-Hill: New York, 1973; pp 3.76-3.81. Sheats, G. F.; Strachan, A. N. Rates and activation energies of nitronium ion formation and reaction in the nitration of toluene in ~ 7 8 %sulphuric acid. Can. J. Chem. 1978,56, 1280. Stock, L. M. The Mechanism of Aromatic Nitration Reactions. ACS Symp. Ser. 1976,22,45-72. Strachan, A. N. T w o Phase Nitration of Toluene in Constant Flow Stirred Tank Reactors. ACS Symp. Ser. 1976,22, 210-218. Received for review October 7 , 1991 Revised manuscript received January 31, 1992 Accepted February 23, 1992
Nonisothermal Analysis of the Reaction Kinetics for Chlorine in Basic Hydrogen Peroxide Richard A. Davis, Gabriel Ruiz-Ibanez, and Orville C. Sandall* Department of Chemical and Nuclear Engineering, University of California, Santa Barbara, Santa Barbara, California 93106
The effect of temperature on the reaction kinetics of chlorine with basic hydrogen peroxide (BHP) was investigated for the system of C12 a t atmospheric pressure absorbing into 4 M KOH in aqueous hydrogen peroxide for the temperature range of 0-20 "C. This reaction is important for the production of singlet delta oxygen [02(lA )] used in the chemical oxygen-iodine laser (COIL). The kinetics experiments of Ruiz-Ibanez and Sandall for C12 diffusing and reacting in BHP in a laminar liquid jet absorber were modeled by material and energy balances which were solved numerically. Our results for the second-order rate constant were correlated for temperature dependence by the Arrhenius expression k(m3/(kg-mol s)) = 1.2 X 103l exp[-15800/T(K)]. These results show an order of magnitude increase for the rate constant over the approximation of Ruiz-Ibanez and Sandall due to the depressed solubility and diffusivity of C12 in BHP arising from ion effects in the liquid phase.
Introduction The chemical reaction between chlorine and basic hydrogen peroxide (BHP) to produce singlet delta oxygen [02(1$)] is of interest because of the use of 02(1$)in the chemical oxygen-iodine laser (COIL). Reliable reaction rate information is useful in modeling 02(1$) production (Aharon et al., 1991). The overall stoichiometry for this reaction is Cl2 + 2H002C1- + H2Oz + 02(lAg) (1)
-
The addition of base to an aqueous solution containing excess hydrogen peroxide will result in a rapid approach to equilibrium as follows: OH- + H202 HOO- + H2O (2)
*
According to the equilibrium constant data of Balej and Spalek (1979), the perhydroxyl anion formation is strongly favored. Thus, for solutions with excess hydrogen peroxide, the concentration of the hydroxyl anion is negligibly small with respect to the perhydroxyl anion concentration for the temperature range of interest here. The kinetic mechanism for the reaction of chlorine with BHP is thought to be that proposed by Storch et al. (1983). This mechanism may be expressed by eqs 3-6. Clz + HOO- -!L C1- + HOOCl HOOCl ClOO-
k2
k, +
(3)
H+ + C100-
(4)
+ C1-
(5)
02('Ag)
Due to the excess HOO- the following recombination occurs:
H++ HOO- 2H202
(6)
The rate-limiting step for the overall reaction is thought to be eq 3. Ruiz-Ibanez and Sandall (1991) have reported experimental kinetics data for this reaction with the objective being to determine the limiting rate constant, k,. Chlorine gas at atmospheric pressure was absorbed into a laminar liquid jet stream with an initial liquid concentration of approximately 4 M HOO-. The exposed jet was 1.23 cm long with a 0.505-mm diameter. The gas-liquid contact time was kept in the range of 2.6 X to 2.9 X s. It was not possible to operate in the first-order regime (in which data analysis is more straightforward) in this case because of the limit on the concentration of KOH that could be used in order to prevent rapid decomposition of the peroxide. Thus, data were obtained in the secondorder regime and an approximate analytical procedure was developed to analyze the data assuming constant temperature in the liquid phase. In this study a procedure was developed to reanalyze these data in order to better account for the effects of temperature and ion concentration on the physicochemical properties such as diffusivity, C12 solubility, and the reaction rate. The model and numerical technique developed here remove the restrictive assumptions regarding the physicochemical properties and temperature profile within the liquid. This numerical procedure analyzes the si-
0888-5885/92/2631-1461$03.00/0@ 1992 American Chemical Society
1462 Ind. Eng. Chem. Res., Vol. 31, No. 6, 1992
multaneous heat transfer and mass transfer of all species in order to determine the rate constant kl that best fits the experimental data. The temperature and concentration dependence of the physical properties required in the model are presented, followed by the results of the analysis.
Model Development Let A, B, C, H and K represent the species Clz, HOO-, and K+, respectively. For irreversible second-order Cl-, H+, reaction kinetics, the rates of depletion per unit volume of Clz and HOO- are RA = klCACB (7) (8) RB = klCACB + k4CHCB Assuming eq 3 to be the rate-limiting step, the rate expressions for HOO- and C1- become RB=-Rc = ~ R A (9) The coupled species balance equations for Clz,HOO-, and C1- in the laminar liquid jet are
-[
acj 1 a -= az
r ar
rD.
-1
acj ar
-Rj
for j = A, B, C
(10)
where the laminar liquid jet is modeled as a cylindrical column of liquid with a uniform velocity u in the positive z direction. The laminarliquid jet apparatus was designed to produce a flat velocity profile in the liquid stream (Ruiz-Ibanez et al., 1991); thus the velocity is assumed to be constant with respect to the radial as well as axial coordinates. Djis the diffusion coefficient of species j and is temperature as well as concentration dependent. In this analysis axial diffusion is neglected. The global electroneutrality constraint on the ionic species in the liquid is s,(CB
+ Cc - CK) dV = 0
cKi
(13)
where CBiand CKiare the inlet concentrations of HOOand K+ in the liquid. The inlet conditions for Clz and HOO- concentrations are CA = O
CB=
CBi
atz = O
(14)
The boundary conditions at the center of the liquid jet are by symmetry taken to be
ac,
-ar= o
atr=O, j = A , B
H
0.8
i
c 0.2
I
1
(15)
At the gas-liquid interface the nonvolatile HOO- is confined to the liquid phase while Clz in the gas phase is assumed to be in equilibrium with the liquid at the gasliquid interface. Thus the boundary conditions at the gas-liquid interface take the form
where ro is the radius of the liquid jet. The equilibrium relationship for Clz at the gas-liquid interface is given by Henry's law where He is Henry's constant for the solubility of C12in the liquid and is a function of temperature and
4
I 0.0 0.99970 0.99975 0.99980 0.99985 0,99990 0.99995 1 .OOOOO I
I
I
,
r.
Figure 1. Dimensionless concentration and temperature va dimensionless radius, r* = r/ro, in the reaction zone near the gas-liquid interface at the dimensionless axial distance z* = z/L= 0.1 for = 8.9 "C, u = 4.32 m/s.
concentration of the liquid-phase species and PA is the partial pressure of Cl, in the gas phase. To account for any temperature rise in the liquid phase near the gas-liquid interface, an energy balance for the liquid was incorporated into the model.
subject to the initial and boundary conditions
(11)
where V is the volume of the liquid jet. From the common assumption that the diffusivities of all the ionic species are the same, it can be shown that eqs 10 and 11 for the chloride and potassium ion concentrations simplify to cc = CBi - C B (12) CK =
1 " ' ~ l " " I ~ " ' I ~ " ' I " ' ~
...................................................................................
T=IP
atz=O
(18)
-dT Go dr
atr=O
(19)
aT = -AHODA aCA
at r = ro (20) dr ar where T is the liquid temperature, TL is the inlet liquid temperature, p is the liquid density, cp is the specific heat of the liquid, K is the liquid thermal conductivity, AHr is the heat of the overall reaction, and AH0 is the heat of absorption for Cl, in BHP. The model assumes negligible heat transfer to the surrounding gas phase. -K
Numerical Analysis of the Data The mass and energy balances, eqs 10-20, were solved numerically using the Crank-Nicholson finite-difference method in order to find a value of kl that best fit the experimental kinetics data. Initial solutions indicated that the reaction kinetics were in transition from the fast to instantaneous-reaction regimes. Representative concentration and temperature profiles are plotted in Figures 1 and 2. A nonuniform spacing of the finite-difference grid was employed to capture the effects of the large concentration gradients at the liquid jet entrance and in the reaction zone near the gas-liquid interface. The numerical procedure required iterations about the concentration and temperature profdes at each step in the axial direction due to the nonlinear reaction terms. The solution method consisted of guessing a value for the rate constant, kl, and integrating for CA, CB,and T over the liquid jet. The numerical solution for the chloride ion mixing-cup concentration, Cco,at the liquid jet outlet was compared with experimental results. The estimated value
Ind. Eng. Chem. Res., Vol. 31, No. 6, 1992 1463 Table 1. Coefficients for the BHP Viscosity Correlation of Bateman and Welch (1989) species i 'Y1i 'YZi i 4 K+ 1 22.6084 -0.00051296 Cl2 -22.63292 0.00023969 H202 3 0.0047006 -0.0875 1 -0.0002883 KCI 2 -0.0013616 c
\
Ai 0.2
4
..,...,.v * I.,..,,,....,..,.,.....,,, ...I..
j"';";..~rry..ppr+,.~~~,,,+
0.0
0.4
0.2
0.8
0.6
1 .o
I '
Figure 2. Dimensionless asid profiles at the gas-liquid interface - Tz-J; CA* for I" = 8.9 'C, u = 4.32 m/s. T* = (T- Tz=~)/(Tz-~ = CA/cA& cB*= CB/CBz=O.
for klwas upgraded by the secant method until satisfactory convergence on kl was achieved such that the numerical and experimental results for Cco agreed. The physical properties required in the model were obtained from the literature and are discussed in the next section.
Treatment of the Physical Properties In the original work of Ruiz-Ibanez and Sandall (1991) it was assumed that the absorbing liquid was isothermal and that, since the concentration of HOO- was taken to be small near the gas-liquid interface, the physical properties (diffusivity and solubility of C12)could be taken to be that for the corresponding aqueous H20zsolution. The work reported here attempts to account for the axial and radial variation in physical properties due to the change in concentration of the reacting species and temperature of the liquid phase. Setchenov's equation, which corrects for ionic effeda on solubility, was used to determine the effects of variable ion concentrations at the gas-liquid interface:
where Heo is Henry's constant for the solubility of Clz in the solvent, h is a solubility parameter, and I is the ionic strength of species j . There are two ionic systems that affect the solubility: (1)K+ and C1-; (2) K+ and HOO-. The solubility parameters are defined as (22) hili = [ h ~++hcr + hci21(C~'- CB)
hZIZ = [hK++ hHO0- + hClzlCB
(23)
The h values used in this work are those recommended by Ruiz-Ibanez et al. (1991). These values are hK+= 0.074, hcl- = 0.021, hHW- = 0.066 and (24) hclz= 0.7449 - 2.72 X 10-3T(K) Henry's constant for the solubility of C12 in aqueous hydrogen peroxide (Ruiz-Ibanez et al., 1991) is In He"
(-)
m3 atm kg-mol
= 16.94 -
4149 T(K)
(25)
A similar treatment of the solubility was done recently by Aharon et al. (1991) in a study of 02('$)generation by
the same reaction. However, they did not account for temperature effects in their modeling of the diffusionreaction process. For sparingly soluble gases in liquids, the heat of absorption can be obtained from a Clausius-Clapeyron type correlation for solubility with temperature over the temperature range of interest (Astarita et al., 1983). The heat of absorption as calculated from the Clz and O2solubility data of Ruiz-Ibanez et al. (1991) is A", = 4.40 X lo3 kcal/kg-mol. The heat of reaction was estimated by application of Hess' law to the standard heats of formation for the products and reactants involved in the overall reaction. Using the values supplied by Storch et al. (1983), this was found to be A", = -5.2 X lo4 kcal/kg-mol assuming that the 02(1$) is quenched by water in the liquid phase. The diffusion coefficient for C12 was taken from the measurements of Ruiz-Ibanez et al. (1991) in aqueous hydrogen peroxide. The diffusion coefficient for HOO- was taken from the measurements of Martin (1989) in aqueous potassium hydroxide.
D,"(
F)
+ 8.18 X 10-12T(K)
= -1.904 X
DBo(
$) = 7.83
X
lo* exp(
(26)
z)
(27)
The diffusion coefficients of all species were corrected for concentration effects through the liquid viscosity as recommended by Martin (1989): r]"Dj" Dj = (28) 7
where qo and q represent the viscositiea of the solvents with and without BHP respectively at the temperature of interest. The viscosity of the BHP solution was obtained from the following correlation of Bateman and Welch (1989). q(cP) = 1.716 exp
I
3 j=ll
a1ici
+ (~2jCi- 0.02641[T(K) -
I
273.151 C 2 SjCj (29) j=1
where the subscripts i and j correspond to the species listed in Table I. The concentration coefficients a and p are given in Table I. The units of C are g-mol of solute/kg of solution. The heat capacity used in this work, cp = 0.85 kcal/(kg K), was for 35% aqueous hydrogen peroxide at the average temperature of the liquid (Schumb and Satterfield, 1955). The thermal conductivity, K = 1.5 x lo4 kcal/(m s K), was taken as the value for water corrected for the ionic effects as outlined by Reid et al. (1977) at the average liquid temperature.
Results The model equations were solved for each experimental run of Ruiz-Ibanez and Sandal1 (1991) to determine the
1464 Ind. Eng. Chem. Res., Vol. 31,No. 6, 1992 Table 11. Experimental Parameters for the Laminar Liquid Jet Absorber and Numerical Results for the Frequency Factor, k,: (Jet Dimensions: r o= 2.55 X lo-' m, L = 1.23 X lo-* m (Run-Ibanez. 1990)) Go, 10-31k kg-mol/m3 m3/(kg-mol s) u , m/s Ti,K 0.0638 1.05 274.95 4.65 0.92 4.65 0.0629 274.95 0.0653 1.34 274.95 4.65 0.0761 1.09 279.85 4.32 0.0759 1.03 279.85 4.32 0.0770 1.46 279.85 4.32 0.0800 1.18 282.05 4.32 ~~
kl values shown in Figure 3. The improved approximation of the second order rate constant for eq 3 is
- - - Arrhenius correlation of k g v g ..... A
Ruiz-lbanez and Sandall (1991) Sandall et al. (1961) Held et ai. (1976)
I r
"'3.35
3.40
3.45
3.50 T
3.55
3.60
3.65
(1.2f 0.2)X
-'x103(K-')
Figure 3. Arrhenius plot comparing results for kl.
value of kl that best fit each set of data. It was found that several data sets were in the instantaneous-reaction regime and were therefore left out of the analysis since for these cases the rate of absorption was diffusion limited and the calculations were insensitive to the rate of reaction. Originally, the calculations were performed neglecting the variation of k1 with temperature within the laminar liquid jet. It was found that in some runs the temperature rise at the gas-liquid interface over the bulk liquid temperature was as much as 12.5 "C. The variations in temperature with respect to the radial and axial positions are demonstrated in Figures 1 and 2,respectively. There is a sharp rise in the liquid interfacial temperature near the liquid jet entrance corresponding to a rapid depletion of HOO- near the gas-liquid interface. To account for the effect of this variation in temperature on the kinetic rate constant, the calculation procedure was refined in the following manner. It was assumed that the temperature variation of the kinetic rate constant is described by the Arrhenius expression. The concentration and temperature profiles in Figure 1 show that the thermal boundary layer is much larger than the reaction boundary layer and that the temperature in the reaction zone is well approximated by the temperature at the gas-liquid interface. An approximation for the activation energy was obtained by an Arrhenius correlation of the average rate constants obtained as described above with the average interfacial temperature for each run. This plot is shown in Figure 3 where the rate constants determined for an average temperature are plotted as hollow circles. A least-squares fit of In kl vs 1/Tgives the activation energy as E, = 31400 f 6800 kcal/kg-mol. The model equations were solved again with kl expressed as
I y;J r
kl = k I 0 exp --
. 1
(30)
where k10 is the frequency factor and R, = 1.9872 kcal/ (kg-mol K) is the ideal gas constant. The model was applied to find a value of the frequency factor that best fit each experimental run, The results for k10 are listed in Table 11. The average value of the frequency factor from Table 11is close to the value found from fitting the average
1
. I
exp - 3140:>6800
(31)
The error limits on k10 and E, represent 95% confidence intervals. The correlation applies to a temperature range of 0-20 "C. The sensitivity of the activation energy and frequency factor with respect to the heat of reaction was investigated by repeating the above procedure with a 10% change in AH,. The heat of reaction has the effect of raising the temperature of the liquid which gives rise to larger diffusivities and lower solubilities of the volatile species in the liquid phase. In the case of high heat of reaction, AHr = -5.72 X lo4 kcal/kg-mol, the activation energy is 26000 kcal/kg-mol and the frequency factor is 5.9 X m3/ (kg-mol s). The activation energy for a low heat of reaction equal to -4.68 X lo4 kcal/kg-mol is E, = 40200 kcal/kgmol with the frequency factor of 9.7 X 103' m3/(kg-mol 8). These results for the activation energy fall roughly in the range of the estimated error on the activation energy in eq 31. Thus, a 10% difference in the heat of reaction corresponds to a -20% change in the estimation of the activation energy and ultimately in a 30% difference in the estimation for the rate constant. As the heat of reaction and the liquid-phase temperature rise, the effects of increased diffusivities outweigh the effects of lower solubilities of volatile species and the estimated rate constant is less sensitive to temperature.
-
Conclusions Our analysis shows that, due to the high rates of gas absorption with reaction, the temperature in the reaction zone of the liquid phase near the gas-liquid interface is predicted to be as much as 12.5 "C higher than the bulk liquid temperature. It was expected that the increase in the liquid-phase temperature would have the effect of lowering the C12solubility while increasing the diffusivities of all the solvated species according to eqs 25-27. It was found from the model, however, that the solubility of C12 at the gas-liquid interface remained relatively constant as shown in Figure 2. This was due to the combined effects of temperature and reaction on the composition in the reaction layer. As the reaction proceeds, there is a sharp rise in the temperature and the concentration of HOOanions at the gas-liquid interface are replaced by C1anions according to eq 12 which have a slightly smaller correction factor h in eq 22. Also, in eq 24,the contribution of C12 to the h parameters in eq 21 decreases with increasing temperature. Thus, there is a cancellation between the temperature and composition effects on Cl2
Ind. Eng. Chem. Res., Vol. 31, No. 6,1992 1465 solubility in the liquid. The net result is that the concentration of Clz a t the surface remains fairly constant. The resulta for klfrom this work are compared in Figure 3 with the approximate solutions for the rate constant from Ruiz-Ibanez and Sandall (1991) and with estimates from Sandall et al. (1981) and Held et al. (1978). We find a kl that is of the same order of magnitude as the approximation of Held et al. (1978) and an order of magnitude higher than that reported earlier by Ruiz-Ibanez and Sandall (1991), who did not account for changes in temperature and composition in their simplified analytical procedure. These results indicate that the reaction rate is necessarily larger than the previous estimate of RuizIbanez and SandaJl(1991) in order to compensate for the decreased solubility of Clzdue to a rise in temperature and the effect of the ions at the gas-liquid interface.
Nomenclature = heat capacity of the liquid, kcal/(kg K) = concentration of species j , kg-mol/m3 Dj = diffusion coefficient for species j , mz/s E, = activation energy, kcal/kg-mol h . = solubility parameter for species j , m3/kg-mol d e = Henry’s law constant, m3 atm/kg-mol AHa = heat of absorption, kcal/kg-mol AHr = heat of reaction, kcal/kg-mol I j = ionic strength for species j , kg-mol/m3 kl = second-order reaction rate constant, m3/(kg-mol s) klo = frequency factor for kl, m3/(kg-mols) L = jet length, m p A = partial pressure of chlorine in the gas phase, atm r = jet radial coordinate, m ro = jet radius, m R, = ideal gas constant, 1.9872 kcal/kg-mol R . = rate of depletion of reactant j , kg-mol/(m3s) T‘ = temperature, K u = jet velocity, m s V = jet volume, m z = jet axial coordinate, m
2
l
Greek Symbols 7 = liquid viscosity, CP K
= liquid thermal conductivity, kcal/(m s K)
p
= liquid density, kg/m3
Subscripts
A = chlorine B = perhydroxyl anion C = chloride anion
H = hydrogen cation K = potassium cation 0 = center of jet 1 = jet surface Superscripts
i = inlet condition o = exit condition * = dimensionless parameter O = solvent condition
Literature Cited Aharon, 0.; Elior, A.; Herskowitz, M.; Lebiush, E.; Roeenwake, S. 02(’A) Generation in a Bubble Column Reactor for Chemically Pumped iodine Lasers: Experiment and Modeling. J. Appl. P h p . 1991, 70,5211-5330. Astarita, G.; Savage, D. W.; Bisio, A. Gas Treating with Chemical Solvents; Wiley: New York, 1983. Balej, J.; Spalek, 0. Calculations of Equilibrium Composition in More Concentrated Systems H2OZ-KOH(or NaOH) -HzO. Collect. Czech. Chem. Commun. 1979,44,488-494. Bateman, B. R.; Welch, J. F. Viscosity of BHP. Measurement of Viscosity of BHP Solutions from 253 to 293 K and Correlation of Results. Paper presented at contractor’s meeting, Kirtland Air Force Base, March 1989. Held, A. M.; Halko, D. J.; Hurst, J. K. Mechanisms of Chlorine Oxidation of Hydrogen Peroxide. J. Am. Chem. SOC.1978,100, 5732.
Martin, L. R. Measurement of Aqeuous Diffusion Coefficientsfor the Singlet Oxygen Generator; HOO-, ClO,, Cl-. Paper presented at contractor’s meeting, Kirtland Air Force Base, March 1989. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hik New York, 1977. Ruiz-Ibanez, G. Kinetic Study for the Reaction Between Chlorine and Basic Hydrogen Peroxide; Ph.D. Dissertation, University of California, Santa Barbara, 1990. Ruiz-Ibanez, G.; Sandall, 0. C. The Kinetica of the Reaction between Chlorine and Basic Hydrogen Peroxide. Znd. Eng. Chem. Res. 1991,30, 1105-1110.
Ruiz-Ibanez, G.; Bidarian, A.; Davis, R. A.; Sandall, 0. C. Solubility and Diffusivity of Oxygen and Chlorine in Aqueous Hydrogen Peroxide Solutions. J. Chem. Eng. Data 1991, 36, 459-466. Sandall, 0. C.; Goldberg, I. B.; Hurlock, S. C.;Laeger, H. 0.;Wagner, R. I. Solubility and rate of hydrolysis of chlorine in aqueow sodium hydroxide at 273 K. MChE J. 1981,27,856-859. Schumb, W. C.; Satterfield, C. N.; Wentworth, R. L. Hydrogen Peroxide; R e i i o l d London, 1955. Storch, D. M.; Dymek, C. J.; Davis, L. P. MNDO Study of the Formation by Reaction of Clz with Basic Mechanism of 02(’4) HzOz. J. Am. Chem. SOC.1983,105, 1765-1769. Received for review October 1, 1991 Accepted March 16,1992
