Abstract
The kinetics and equilibrium of the solid state reaction between barium carbonate and cupric oxide have been examined thermogravimetrically. The reaction rate is found to be dominated by effects of nucleation and diffusion of carbon dioxide produced. A mathematical model incorporating these effects, along with considerations of heat transfer, is found to satisfactorily correlate the conversion-time data. The reaction is found to follow the stoichiometry BaCO3 + CuO ⇌ BaCuO2 + CO2 although at temperatures above 1123 K, some evidence of BaO is also seen through X-ray diffraction. In the pelletized samples, incomplete conversion is noticed indicative of pore closure effects leading to transport limitations. The latter is also independently confirmed by porosity and surface area measurements. Data on the reaction equilibrium are also obtained and, in conjunction with Van’t Hoff’s relation, are used to obtain a correlation for the endothermic heat of reaction as a function of temperature.
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Abbreviations
- C :
-
concentration of CO2 in product layer
- C 0 :
-
external bulk concentration of CO2
- C*(T) :
-
equilibrium concentration at temperatureT
- C*0 :
-
C*(T0), equilibrium concentration at bulk temperature
- D(T) :
-
effective diffusivity at temperatureT
- Dc :
-
D(Tc), effective diffusivity at core temperature
- D s :
-
D(Ts), effective diffusivity at surface temperature
- D 0 :
-
D(T0), effective diffusivity at bulk temperature
- H :
-
Ds/kgR0
- h :
-
heat-transfer coefficient
- ΔH(T) :
-
heat of reaction at temperatureT
- ΔHc :
-
ΔH(Tc), heat of reaction at core temperature
- k :
-
nucleation rate constant
- k g :
-
mass-transfer coefficient
- k s :
-
thermal conductivity of solid
- K e :
-
equilibrium constant
- n :
-
constant, Eq. [7]
- P CO 2 :
-
partial pressure of carbon dioxide
- r :
-
radial position in pellet
- r c :
-
core radius
- r s :
-
pellet radius at any time
- R 0]:
-
initial pellet radius
- R g :
-
ideal gas constant
- S :
-
external surface area of pellet
- t :
-
time
- T :
-
temperature
- T 0 :
-
bulk temperature
- T c :
-
core temperature
- T s :
-
surface temperature
- V :
-
pellet volume
- X :
-
conversion
- z :
-
ratio of volume of product pellet to that of reactant pellet
- α :
-
Eq. [17]
- βc :
-
Eq. [18]
- ξ :
-
r/R0
- ξc :
-
rc/R0
- ξs :
-
rs/R0
- λ:
-
k s /hR0
- ψ:
-
C/C*0
- ψ:
-
C*(Tc)/C*0
- ψ0 :
-
C 0/C*0
- ρ :
-
molar density
- θ :
-
T/T 0
- gqc :
-
Tc/T0
- θs :
-
Ts/T0
References
M.K. Wu, A.R. Ashburn, C.J. Torny, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang, Y.Q. Wang, and C.W. Chu:Phys. Rev. Lett., 1987, vol. 58, pp. 908–10.
E. Ruckenstein, S. Narain, and N. Wu:J. Mater. Res., 1989, vol. 4, pp. 267–72.
H. Midgeon:Rev. Chem. Mineral., 1976, vol. 13, p. 440.
E. Lambert: JCPDS Report No. 33-511 of Mineral Petrogr., University of Heidelberg, Heidelberg, 1981.
C. Michel and B. Raveau:J. Solid State Chem., 1982, vol. 43, pp. 73–80.
I. Halasz, I. Kireschner, T. Porjesz, Gy. Kovacs, T. Karman, Gy. Zsolt, Cs. Sukosd, N.S. Rozlosnik, and J. Kurti:Physica C., 1988, vol. 153, pp. 379–80.
S.G. Acharya: Master’s Dissertation, Indian Institute of Technology, Bombay, 1991, p. 40.
J. Szekely, J.W. Evans, and H.Y. Sohn:Gas Solid Reactions, Academic Press, New York, NY, 1976.
H.Y. Sohn:Metall. Trans. B, 1978, vol. 9B, pp. 89–96.
D.A. Young:Decomposition of Solids, Pergamon Press, Oxford, 1966.
B.V. Erofeef:Compt. Rend. Acad. Sci. U.R.S.S., 1946, vol. 52, p. 511.
M. Avrami:J. Chem. Phys., 1940, vol. 8, pp. 212–24.
G. Narsimhan:Chem. Eng. Sci., 1961, vol. 16, pp. 7–20.
A.W.D. Hills:Chem. Eng. Sci., 1968, vol. 23, pp. 297–320.
J. Mu and D.D. Perlmutter:Chem. Eng. Sci., 1980, vol. 35, pp. 1645–56.
K.B. Bischoff:Chem. Eng. Sci., 1963, vol. 18, pp. 711–13.
D. Luss:Can. J. Chem. Eng., 1968, vol. 46, pp. 154–56.
G.S.G. Beveridge and P.J. Goldie:Chem. Eng. Sci., 1968, vol. 23, pp. 913–29.
S.K. Bhatia:Chem. Eng. Sci., 1985, vol. 40, pp. 869–72.
R. Aris:The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vol. 1: The Theory of the Steady State, Oxford, London, 1975, pp. 123–24.
M. Hartman and R.W. Coughlin:AIChE J., 1976, vol. 22, pp. 490–98.
J.A. Pask and L.K. Templeton:Kinetics of High Temperature Processes, MIT Press, Cambridge, MA, 1959, pp. 255–64.
S.K. Bhatia and D.D. Perlmutter:AIChE. J., 1983, vol. 29, pp. 79–86.
D.R. Clarke, T.M. Shaw, and D. Dimos:J. Am. Ceram. Soc., 1989, vol. 72, pp. 1103–13.
Y.J. Hao and T. Tanaka:Int. Chem. Eng., 1990, vol. 30, pp. 244–52.
A. Rehmat and S.C. Saxena:Ind. Eng. Chem. Proc. Des. Dev., 1976, vol. 15, pp. 343–50.
J.M. Smith:AIChE. J., 1968, vol. 14, p. 650.
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Acharya, S.G., Bhatia, S.K. & Shankar, H.S. Kinetics of solid state reaction between barium carbonate and cupric oxide. Metall Trans B 23, 493–503 (1992). https://doi.org/10.1007/BF02649668
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DOI: https://doi.org/10.1007/BF02649668