KINETICS OF CHEMICAL REACTIONS
,313
(3) D H ~ RC.,~ AND , RAFFY,A , : Compt. rend. soc. biol. 119, 232 (1935). (4) DUTTON, H.J . , AND MANNING, W . M . : Am. J. Botany 26,516 (1941). (5) EMERSON, R . , AND LEWIS,C. M.: J. Gen. Physiol. 26, 579 (1942). R., AND LEWIS,C. M . : In press. (6) EMERSON, J., FRENCH, C. S., AND PUCK,T.T.:J. Phys. Chem. 46,1268 (1941). (7) FRANCK, (8)OPPENHEIMER, J. R . : Phys. Rev. 60, 158 (1941). W. M . : J. Biol. Chem. 144,625 (1942). (9) STRAIN,H . H., AND MANNING, D., WASSINK, E . C., AND REMAN,G. H.:Enzymologia 4, 254 (1937) (10) VERMEULEN, (11) WILSCHKE, A . : 2. wiss. Mikroskop. 31, 338 (1914).
A METHOD O F STUDY OF THE KINETICS OF CHEMICAL REACTIONS FRANCOIS OLMER' Laboratory oj Chemistry, &ole Nationale Supdrieure des Mines de P a r i s , France Received J u l y $4, 1848
The author has developed a new method for the study of chemical reactions. This method consists in raising the temperature of a chemical system linearly (that is, proportionally to the time) and observing the variations of some physical property of the system, for instance, the mass of one of the reagents. This method was first described by Guichard (1) and was applied to the study of the dehydration of certain hydrates by Vallet ( 5 ) , but has not yet, to the author's knowledge, been employed for the study of the kinetics of a pure chemical reaction. HOMOGENEOUS REACTIONS OF THE FIRST ORDER
In the case of a reaction in which two reagents, M and N, are both either liquid or gaseous and in which one of them, M, is in excess, the speed of the reaction a t a given temperature depends only on the mass x of the reagent N: dx = -kx dt
IC being the van't Hoff constant determined by the temperature 8: K = Aa"' where A, a, and CY are constants. If the temperature of the system increases uniformly with the time t,
e
= gt
the speed of the reaction may be written
1
Present address: Diamond Alkali Co., Painesville, Ohio.
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FRANCOIS OLMER
Consequently, expression 1 becomes
By integration, the expression of the theoretical curve of the variation of the mass of N with the temperature is
Lx = Lxo being the initial mass of the reagent lated from expressions 2 and 3: 20
A dB gLa
(3)
IT. The slope of the curve may be calcu-
The curve representing the variation of expression 3 is shown in figure 1. The curve has the horizontals x = xo and x = 0 as asymptotes. HETEROGENEOUS REACTIONS
The speed of heterogeneous reactions is more difficult to determine mathematically in the general case2. For instance, in the action of hydrogen on an oxide a distinction must be made between the speed of the penetration of the hydrogen inside a granule of the oxide, the speed of the reaction properly speaking which then takes place, and the speed at which the water vapor is eliminated after the reaction. In certain cases, adsorption of gaseous reagents on the surface of the solid may complicate the determination of the speed of the actual reaction still further. Of all these phenomena, only the speed of the slowest one, influenced more or less by accessory phenomena, will be observed. However, the experimental curves obtained by the method discussed do have great practical interest, since they show the kinetics of the global phenomena. Several such experimental curves are considered here. The temperature, a function of the time, is used as abscissa, while the ordinate represents the mass of reagent.
A . Simple heterogeneous reactions Figure 2 shows the cum8 corresponding to the reduction of zinc oxide by hydrogen present in excess. The experiment starts a t room temperature; the reduction itself begins a t 315°C. (4),as may easily be seen on the curve (point A ) . The portion BC of the curve is very nearly linear. The end of the reaction is indicated a t C by a sharp break in the curve. This curve, typical of many curves obtained by the author, is strikingly similar to the theoretical curve represented in figure 1. It appears that the kinetics of the type of heterogeneous reaction studied are very much the same as those of
* This theory has been examined in an earlier study (2).
3 15
KINETICS OF CHEMICAL REACTIONS
homogeneous reactions. In other words, the curves of heterogeneous reactions which are shown here represent very closely the kinetics of the chemical reaction; most of the theoretical conclusions drawn from the theory of homogeneous SYStems do apply to them.
B . Complex heterogeneous reactions One or several intermediate compounds may appear in a reaction; the first reaction, A + B, is inscribed on a curve similar to the curve of figure 2. When
FIG. 1 FIG.2 FIG. 1. Curve represeuting the variation of expression 3 FIG.2. The curve corresponding t o the reduction of zinc oxide by hydrogen present in excess
I
Kx)
l
l
400
I
I
600
I
I
800
I
I
loo0
FIG.3. The notion of hydrogen in excess on an intimate mixture of ferric oxide and silica
the reaction is completed, no further chemical change taking place, the mass of the compound remains the same and the curve shows a plateau. As the temperature increases and the reaction B + C occurs, the curve, in turn, takes the familiar pattern, and eo on for successive reactions. Figure 3 illustrates a complex heterogeneous reaction, the action of hydrogen in excess on an intimate mixture of ferric oxide and silica. Three intermediate compounds are formed. Since the mass of the initial compound is known, the composition of the intermediate compounds may easily be determined from the ordinate of the horizontal stretches of the curves.
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FRANCOW OLMER
The horizontal stretch may not, however, appear on the curve if the reaction A -+ B has not been completed when the reaction B -+ C begins. The curve then shows only a break (point P , figure 4) corresponding to the end of the reaction A + B ; this point P corresponds to point C on curve 2. The point P always has a smaller ordinate than that which corresponds to the formation of the intermediary compound, since the reaction R C is already in progress when the reaction .4 -+ B ceases. The abscissa of point P is not fixed and depends on the rate of increase of the temperature. The slope of the curves, given by expression 4, shows that dx/dO i s in\-ersely proportional to the rate of increase 8. The lower the rate of increase of the temperature of the experiment, the IoTrer the temperature at which a reaction is completed, Thus, the end of reaction A + B and the beginning of reaction B -+ C nil1 be distinct, and the usual plateau is obtained instead of point P. .--)
300
e,
700
FIG.4. The action of hydrogen i n excess on an intimate mixture
of ferric oxide and
calcium oxide.
C. Heterogeneous reactions ?oathchangzng kinetics If the mechanism of the reaction changes at a certain temperature, the curve shows a definite break there. For instance, the reaction may be X -+ R below a temperature 0 and h ---f C above this temperature. The abscissa of this break, contrary to that of point P in the preceding case, is alnays the same, whatever the rate of increase in the temperature of the experiment. Its ordinate, on the contrary, is not fixed. An interesting example of such a change in the mechanism of a reaction will be given in a subsequent note. .in allotropic transition of one of the reagents may occur during the reaction. If this transition influences the speed of the reaction, it will also be shown on the curve by a break, the abscissa of which indicates the temperature of this transition. CONCLUSIO~S
The study of chemical reactions by a new method of linearly increasing temperature gives the following information: (a) the temperature of the start of each reaction; ( b ) the number and the composition of any intermediate compounds;
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REDUCTION OF FERRIC OXIDE BY HYDROGEN
(c) the temperature a t which each secondary reaction begins; (d) the relative speeds of partial reactions; (e) the temperature of a modification in the kinetics of the reactions; and (f) the temperature of a modification in the kinetics of the reactions. From the inspection of curves obtained by the method, it is possible to study the various chemical reactions which occur in an industrial process. The reduction of ore in a blast furnace, the carburization of steel, the chemical reactions between the constituents of glass during the fusion, and the decomposition of an organic compound are all possible practical applications. One such example (the catalytic decomposition of carbon monoxide by ferromagnetic metals (3)) has been studied in detail by the author. A subsequent paper will set forth a practical and interesting realization of the method. REFERENCES (1) GUICHARD, M.: Bull. soc. chim. 39, 1113 (1926).
F. J.: Thesis, “Reduction des oxydes de fer”, Rey, Lyon, France, 1941. (2) OLMER, (3) OLMER, F. J.: J. Phys. Chern. 46,405, 1942. (4) ST.JOHN,J. L.: J. Phys. Chem. 38, 1438 (1929). (5) VALLET,P.: Thesis, “Recherches sur la methode d’Btude des systemes chimiques en temperature variable”, Jouve, Paris, 1936.
REDUCTION OF FERRIC OXIDE BY HYDROGEN FRANCOIS OLMERI Laboratory of Chemistry, &ole Nationale Supbrieure des Mines de Paris, France
Received July 84, 194.8
Although numerous authors have studied the reduction of the oxides of iron in hydrogen, the kinetics of these reactions have not yet been clearly explained. Most of the hypotheses presented in the case of ferric oxide may be classified as follows: (1) Fes03-+ Fe (8, 12) (2) Fen08 3 FesOa 3 Fe (2,19) (3) Fez03-+ FeO + F e (5) (4) FezOs-+ FesOc 3 FeO -+Fe (13,17) (5) Fez03 -+ simultaneous mixture of all oxides 3 Fe (6) (Fez03 FesOc -+ Fe a t low temperature (16) \F@Os -+ Fe at high temperature
(4,11)
---f
A new method of studying the mechanism of chemical reactions by means of linearly increasing temperatures (14) has been applied to the question by the author of this paper. 1
Present address: Diamond Alkali Co., Painesville, Ohib.
