Icinetics of Ammonia Synthesis P. H . Emmett and J . T.ICummer THE JOHNS HOPKINS UNLVERSITY, BALTIMORE, MD., AND U. S. DEPARTMENT OF AGRICULTURE, WASHINGTON, D. C.
A recent paper by Temkin and Pyshev (9) suggested fundamental equations f o r the rate of adsorption and desorption of nitrogen on iron catalysts and f o r the equilibrium pressure of nitrogen over such catalysts; they lead t o a theory for the catalytic synthesis and decomposition of ammonia which is the most satisfactory proposed t o date. Predictions of their kinetics are tested by applying them to some hitherto unpublished data on the rate of synthesis as a function of gas composition, pressure, space velocity, and temperature. The agreement between theory and experimental results is suficiently good to warrant confidence in their fundamental assumptions and general conclusions. Their kinetic treatment, together with the recent calculations by Brunauer, Love, and Keenan (2), greatly enhances our knowledge of the synthesis mechanism over doubly promoted catalysts. O n the other hand, the theory does not account for the peculiar behavior toward ammonia decomposition of iron catalysts promoted with a single promoter, alumina.
F
E W catalytic reactions have received such intensive
study as the synthesis of ammonia. For the past thirty years at least one large research laboratory has always been endeavoring to throw light on the mechanism of the reaction and to interpret the dependence of the rate upon space velocity, temperature of the catalyst, and partial pressures of the reacting gases and the product. During this time a long series of publications (summarized by Frankenburg, Emmett, etc., 4) made the catalytic synthesis more understandable, but failed to correlate the kinetics of the formation and decomposition of ammonia with the suspected mechanism for its synthesis. I n 1940 Temkin and Pyzhev (9) offered a satisfactory kinetic approach to the synthesis and decomposition of ammonia over doubly promoted iron catalysts. The purpose of this paper is to outline the theories of these authors and to show that their work has pointed the way to a better picture of high-pressure ammonia synthesis. Winter (10) found the decomposition of ammonia proportional to the ratio (PNH~)/(PH~)"~ and concluded that the slow step in the decomposition was the escape of nitrogen atoms from the catalyst surface, Temkin and Pyzhev point out that this mechanism is impossible, since the escape of a nitrogen atom from the surface would entail an energy of June, 1943
activation of at least 90,000 calories per mole of ammonia decomposed. They suggested that nitrogen escapes from the surface as molecules and not as atoms, but that the rate depends strongly on the fraction of the surface covered by adsorbed nitrogen. They proposed the use of several equations (6, 6, 11) for the adsorption equilibrium between gaseous nitrogen and iron, and for the rate of adsorption and desorption of nitrogen, as follows:
where
e = fraction of surface covered by adsorbed nitrogen p = equilibrium nitrogen pressure
B = rate of nitrogen adsorption, molecules/sec. P = instantaneous nitrogen pressure w = rate of nitrogen desorption, molecules/sec. k,, f, ao,k d , g = constants
Using these three equations, Temkin and Pyzhev proposed an explanation for the kinetics of ammonia decomposition and synthesis that agrees with the kinetic results obtained by Winter; at the same time, it gives an approximately correct value for the energy of activation for the decomposition as well as for the synthesis. EQUATIONS OF TEMKIN AND PYZHEV
I n applying these equations the authors assumed that the adsorption of nitrogen on iron in the presence of an ammoniahydrogen mixture is the same as it would be when ai? equilibrium with the partial pressure of nitrogen equivalent to the existing partial pressure of ammonia and hydrogen in the gas mixture. Thus, since the equilibrium constant for ammonia synthesis is
K
=
(PNHZ)'/(PHZ)~(PN,)
the partial pressure of nitrogen can be represented as being equal to ( P N H a ) 2 / K ( P H z ) 3 . Accordingly, in Equation 1 Temkin and Pyzhev replaced the pressure p by the equivalent pressure of ammonia and hydrogen to obtain: (4)
and pointed out that if the slow step in the decomposition of ammonia is the escape of nitrogen molecules from the surface of the catalyst, the rate expressed as number of molecules of nitrogen formed per second per unit volume of catalyst is given by the equation:
This equation is identical to the one obtained by Winter, provided we assume that h/f is With this assumption the
INDUSTRIAL AND ENGINEERING CHEMISTRY
671
where NXH,= number of NH, molecules present at contact time t At one atmosphere total pressure the equilibrium per cent ammonia is so small (0.23 per cent at 450" C. from a 3 to 1 ratio of hydrogen to nitrogen, for example) that the volume change during synthesis can be neglected and the ("a,) term can be taken as proportional to the partial pressure of ammonia. Hence,
(10)
Khere k'
= a
proportionality constant
If we neglect the back reaction because the partial pressure of ammonia is small, and let u equal the fraction of nitrogen in the nitrogen-hydrogen mixture,
By integration, Anhydrous A m m o n i a Is Stored i n These 2500-Barrel Hortonspheres, under a Pressure of 50 P o u n d s p e r Square I n c h , a t a Pacific Coast Chemical P l a n t
apparent temperature coefficient of ammonia decomposition was shown by Temkin and Pyzhev to be: Adrc. = A
+
1/2g0
16,000
where A:
=
go = Q =
2tc
ku(1 - u)l.K
(12)
Clearly, at a given flow rate and hence a given value for t,, PNH* in the exit gas will be a maximum when u = 0.4. This was pointed out by Temkin and Pyehev, and agrees with the data quoted by them (9) as follows:
+Q
+ '9+ 13,000 = 46,500cal.
=
yo NHs in Exit,Gas a t 30,000 Space Velooity 400' C .
(6)
1.0 1.5 3.1 6.1
energy of activation of nitrogen adsorption per mole on the iron heat of adsorption per mole nitrogen heat of formation per mole ammonia
This value for the apparent energy of activation for ammonia decomposition is in good agreement with those ranging from 40,000 to 50,000 calories (approximately) reported by various workers (4,8,9,10). Temkin and Pyzhev applied their kinetic treatment to synthesis, both at one atmosphere and at high pressure. According to Equations 2 and 4,the rate of nitrogen adsorption per unit volume of catalyst is given by:
0.073 0.094 0,099 0,092
0.5
0.082 0.069
8.5
The rate of synthesis, according to these results, goes through a maximum a t about u = 0.4. Equation 10 can be checked in another way by synthesis data a t one atmosphere. By letting x = P N H 8 / P N E ~ ( e q u i l i b . ) and assuming a constant ratio of hydrogen to nitrogen, Equation 10 can be rearranged and integrated to:
(7)
where
Par y = (4/3) Ptotal
Therefore,
time of contact = k =
Hence :
This conforms to the equation developed by Benton ( I ) , in SO far as it shows an inverse proportionality between the rate of synthesis and the partial pressure of ammonia. The fundamental synthesis equation now becomes:
where k
=
5
(y)1.6 p1/2V
1 In __ 1 - 22
(273) ($) knk'
(:)'*' T
V = space velocity I n support of this equation, Temkin and Pyzhev cite the data given in Table I.
678
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. 6
TABLEI. KINETICSOF AMMONIA SYNTHESIS AT ONE ATMOSPHERE PRESSURE OVER AN IRON CATALYST (9) Temp., Space p L 2 C. Velocity P N * "a, % 400 2.93 0.155 400 0.133 3.0 0.107 400 3.0 0.111 400 1.48 0.093 400 6.0 0.134 3.0 450 450 0.157 3.0 0.199 450 3.0 5 This value is too close to equilibrium to
X
L
0.373 1.0 x 103 0.320 1.1 x 103 1.01 x 108 0.258 0.294 0.96 X 108 1 . 2 x 103 0.259 7.73 x 103 0.629 7.84 x 103 0.738 (9.3 x 108)Q 0.934 yield a good constant.
The equation as actually derived by Temkin and Pyzhev (9) is:
But by definition,
+
Equation 22 differs from 21 only by having a (1 Z) term instead of a (1 Z)a term in the denominator of the righthand side. Equations 21 and 22 can be evaluated with the help of Simpson's rule or other suitable approximations. Temkin and Pyzhev illustrate the applicability of their high pressure equation by calculating with it the reaction rate constants from the high pressure experiments of Larson and Tour ( 7 ) . The extent to which Equation 22 agrees with the measurements is illustrated by Table 11. It seems to account fairly well for the effect of changes in space velocity and approximately for the influence of pressure; however, the data are inadequate for illustrating the influence of pressure on the rate, in view of the fact that the 100-atmosphere runs may have been made in a different apparatus from that employed for the 31.6-atmosphere runs and on a different sample of a given catalyst preparation.
+
Therefore: In
(15)
Inserting the above values for kaoo C . and k4so0 C . in Equation 15, Adec., the apparent energy activation of ammonia decomposition, becomes 40,000 calories per mole of nitrogen evolved, in agreement with many previous temperature coefficient data for ammonia decomposition. Since by definition Adeo.- A,,,. = heat evolved per mole of nitrogen reacting, A,,,. = 40,000
- 26,000 = 14,000 calories
This value is in good agreement with the activation energy of nitrogen adsorption on iron (3). For high pressure synthesis, Temkin and Pyzhev derive equations to show the application of their theory. starting with-the following1:
where W = volume of catalyst used Letting 2 equal the mole fraction of ammonia present
( P N H ~ / P ~and ~ ~assuming *I) perfect gases, Equation 16 becomes:
APPLICATION TO KINETIC DATA ON AMMONIA DECOMPOSITION
Brunauer, Love, and Keenan ( 2 ) derived the general equations for the rate of adsorption and desorption of nitrogen on iron, and for the variation of the amount of adsorption with pressure; they showed that Equations 1, 2, and 3 are approximations holding true over intermediate partial pressures of nitrogen. They succeeded in calculating for the first time an adsorption isotherm from data on the rate of adsorption. The general rate equation for nitrogen adsorption used by them was: du = k,PN,v,e dt
where 1
Zequilib. - ZBq"iiib. = L
(18)
N o may be taken as the number of molecules of 3 to 1 gas in the catalyst voids a t the temperature and pressure of synthesis. Furthermore for a flow system,
where Vo
entering space velocity UZ exit gas flow (S. T. P.) +. = fraction of voids in catalyst = =
Substituting the value of dt in Equation 17 and replacing N o by A+WP/RT, where A is Avogadro's number, 1
by d ( P N H s ) / d t . The only final effect of their approximation is the replacement of the (1 2 ) a term in the denominator of the right-hand side of Equation 21 by (1 2 ) . Since 2 is usually less than 0.05, this causes only s slight error.
+
June, 1943
+
(23)
The constants k,V,, kdV,, J/V,, and B / V mwere evaluated from data of Emmett and Brunauer (3) by an approximation method and found to have values of 0.02, 0.000957, 2100 calories, and 800 calories, respectively. From Equation 23 it was shown that the equilibrium pressure of nitrogen for the adsorption isotherm would be given by I n P = In-k d IC,
+J + B__ V,RTv
(24)
Inserting the constants as evaluated by Equation 23 into Eauation 24 gave a series of calculated adsomtion eauilibrium d u e s for niGogen on doubly promoted cataGst 931 i t 396' C. that agree closely with the observed values:
Strictly speaking, Equation 16 is not the one used by Temkin and 1 They introduced an approximation by replacing I d ( N N H ~ ) / ~ ~
Pyahev.
BO - -V mJuR T - kdvme VmRT
P, Mm. 25 53 150 397 768
-v,
Obsvd. (3) 2.83 3.22 3.69 4.14 4.55
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Cc. at S. T. P.Calcd. (3) 2.88
3.22 3.70 4.15 4.45
679
t
5 Y 2 2 I
C 3
3.
€xi Figure 1. R a t e of A m m o n i a Synthesis on 3 Hydrogen1 Nitrogen Gas Top. 100 atmospheree; 0 r u n 1, X run 30, + r u n 32, 0 run 2, @ r u n 3, Y run 33. Center. 66.6 atmospheres; 0 run 4, + r u n 34, 0 run 5, X run 35, r u n 6, Y run 36. B o t t o m . 33.3 atmospheres; 0 r u n 7, + run 31, run 8, X run 38, run 9, Y run 39.
680
J- S p a c e
Ve tocity x IO-+
Figure 2 . R a t e of A m m o n i a Synthesis on I Hydrogen-1 Nitrogen Gus T o p . 100 atmospheres; 0 r u n 12, + r u n 10, 0run I S ,
X run 11, run 14. Center. 50 atmospheres; 0 run 15, 0 r u n 15, r u n 17. B o t t o m . 33.3 atmospheres; 0 run 18, C run 19. r u n 20.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. 6
TABLE11. SYNTHESIS OF AMMONIA ACCORDING TO LARSON AND TOUR (7) Temp., O
c.
420
460
Pressure,
Space Velocity 0 6,000 10,000 20,000 40,000
2.98 2.65 2.19 1.71 1.35
31.6 31.6 31.6 31.6 31.6
0 5,000 10,000 20,000 40,000
8.48 6.65 5.46 4.24 2.88
10 10 10 10
0 10,000 20,000 40,000
2.11 1.95 1.71 1.60
3 . 2 x.104 4.1 x 104
31.6 31.6 31.6 31.8 31.6
0 5,000 10.000 20,000 40,OUU
6.13 5.85 5.41 4.66 3.71
3 . 5 'X' 101 4.0 x 104 4.1 x 104
Atm. 10 10 10 10 10
100 100 100
100 100
0
6,000 10,000 20,000 40,000
k (fFom Equation 22)
"a,
%
'face concentration of adsorbed nitrogen atoms, ( N , )(Ns),then since adsorption data (3) show the concentration of adsorbed nitrogen proportional to (PNJ"'it follows that
1.i.x io' x 104
1.1 1.1 1.1
x x
104
104
which is in good agreement with the observed kinetic data c Love and Emmett (8).
1 .o 'x.104
1.1 x 104 1.2 x 104 1.0 x 104
.... ....
16.43 14.10 11.60 9.50 7.00
1.9 .X.lO& x 10' x 104 x 104
1.9
2.3 2.3
The constants evaluated from Equation 23 also permitted calculation of the kinetics of ammonia decomposition over the catalyst. It was shown that of Equation 5 is given by J ) from Equation 23 and is therefore equal to B/(B 800/(800 2100) = 0.276; a! of Equation 8 is then 0.724. Accordingly, the rate of ammonia decomposition over catalyst 931 at about 400' C. would be given by
++
APPLICATION TO HIGH PRESSURE SYNTHESIS DATA
A few years ago a t the Fixed Nitrogen Research Laboratory, Emmett made a number of measurements of the dependence of the rate of ammonia synthesis on space velocity, temperature, pressure, and gas composition. Since this work cannot at present be continued and extended, the results will be summarized and compared with the equations of Temkin and Pyzhev. The rate measurements were made in a special bomb; the copper chamber for the catalyst was about 1 cm. in diameter and held 1 cc. of catalyst. The copper thermocouple well extended down into the center of the catalyst, leaving a 2-mm. space between the thermocouple well and the copper catalyst tube. Frequent cross checks were made to make certain that the catalyst activity was not changing. Points were always taken from lower to higher space velocities and back again. A broken high pressure connection caused a slight oxidation of the catalyst between runs 11 and 12. A decrease in the activity resulted for a short time but nearly disappeared with continued reduction of the catalyst. Data taken before and after this accident are carefully differentiated in the figures The catalyst (660) contained 0.94 per cent potassium oxide and 3.02 per cent alumina as promoters. The experimental data are plotted in Figures I, 2, and 3 for all temperatures, pressures, space. velocities, and gas compositions covered. Table I11 summarizes the values of k calculated by Equation
in good agreement with the results of Love and Emmett ( 8 ) for this same catalyst for which the exponents expressing the dependence of the rates on the partial pressures of ammonia 22. and hydrogen were 0.6 and -0.85, respectively. The kinetics upon which Equations 21 and 22 are based The theory of Temkin does not seem to apply to catalysts are those found by Winter (10)and then used by Temkin and sin& momoted with alumina. The decomposition kinetics Pyzhev (9). ons;ch a catalyst are abnormal, both as regards dependence on the partial pressures of ammonia and hydrogen 21, 28, .4ND 29" TABLE 111. VALUES FOR k FRDbf EQUATIONS and as regards the variation with -k a t 370' C.-k a t 450' C.-k a t 400' C 8 ace temperature (8). There is a consid100 66.6 33.3 VePocity 100 66.6 33.3 100 66.6 33.3 atm. atm. atm. (Exit Gas) atm. atm. atm. atm. atm. atm. erable temperature range (400' t o 450' C.) over which the rate of am3 Hydrogen-1 Nitrogen Gas (30.100) 2390 3400 5240 298 SO6 915 25,000 monia decomposition is inversely pro. . . b (38.100) [55.000) (39;500) (54.000) portional t o (PNH,)".~ and directly 218 465 828 2290 3350 4950 50,000 (31s200) { 34 GOO 49 600 proportional to ( P H ~ ) I~n. this ~ . same (31,000) (38:800) (51,'900) 192 402 790 2080 3250 4760 75,000 25200 34500 44 100 region the temperature coefficient of (29:300) (37:OOO) (50:900) 4540 164 359 764 1860 2960 100,000 23300 33.600 43,200 ammonia decomposition is approxi(30:300) (36,500) (49,000) 1680 2660 4110 130 326 749 125,000 23,200 32,400 41,100 mately zero. Accordingly, for singly promoted iron catalysts the detailed 1 Hydrogen-1 Nitrogen Gas 24,200 29,600 37,000 2590 30OOc 3520 436 415C 449 mechanism must still be considered 35,000 26,200 33,200 35,800 (3090) 3050 532 391 465 3860 75,000 unknown and not explained by the equations of Temkin and Pyzhev. 3550 351 487 53 100,000 27,600 31,600 34,600 2690 Direct high pressure kinetic data on 25,500 29,200 34,003 (2400) 2380 302 391 470 3300 125,000 a singly promoted catalyst are not a t 1 Hvdroaen-3 Nitrogen Gas present available but would be of 3710 436 460 692 2030 2380 16 450 20,410 -22,900 35,000 great importance. 3780 423 501 770 2170 2485 24,400 21,000 17:700 75,000 701 3820 403 494 2180 2390 25,200 17,800 20,200 100,000 An approximate method of applying 3560 621 369 450 2090 2295 17,800 19,600 25,600 125,000 the Temkin equation may help to make Actually the k values in Tables 111 and I V were oalculated by an equation using (1 + P) instead of its fundamental concept clear. If the ( 1 + z)a d d e ? the inte rrtl sign in Equations 21, 27. 28, and 29, respectively. Also, they ,were Sinae neither of these factors oauses enough inonrrentlv __ miiltmlied hv 8,273. - change in the relative k rate of escape of nitrogen molecules is values to alter,any of thk &&sions, corrections have not been made b Numbers in parentheses refer to activities before the accidental poisoning preceding run 12 The assumed to be the slow step in the de400° and 370° C. runs on 3:l gas were the same after run 12 as before. composition of ammonia and to be The intermediate pressure runs with 1:l gas were at 50 instead of 66.6 atmospheres pressure. proportional to the product of the sur-
-
I
.-T
.
5
____r.__-
C
June, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
681
The value of k for a given pressure and temperature is, nearly constant over the space velocity range 25,000 to 125,000 except a t the lowest temperature, 370" C. At this temperature the reaction velocity constants decrease by about 50 per cent as the space velocity increases fivefold. It seems reasonable that some cooling of the catalyst by the highvelocity gas flow occurred and may have been sufficient to account for this decrease in k with the increase in space velocity a t 370" C. A convincing indication of the general soundness of the kinetic treatment is given in Figure 4. As shown in Equation
21, reaction velocity k is proportional to kz, the reaction velocity constant for the decomposition of ammonia. A plot of log k against 1/T a t a given space velocity should yield a straight line whose slope is the apparent energy of activation of ammonia decomposition. As indicated, values for the apparent energy of activation calculated from Figure 4 are in satisfactory agreement with the value 45,600 * 2000 calories reported by Love and Emmett (8) for measurement on the decomposition of ammonia over a doubly promoted iron catalyst a t one atmosphere pressure. I n drawing the curves of Figure 4, less weight was given to the runs a t 370" C. because there may have been some cooling of the catalyst by the gas flow at the lower temperature. Similar plots for the other space velocities and gas mixtures gave results in satisfactory agreement with Figure 4. The apparent energies of activation were always in the range 40,000 to about 55,000 calories. The fact that high pressure synthesis data can be used to calculate the energy of activation for the decomposition of ammonia attests to the correctness of the postulates and assumptions used. Although Equation 21 seems to account satisfactorily for the dependence of rate upon space velocity and temperature, it clearly does not compensate correctly for pressure changes. Much better agreement, as far as pressure dependence is concerned, would be obtained if the pressure term in Equations 21 and 22 entered as the first power instead of the square root. A similar observation could be made by comparing k a t 31.6 atmospheres with k a t 100 atmospheres (450" C.) in Table 11. I n calculating the results in Table 111, a and /3 in Equations 5 and 8 were both considered equal to l/2, a value consistent with the data of Winter on ammonia decomposition. It seemed possible that better agreement with the experimental data might have been obtained if kinetics corresponding more nearly to those found by Love and Emmett for ammonia decomposition were applied. Values were therefore calculated in which the rate of decomposition TVBS assumed proportional to (PNH,)O.~~ and inversely proportional t o (&) ; but on the whole, they gave poorer agreement (Table IV) with the experimental data than the calculations in Table I11 based on Winter's kinetics. The correct equation for calculating the data in Table IV for 3 to l hydrogen-nitrogen gas is:
The kinetic data for ammonia decomposition were determined on catalyst 931 (1.59 per cent potassium oxide and 1.3 per cent alumina); the synthesis data, on catalyst 660 (0.94 per cent potassium oxide and 3.02 per cent alumina). The data on ammonia decomposition are insufficient for us to say
E x i t Space V e l o c i t y xtO-'+ Figure 3.
R a t e of A m m o n i a Synthesis on 1 Hydragen3 Nitrogen Gas
T o p . 100 atmospheres; 0 run 21 0 run 22 0 r u n 23. Center. 66.6 atmospheres. 0 24, 0 25 run 26. B o t t o m . 33.3 atmosphere;; 0 run 27, 3 run Zd, run 29.
rdn
cia2
T Figure 4 . Apparent Energy of Activation of A m m o n i a Decomposition over Catalyst 660 (Iron-Potassium OxideA l u m i n a ) , ,from Measurements on t h e Rute of Synthesis f o r 3 t o 1 Gas a t 25,000 Space Velocity ( f r o m Figure 1)
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. 6
whether Winter's kinetics or those of Love and Emmett more nearly represent the actual dependence of rate of ammonia decomposition over catalyst 660 as a function of the partial pressures of ammonia and of hydrogen. The modifications of Equation 21 needed for calculating k for 1 to 1 and for 1 to 3 hydrogennitrogen gas follow, respectively:
f
Space Velocity Exit Gas
+
2 ) 3 p
16 - (1 27
p
100
atm.
FROM
EQUATION 2P
3 Hydrogen-I Nitrogen Gas k at 450' C.-k at 400" (3.-66.6 33.3 100 66.6 33.3
atm.
$!%
25.000 75,000 125,000
(6080 b (5200{ (4760)
35,000 75,000 125,000
5650 5590 4850
6660C 6710 5240
35,000 75,000 125,000
4650 4460 3950
5400 5100 4350
(5410)
(IO 810
(8'540{ (7:310)
402 285 204
570 463 334
--k
100
at 370° C.-
atm.
atm.
66.6
33.3
888 662 517
41.6 20.6 11.9
87 47.6 33.8
140 96.4 82.7
665 650 495
76.4 58.4 39.7
68.9e 69.2 51.9
69.6 74.5 59.5
900 835 693
97.7 82.0 65.1
99.1 97.0 77.2
atm. atm. atm. atm. 3 Hydrogen-1 Nitrogen Gas
atm.
1 Hydrogen-I Nitrogen Gas
a
z(i - 2 2 ) 3 ~ 2 d z
2
0 (1
TABLEIV. VALUESFOR IC
b c
- 2Z)* - Zzl
7,850 6,910 6,000
525 440 328
610e 545 376
1 Hvdroeen-3 Nitroeen Gas 5,850 515 585 5,810 478 544 5,480 397 450
149 148 104
See footnote" Table 111. Numbers in arentheses refer t o activities before the accidental poisoning preceding run 12. At 50 instea3 of 66.6 atmospheres pressure.
(28)
VOPlI2 k = - (*)"'
f
Z(l - 52)3'2dZ
2
0
(1
+ 2)s [&
(3
+ Z)(1 - 52J8 - Z z ] (29)
Furthermore, the modification of Equation 27 for calculating correctly the constant k for 1 to 1 and 1 to 3 hydrogennitrogen gas according to the kinetics of Love and Emmett can be obtained by making the same changes in exponents in Equations 28 to 29 that were made in obtaining Equation 27 from 21. Although these are believed t o be correct transformations of Equation 21, they do not yield very good agreement with the experimental data. Thus, whereas the value kz calculated for a given pressure, temperature, and space velocity should be the same for 3 to 1, 1 to 1, and 1 to 3 hydrogen-nitrogen gas in Table 111,they actually vary by a factor of about 2 at 450" C. The agreement a t 400" and 370" C. is fair. The equation for expressing the rate of high pressure synthesis in the 300-1000 atmosphere range should be formulated in terms of fugacity and not partial pressure. However, the complete derivation of the equation using fugacities seems to have many complications. Since the present data extend to only 100 atmospheres, the more rigorous derivation of the equation in terms of fugacities was not attempted, although this would be desirable when and if reliable synthesis data in the pressure range 300-1000 atmospheres become available. In conclusion, one additional deduction of Temkin and Pyzhev from their theoretical equations should be mentioned. Since kl and k z in Equation 16 are given by
- -Anum kl = ble
RT
-Adao.
and kz
=
bzeT
(30)
where AaYn,&eo. = apparent energies of activation of ammonia synthesis and decomposition, respectively, it follows that differentiation of Equation 16 with respect t o temperature yields the following:
Then for a maximum in the rate of synthesis, the right-hand side of this equation becomes equal to zero and
Hence for a mixture with definite partial pressures of ammonia, hydrogen, and nitrogen, the maximum rate of amJune, 1943
monia synthesis will be obtained a t the temperature a t which the equilibrium constant is: (33)
According to Equations 16 and 33, it is necessary merely to for a particular catalyst know the values for (&o./.&yn.) to be able to select the optimum temperature of operation for yielding a gas with a given ammonia, hydrogen, and nitrogen composition. Thus, for a catalyst for which the values of Adeo. and Asyn.were 40,000 and 14,000, respectively, as selected by Temkin and Pyzhev, the optimum temperature of operation would correspond t o an equilibrium constant, K , equal to ( P ~ ~ ~ ) ~ / ( 0 . 3 5 ) (PNJ. It should be emphasized finally that the new data in the present paper should be considered more illustrative than representative of an extended experimental study of high pressure ammonia synthesis kinetics. The authors are aware that more research will be needed to eliminate the uncertainty due to probable temperature inhomogeneities in the catalyst bed. Nevertheless, the data are sufficiently good to assure that the treatment by Temkin and Pyzhev represents a real contribution to the theory of ammonia synthesis over doubly promoted iron catalysts; together with recent calculations of Brunauer, Love, and Keenan (IO), it points the way to a clearer understanding of this catalytic reaction than has hitherto existed. LITERATURE CITED (1) Benton, A. F., IND. ENQ.CHIM., 19,494-7 (1927). (2) Brunauer, S., Love, K. S., and Keenan, R. G., J. Am. Chem. SOC., 64, 751-8 (1942). (3) Emmett, P. H., and Brunauer, S., Ibid., 56, 35 (1934). (4) Frankenburg, W., 2. Elektrochem., 39, 45-50, 97-103, 269-81, 818-20 (1933); Emmett, P. H., in Curtis' "Fixed Nitrogen", Chap. VIII, New York, Chemical Catalogue Co., 1932, and in 12th Rept. of Committee on Catalysis, Natl. Research Council, Chap. XIII, New York, John Wiley & Sons, 1940. (5) Frumkin, A., and Shluigin, A., Acta Physicochim. ( U . 8. 9. R.), 3, 791-818 (1935). (6) Langmuir, I., J. Am. Chem. Soc., 54, 2798 (1932). (7) Larson, A. T., and Tour, R. S., Chem. &. Met. Eng.,26, 647-54 (1922). (8) Love, K., and Emmett, P. H., J. Am. Chem. SOC., 63, 3297 (1941). (9) Temkin, M. I., and Pyzhev. V., Acta Phusicochim. (U.S. 8. R.). ,. 12, 327-56 (1940). (10) Winter, E., Z . physik. Chem., B13, 401 (1931). (11) Zeldowitsch, Ya., Acta. Physicochim. (U.S. S. R.), 1, 449 (1934) PRESENTED as part of the Symposium on Industrial Reaction Rates, held under the auspices of the Division of Industrial and Engineering Chemistry, AMERICAN CHEMICAL SOCIETY,at Chicago, Ill.
INDUSTRIAL AND ENGINEERING CHEMISTRY
683
