dimethylformamide layer 0.2 cm. thick. Because dimethylformamide is a much better conductor than iso-octane, the electrical field is almost wholly within the oil, and the dimethylformamide surface is the lower electrode ; electrode separation is only 1 cm. If the applied potential is 10 kv., dielectric constant of the oil is 2.0, and ko is 8.85 X substitution gives: Fs = =
(2) (8.85) (10-12) (1 x 104)~ (2) (1 x 10-*)2 9 neutons/sq. meter
=
90 dynes/sq. cm.
Although the calculation has been simplified by assuming that the electric field in the mixing cells is uniform, this result indicates the order of magnitude of force on the interface. As a first approximation, mixing action appears to be initiated largely through the electrostatic force exerted by the upper electrode on the solvent. As a result of this force, droplets of solvent are torn away from the interface and attracted to the upper eIectrode. I n addition, the extremely nonhomogeneous field in the region of a point polarizes nearby droplets and this results in another force that tends to accelerate them toward the charged point. This secondary effect enhances the mixing action initiated by the force a t the liquid interface.
Conclusions In mixing liquids with electrostatic forces, there is essentially no field below the surface of the solvent. For mixing action to be efficient, the solvent layer must be shallow, otherwise the rate of diffusion downward from the interface lowers the efficiency of the process. The advantage of mixing with an electrostatic field over conventional methods of mixing is that no moving equipment. such as impellers or circulating pumps, is required. Packing glands for rotating shafts are not needed for stirring or mixing in high-pressure vessels. T h e process would seem to offer promise for mixing liquid SO2 or liquid H F with hydrocarbons.
literature Cited (1) Bailey, E. I., U. S. Patent 2,296,239 (Sept. 22, 1942). (2) Cofman, Victor, J . Phys. Chem. 29, 1289 (1925). (3) Hansen, G. B., U. S. Patent 2,033,429 (March 10, 1936). (4) Harnwell, G. P., “Principles of Electricity and Electromagnetism,” 1st ed., p. 50, McGraw-Hill, New York, 1938. (5) Karagounis, G., Helv. Chim. Acta 31, 1929 (1948). 6) Phillips, R. J., Petrol. Rejiner 35, No. 11, 202 (1956). 7) Pohl, H. A., J . Ab$. Phys. 22, 869 (1951). (8) Ibid., 29, 1182 (1958). (9) Seelig, H. S., Cropper, W. P., U. S. Patent 2,844,375 (April 28, 1959).
I
RECEIVED for review March 20, 1961 ACCEPTEDSeptember 8, 1961
THERMODYNAMICS OF SELECTED CHEMICAL SYSTEMS POTENTIALLY APPLICABLE
TO PLASMA JET SYNTHESIS C. W. M A R Y N O W S K I , R. C. P H I L L I P S ,
J.
R . P H I L L I P S , A N D N. K. H I E S T E R Stanford Research Institute, Menlo Park, Calif.
HEMICAL
PROCESSING at temperatures above
3000’
K.
C has been considered by many chemists and engineers as technically and economically infeasible. Now, the availability of reliable and efficient plasma generators prompts critical review of high temperature syntheses. Even the predominantly qualitative and empirical research on plasma chemistry reported to date indicates that this new technology has significant potential. T h e plasma jet, as a chemical processing tool, is virtually unique in its capability for raising reactants to ultrahigh temperatures (or, more properly, to ultrahigh enthalpy levels) a t reasonable energy efficiencies. At atmospheric pressure, commercial plasma jets can readily impart over 7000 B.t.u. per pound of working fluid (sufficient to raise the temperature of noble gases as high as 15,000° K., or that of diatomic gases as 52
I & E C FUNDAMENTALS
high as about 8000’ K.). At these high enthalpy levels, the course of competing chemical reactions is governed by equilibria and kinetics that are far different from those of more conventional processing conditions. I n some instances, the equilibria can be favorable for the Cormation of desirable end products (such as H C N or C2H2) that are metastable a t ambient conditions. More commonly. however, the chemical species that are stable or metastable at plasma-jet conditions are completely unstable at ambient conditions. Among such species are ions (in low concentrations and with very short lifetimes), excited and unexcited atoms, and molecular radicals that either are stable or are metastable for significant residence times. Thus, in the majority of cases, the production of desirable end products must involve more than merely trapping the species produced in t h r
With the advent of plasma jets operating in the megawatt
perature equilibria for the three-element system containing
range, the potentiol utility of this gas-stabilized, high en-
atomic and simple moleculor species of carbon, hydrogen,
thalpy a r c for conducting commercially profitable chemical
and nitrogen a r e calculated os o function of temperature for
syntheses needs to be evaluated, porticularly in temperature
2000'
regions not attainable by other devices.
Factors affecting
pressure, temperature, and element ratios a r e determined,
the feasibility of chemical synthesis with the plasma jet ore
with imposition of appropriate conditionol relations for
to 6000" K.
Component partial pressures, total
discussed, and current research in plosmo-jet processes is re-
maximizing the equilibrium concentration of HCN.
The
viewed. As an illustration of the application o f thermody-
applicability of the same dato to evaluation of the three
namic principles to o specific potentiol process, the high tem-
binary systems, C-H, N-H, and C-N, is discussed.
plasma jet. I n general, two avenues of approach are available. The first avenue involves a controlled change in the path of the thermodynamic state (temperature and/or pressure) of the system, from plasma-jet to ambient conditions, so that the normal ambient equilibria are kinetically suppressed in favor of recombination reactions that lead to desirable metastable pmducts. Techniques involving expansion of the reactants through a d e Laval nozzle, quenching by contact with a cooled surface or by injection of a cold inert medium, or combinations of the above, fall into this avenue, T h e second avenue, instead of depending on pxferential recombinations of plasma-jet species, involves interactions between these species and an independently introduced reactive medium. I n this avenue are such techniques as spraying a reactive liquid (or solid) into the jet, dispersal of the jet gases through a reactive liquid, fluidization of a reactive solid with the jet gases, and transpiration-cooling of an expansion nozzle with a reactive liquid. A special case of this avenue is the use of a quench liquid that is unreactive, but becomes reactive when it is partially pyrolyzed by contact with the jet gases. A brief review of the plasma jet and its characteristics may be helpful. For purposes of this discussion the plasma jet is simply a fluid-stabilized, constricted arc which is capable of continuously generating a high velocity, high temperature gas stream. A typical commercial plasma jet is shown in Figure 1. The stabilizing gas, which in this design is introduced tangentially to pmduce vortex flow through the arc chamber, is partially ionized in passing between the thoriated
tungsten anode and the copper cathode. A jet of plasma issues from the cathode nozzle at temperatures up to 15,000" K. From 50 to 70% of the electrical energy is transferred to the gas stream; the remainder is removed by the cooling water. The two-stage plasma jet, shown in Figure 2, is of interest for some chemical applications in which it may be undesirable to pass all the reactants directly through the arc chamber because of corrosive effects on the electrodes. Commercial plasma jets rated up to 5000 kw. are available. A 10,000-kw. plasma generator has been developed by AVCO (22). T h e electric arc, in various configurations, has been used for years in chemical synthesis. However, the plasma jet, with its reasonably high efficiency, its high temperature and high velocity capability, its ease of containment, and the long life of its electrodes, offers new dimensions to arc chemistry. Perhaps the plasma jet's potential for operation at high pressures will become as important in chemical applications as its established capability as a convenient source of ultrahigh temperatures. Plasma jets have been successfully designed for operation at pressures as high as 15,000 p.s.i.a. (with, however, a decrease in an: efficiency and an accentuation of electrode erosion as the pressure is increased) (76). As noted above, the attainment of favorable equilibrium compositions at high temperatures may be an important step in some plasma jet processes. Quenching may be an equally important, and far less developed, second step. The highest practical quench rates are attainable by expansion of the hot gas thmugh a d e Laval nozzle. A cooling rate in the order
ARC GAS (TANGENTIAL ENTRY1 -WATER
COOLING CHANNELS R E A R ELECTROOEITUNGSTENI
GENERATOR FRONT ELECTRODE (COPPER1
\g-.. rT-1
ELECTRICAL A N D WATER NNECTION
FIRST
.
~
SECOND
STAGE STAGE L~NSULATO ~
Figure 1.
Plasmadyne vortex-stabilized plasma jet
Figure 2. VOL 1
Two-stage plasmaI jet
NO. 1 F E B R U A R Y 1 9 6 2
53
of 3 X 107’ K. per second occurs when the gas expands through the nozzle of a typical rocket thrust chamber operated at 1000 p.s.i.a. (77). Somewhat higher rates are possible with smaller nozzles. T h e actual quench rate required to maintain a desirable reaction composition, representing equilibrium a t high temperature, depends on the kinetics of the various possible decomposition reactions. Since these high temperature kinetics are in general not known, it is not possible to predict the approach to frozen equilibrium which would be attained with any given quench rate. Direct experimental evidence on this subject is needed. As de Laval nozzles convert thermal to kinetic energy, the nozzle must be coupled with some device for abstracting the kinetic energy from the gas to prevent reheating. This is the third step in the process. In general, the ideal way to extract the kinetic energy is with a turbine, thus providing a means for converting part of the energy in the gas stream back into electrical energy. A transpiration-cooled turbine, designed to operate as nearly isentropically as possible, may provide a n effective means for decelerating the gases issuing from a de Laval nozzle. Following the turbine, conventional liquidspray techniques may bring the reaction mixture to temperatures appropriate for recovery of products. Current Research in Plasma Jet Processes
At the International Symposium on High Temperature Technology in 1959, a number of plasma jet syntheses were reviewed (78), including the preparation by Stokes and Knipe of titanium nitride, magnesium nitride, cyanogen, and nitrogen dioxide with a nitrogen-stabilized plasma jet (27), and the production of acetylene from natural gas by the Linde Co. ( 4 ) . Current research on plasma jet chemistry includes Baddour’s work with the hydrogen-carbon system ( 1 3 ) and Margrave’s investigation of fluorine compounds (72). At Stanford Research Institute, we have considered the fixation of nitrogen from air and concluded that a plasma jet operated a t 3500’ K. would give a 5 mole % concentration of nitric oxide, compared with 2 mole from the Wisconsin process furnace (78). We have also considered the application of the plasma jet to a process related to the Serpek process. The high temperature step in this related process is the reaction: 5Nz
+ 2A12O.j
+
6 N 0 f 4A1N
The A1N can be hydrolyzed to NH3 and A1(OH)3, and the latter can be calcined to the oxide for re-use in the first step. With conventional conversion of the NO to nitric acid, the over-all process stoichiometry may be represented by : 10N2
+ 9O2 + 18Hz0
-+
12HN03
+ 8NH3
‘4ttainment of favorable equilibrium in the first reaction requires temperatures in the plasma jet range. Finely powdered alumina could be fed into a nitrogen plasma and the reaction could be quenched with a water spray. The feasibility of the process would probably depend on complete vaporization of the alumina to permit rapid conversion to the nitride. We have exposed several halofluorocarbons in a plasma jet and quenched the reaction by bubbling the hot gas through carbon tetrachloride or another halofluorocarbon of low volatility. The products collected in the carbon tetrachloride included nonvolatile liquid residues having average molecular weights of approximately 400. The structure and properties of these materials are being investigated. We have also con54
I&EC FUNDAMENTALS
sidered the synthesis of thiophosphonitrilic compounds with the plasma jet, but have no experimental results to report along this line.
Thermodynamics of a Typical Potential Plasma-Jet Process
Knowing both the rewards and frustrations of Edisonian experimentation with the plasma jet, we attempted to define, by thermodynamic analysis of a typical chemical system, the operating parameters for deriving maximum concentrations of some valuable product. produced in a quasi-equilibrium process. System under Consideration. The H-C-N ternary was selected for this evaluation because it involves the commercially important and valuable compounds, hydrogen cyanide, acetylene, and cyanogen. Although amines, hydrazines, unusual hydrocarbons, and other more complex compounds might be formed to significant extents at some conditions of temperature and pressure in this ternary, attention was focused on the production of hydrogen cyanide. O n the basis of raw materials cost, the synthesis was predicated on the use of elemental nitrogen and methane (or some other inexpensive hydrocarbon) as the sources of nitrogen. carbon, and hydrogen. The process that was envisioned involved a flow reactor a t high space velocity, in which equilibria between simple gaseous compounds could be expected to be approached closely, while equilibria for the formation of complex compounds could be ignored on the basis of kinetics. (Hence, the designation of the process as a “quasi-equilibrium’’ system.) Of course, most relatively complex compounds (C2H6 and higher aliphatics, C6He and higher aromatics. hydrazines, amines, polymeric compounds, etc.) could be ignored on the basis of their instability a t the high temperatures considered. Polyatomic carbon vapor species higher than C3 are stable in high-temperature static equilibria (3, 5, 79). However, such species do not evaporate directly from graphite. but must be formed by consecutive combination reactions in the gas phase. Such consecutive reactions are relatively slow. and so these higher species could be ignored on kinetic grounds, in a flobv process employing short reaction times. Except for ethylene. acetylene, cyanogen, methane, and the methyl radical, the gaseous chemical species that were considered in our calculations included none higher than triatomic. Solid carbon (graphite) was the only condensed species included in the calculations, although the practical effects of ignoring the formation of liquid carbon under some operating conditions were subsequently evaluated. The primary thermodynamic data for the 20 species included in the study are given in Table I for temperatures to 6000° K. Data sources are shown in the list of references, and were screened to incorporate the most recent and reliable data for each species. I t is recognized that some of the values used are subject to revision. Two additional radical species, CZH and CZN, are also suspected to be important under certain operating conditions. Free-energy functions for the former have been reported (ZO), but considerable uncertainty is involved in itr estimated heat of formation. Equilibrium constants for the latter were estimated by us, using an empirical correlation technique based on individual bond-dissociation energies and entropies. Because of the lower precision of the equilibrium data for these two species, they were excluded from the initial calculations. The availatile data for them were subsequently used to evaluate
their probable significance with regard to the conclusions of the study. O u r calculations had the objective of finding the operating conditions at which the mole concentration of H C N was maximum, in the defined high-temperature, quasi-equilibrium reaction mixture. All gaseous species were assumed ideal. Both heterogeneous and liomogeneous equilibria (with respect to carbon) were involbed. The effect of pressure on the fugacitv of graphite was ignored. Statement of Problem. Given adequate data for calculation of equilibria between species a t various temperatures, find the optimum values of T , P, (ZC/Z.\'), and ( Z H / 2 t r ) ,a t which (HC-Y,P) is ax a maximum. Outline of Method of Solution. According to the phase rule, in a three-component system there are four degrees of freedom for homogeneous equilibrium, and three degrees of freedom for heterogeneous equilibrium. For a three-componen t, homogeneous equilibrium system, one may select any conbenient combination of four independent variables to represent the four degrees of freedom. I n general, if there is an optimum value of each selected variable. for which the H C N concentration is a t a maximum, then the partial derivative of H C N concentration. with respect to each variable. may be equated to zero a t the optimum. For added convenience one may substitute any appropriate function of H C N concentration, in place of the concentration itself, as long as the chosen function has either a maximum or a minimum value coincident only with the maximum in the H C S concentration. T h e resulting four equz tions represent four independent relations defining the optimum homogeneous equilibrium system For the heterogeneous case, the rrlation C, = 1-i.e., has unit fugacity-takes the place of the relation involving a partial derivative with respect to a carbon species, since in this case all carbon vapor species are constant a t a given temperature. I n the present study it was convenient to select H I , Cl, HCV, and T as the four independent variables. Instead of maximizing (HC.V/P), it was much more convenient (as explained below) to choose the inverse function, (P/HCN), which has a corresponding minimum. In this way, the four defining relations became : 1.
~ ~ ~ ~ I H hCC V ,WT) = ~ o~ ~ I ~ ~ ~ ,
c. > 1
2.
[~(PIHC.~')IC~I~~,= , 0;
3.
[ d ( P / H C ' V ) / d H C N ] ( , yc,, , TI = 0
4.
[ N P / " C ~ ~ ' I a T l ( H ic,
7
HC.V)
= 0
The defining relations could be iterated simultaneously to arrive at the optimum iolution for the chosen independent variables. Optimum valuer of all dependent variables could then be obtained by use of the given equilibrium data. Detailed Calculation Procedure. To facilitate the iterative solution, the followirig procedure was used : To make the expressions for (K,)T involve only integral power functions of species partial pressures, the 17 possible independent chemical reactions (between 20 species of three elements) were written in the form: .Monatomic ideal gaseous vlements + 1 mole of polyatomic (or of condensed phase) product For example, the reaction forming ammonia was written: NI
+ 3H14
3"
and the expression for the equilibrium constant was ( K N H =~ [("~)(Ni)-~(Hi)-~lr
Values of (JQT, evaluated for the range 2000" to 6000" K., are given in Table I1 for the 17 reactions involved. Conversion of the thermodynamic data of Table I to values of ( K z ) T was by means of the relation
(product-reactants) T h e expression of ( I Y ~in) ~ the manner of Table I1 is particularly amenable to estimation of data from a single known value, or to extrapolation to temperatures above the range where data for free energy functions are available. If - (R)ln ( K z ) T is plotted us. 1 / T , the intercept a t T m is essentially a function only of the decrease in the number of moles due to reaction. and not of the qualitative nature of the species involved. This is a consequence of the fact that a t T m all (AH;)o/T values are zero and thus that the Lhange in free energy for any reaction is a function only of the change in entropy (primarily translational entropy). Based on the data of Table 11, the average T m intercept of -(Z?)In(Kz)? is approximately (30.4) times the number of moles consumed in the reaction of formation of any species from the monatomic ideal gaseous elements. T h e value of 30.4 is thus a Trouton constant derived from data in the 2000" to 6000" K. range. At each T , the partial pressures of the 16 gaseous species other than HI, Ct, and H C S were expressed in terms of these three partial pressures and of the 16 independent values of ( K J T for gaseous species. For example, the partial pressure for methane, in terms of integral power functions of Ci and H I was: C H , = (KcEI,),(C,) (HI),. Similarly, the fugacity of C, was expressed in terms of C1 and ( K c 8 ) T . I n this manner the total pressure a t each temperature (being the sum of the partial pressures of all species) was expressed as the sum of integral power functions of the three independent variables other than T. By choosing the inverse function, (P/HC.V), as the dependent variable, it was possible to express the first three of the four defining relations to involve nothing more complex than derivatives of integral power functions of the independent variable, with respect to that variable. Such derivatives, being themselves integral power functions, made subsequent manipulations very convenient. When P was expressed in terms of component partial pressures [ with these in turn expressed as functions of Hz, C1, HCN, and the various (IYz)? values], the derivatives in the first three defining equations could be readily evaluated and the equations could be reduced to the form:
+ 2 S 2 + NH + SH2 + KH3 + CN + 2CzNg + HCN = Hi + 2H2 + CH + 2CH2 + 3CH3 + 4CH4 + 2CiHa + 4C2H1 + NH + 2NHz + 3NH3 + HCN (1) N1 + 2x3 + KH + NH2 + NH, + CN + 2ClNa + H C S C I + 2C2 + 3C3 + CH + CHz + CH3 + CHh + 2C2H2 + 2CpHd + CN + 2C2Nz + HCN; C. 1 (2)
NI
=
Hi
+ Ci + Hz + Cz + C3 + CH + CHz + CH8 + CHI
+ CgHz + CZHI
Np
+ C2N2
(3)
I n simple terms, Equation 1 states that, for maximum (HCNIP), the nitrogen atom fraction of the equilibrium mixture must equal the hydrogen atom fraction. Similarly, Equation 2 states that the nitrogen atom fraction must equal the carbon atom fraction (as long as no condensed phase of carbon is present). These two relations are in accord with the well known thermodynamic principle that a constituent is present in maximum concentration in a n equilibrium mixture when the elements are present in stoichiometric proportions to that conVOL. 1
NO.
1
FEBRUARY 1962
55
IO
--
HETEROGENEOUS REGION -
c
I
I
+
-
HOMOGENEOUS REGION
I
I
I
-
I
I
I
I
I
L
l z
-
I HCN=
-
C
0
c
e
c
I
z
7 I
c
WERE DISREGARDED -
-
t
1 tn
0.001 0
0
2000
4000
6000
T-OK.
Figure 3. Temperature dependence of optimum equilibrium gas composition for HCN synthesis at one typical constant HCN partial pressure
2000
4000 T-OK.
6000
Figure 4. Maximum equilibrium HCN concentration as a function of temperature for three values of HCN partial pressure
0.1 atm.
stituent. Equation 3 states that (HCI\'/P) is a maximum when the aggregate partial pressures of all species containing no nitrogen equal the aggregate partial pressures of all species containing two atoms of nitrogen. (No species containing more than two atoms of nitrogen was considered.) I n effect, this equation defines the optimum pressure a t any given temperature. The iterative solution for the optimum system was as follows. For several chosen values of H C N partial pressure, values of H1 and C1were assumed a t each temperature, and the equilibrium pressures of all species were calculated from the data of Table 11. Subsequent adjustments were then made in H I and C1 until the relations of Equations 1 and 2 were simultaneously satisfied. T h e component partial pressures and the total pressure (excluding the ignored species, C2H and C2N) were plotted us. T , as illustrated in Figure 3 for the case, H C N = 0.1 atm. I n each of these plots, the total pressure was observed to go through a pronounced minimum, corresponding to a maximum in (HC.V/P)Hc.v. From the above plots, a plot was constructed of [(HCN/ P)(HC4',T)]max us. T , with the ordinate evaluated a t several constant values of HCN, and at each constant value of the abscissa temperature. This is illustrated in Figure 4. The locus of optimum temperatures for each H C N partial pressure is shown on this plot. This locus was observed to cross the boundary between homogeneous and heterogeneous equilibria, a t a temperature near 4000" K. The original statement of the problem called for definition of the optimum system in terms of the quantities of engineering interest-namely, T*, P*, ( Z C / Z N ) * , and (ZH/ZN) *. With this objective, the data of Figure 4 were cross-plotted, with [(H%V/P)(,, P)]max as ordinate and P as abscissa, as illustrated in Figure 5. I n this plot the locus of optimum temperatures for each pressure is tangent to the envelope of curves a t constant temperature. Similarly, the locus of optimum pressures a t each temperature passes through the maximum point of each curve representing a constant temperature. The two loci converge near 6000" K. and 106 atm. 56
l&EC FUNDAMENTALS
With the same objective, the data on which Figure 4 was based were used to plot ( Z C / X N ) * ( T , p )as ordinate us. T as abscissa, for aeveral values of P (this plot is not shown). T o facilitate interpo!ation and extrapolation to other pressures a cross plot was constructed (shown in Figure 6) in which curves of constant (ZC/ZN)*(,, p ) are shown for various combinations of T and P. No analogous plot was necessary for (ZH/ZN)*,,. p ) , since this ratio was necessarily unity (corresponding to the desired product, HCN), because no condensed phase of either H or N was ever present under the conditions considered. The curves of Figure 6, for (ZC/ Z N ) * ( T , p ) values less than the unity ratio in HCN, obviously represent heterogeneous equilibria with respect to carbon, with some of the carbon having shifted from the gaseous to the condensed phase. The shaded area in Figure 6, and the significance of the melting point of carbon, is discussed below. Figures 5 and 6 actually contain the solution for the optimum system. I t is represented by the point of intersection of the two loci in Figure 5, and the corresponding element ratios of Figure 6. T o show this in another way we may state that, if P, ( Z C / Z N ) , and ( Z H I Z N ) are each maintained a t their optimum values at each temperature, the H C N concentration will be a function only of temperature. If there is a n optimum temperature, the total derivative of ( H C N / P ) with respect to T must vanish a t the optimum:
3
d p (Hcill/P)[(P)*T,( Z C I Z N ) * T
,(ZH/Z.V)*T]
1
=
0
This is a form of the fourth independent relation defining the optimum system, that is amenable to graphical solution, using the data of Figures 5 and 6. The function being differentiated is identical with [(HCN/P)T],,, and may be plotted us. T , as shown in the lower graph of Figure 7. T h e slope of the resulting curve becomes very small at temperatures above 5000" K., zero near 6000" K., and negative a t higher temperatures (not shown in Figure 7). Thus, 6000" K. is the temperature of the optimum system, within the precision of the graphical solution. The corresponding maximum HCN concentration is approximately 38 mole %. The middle curve of Figure 7 shows (P)*T plotted us. T . [Because of the many orders of pressure covered, the logarithm of ( P ) * T is
o'6
0.5
'
C
.-
L
0
e
0.4
-u
+-
0
E
I
Z
0.3
r-
-p-P
0.2
0
x
L
a
0.I
0 lo-'
10
I
IO2
I o4
103
lo5
I06
P-6tm
Figure 5. Maximum equilibrium HCN concentration as a function of pressure for five temperatures 2000' to 6 0 0 0 ' K.
used as ordinate.] The pressure corresponding to 6000' K. is between 105 and 1 0 6 atm., and this is thus the pressure of the optimum system. The upper curve of Figure 7 shows (zc/zlv)*, and ( z ~ , t ~ ~ plotted i ~ ) * ,cs, T . 6 0 0 0 ~K , the equilibrium is homogeneous, SO both element ratios are unity for the optimum system.
for this by lowering the partial pressures of the H and N species (to keep H, C, and N in near balance), then the HCN concentration is limited by the dissociation of all pOlyatOmiC species, including HCN. T h e maximum equilibrium HCN concentration obtainable a t 2000 K is less than 2 mole % At temperatures high enough to attain homogeneous equilibrium at a given pressure, the elements can be kept in the optimum stoichiometric balance. For pressures below about lo3 atm., the principal species in competition with H C N are h-2, HI, C1, CP,and C N ; consequently, an increase in pressure
Discussion of Solution. QUALITATIVE EFFECTSOF TEMPRESSURE.At the lowest temperatures considered, the concentration of H C N is limited by the extremely low vapor pressure of carbon. If one attempts to compensate
P E R A T U R E AND
6000
I
I
I
I
I
5000
4000 >:
0
I 3000 c-
2000
I IOoo
t 10-1
'
HETEROGENEOUS REGION
I
I
IO
0
05
*
(ZH/ZN)(T,,)= 1.0 WHENEVER NO CONDENSED PHASE OF H OR N IS PRESEN'
io3
I02
- atrn. carbon-nitrogen ratios for HCN
I o4
I o5
106
P
Figure 6. Optimum perature and pressure
synthesis as a function of tem-
S,hoded area represents heterogeneous conditions where curves o f Figures 3 t o 7 must b e modified to CIIIOWfor significant contributions of C2H and C2N
VOL. 1
NO. 1
FEBRUARY 1962
57
1.2
I
I
$000
3000
4000
-2 2000
I
li
3000
4000
I
I/
frulrtdl:
(.XC/ZN):
I
I
' I
AND
(PHI X N ~ mole f r a c t i o n
LOG(P);
5000
6000
-atm.
0 5 0.4
1
I
I I 5000
I 6000
/ I I
CARBONM P.
0.3 0.2
I
attainable a t any temperature, Although the optimum pressure at 5000"K. is calculated to be 42,000 atm. (giving an H C N concentration of 36.2 mole '%), a pressure as low as 400 atm. still gives the very high concentration of 30 mole yo. It is estimated that 1000 atm. is approximately the foreseeable technological pressure limit. The technological temperature limit must be dictated by considerations of materials of construction, as discussed below. IMPORTASCE O F MAINTAISING HETEROGENEOUS EQUILIBRIUM. Except at unattainably high pressures. operation at 5000"K. involves the homogeneous equilibrium region (see Figure 6), where requirements for materials of construction for a reactor vessel would be prohibitive. The calculated transition from homogeneous to heterogeneous equilibriom lies a t about 4900" K. a t 1000 atm., and at about 4700' K. at 100 atm. If the forniation of liquid carbon was ignored, these sets of operating conditions would appear to be feasible, as they would represent a state of dynamic equilibrium between a graphite-lined reactor and the gaseous reactants. COXSIDERATION OF FORMATIOX OF LIQUIDCARBON.I t is necessary at this point to recall that the formation of liquid carbon was ignored in these calculations, and that the reported (75) triple point temperature of carbon is about 4020" K. Obviously the formation of liquid carbon must be prohibited, both for mechanical reasons (at the reactor walls) and because its presence would necessitate consideration of polyatomic carbon vapor species higher than C3, which could be expected to evaporate directly from the liquid. O n this reasoning, the optimum temperature would have to be no higher than about 4000" K., corresponding to a n optimum pressure of about 1000 atm., and giving an effluent H C N concentration of about 28 mole %. The melting point of carbon (assumed constant) is indicated in Figure 6 to emphasize the fact that the region above this temperature is infeasible. CONSIDERATIOX OF FORMATION OF C Z H AND CzN. These two radical species were ignored in our initial calculations because the available equilibrium data for them were considered to be less reliable than data for the species shown in Tables I and 11. Subsequent calculations, using the available data for CzH and C2N, showed that these two species could be important under certain operating conditions (low pressures combined with high temperatures), but that they could safely be ignored at conditions favorable for the synthesis of HCN. The data of Plooster and Reed (20) for C2H extended only to 3000" K., but were extrapolated by us to the 6000' K. region by means of the fitted equation:
I
O.I2000 0
3000
4000
5000
6000
T--OK.
Figure 7. Summary of optimum conditions for maximum equilibrium HCN concentration as a function of temperature
favors the formation of the triatomic H C N by suppressing the competing diatomic and monatomic species. At pressures between lo3 and 106 atm., the principal competing species are Nz and C Z H Z ;further improvement of HClU concentration with pressure is very slow, since one of the competing species is tetratomic. At pressures above 106 atm., further increase in pressure causes a decrease in the H C N concentration, because of the formation of the polyatomic species, C3, CH4, CH3, CzHa, and NHI. At temperatures above about 6000" K., the concentration of H C N is limited by dissociation of all polyatomic species to HI, CI, and NI. Application of sufficiently high pressure can suppress these dissociations, but then the formation of polyatomic carbon species, C2, C3! and higher, a t the expense of HCN, becomes the limiting factor. DePRACTICAL TEMPERATURE AND PRESSURE LIMITATIONS. parting from the theoretical optimum system to a slightly more practical region, operation a t 4000' to 5000" K. gives H C N concentrations within a few per cent of the ultimate optimum 58
I&EC FUNDAMENTALS
log ( K c 2 a ) r= -13.46
+ 62,82O/T
Our own best estimate of the corresponding equation for CzN was: log(Kc,x)r = -13.30
+ 70,64O/T
These two equations were used to calculate the approximate contribution to the total pressure due to CZH and CZN, a t various combinations of the operating conditions represented in Figures 3 to 7. The pressure-temperature area in which these two species together raise the total pressure by lOy0 or more is shown shaded in Figure 6, for the heterogeneous equilibrium case. At 4000' K., all pressures above about 35 atm. lie outside the shaded area. At 1000 atm., the combined contributions of C2H and CzlT result in only a 270 increase in the total pressure, thus reducing the calculated H C N concentration from 2870 to about 27.5yG. At 100 atm. (uncorrected), the corrected total pressure is about 106 atm., corresponding to an H C N concentration of about 24 mole 7 0 .
Table 1.
298
+ 5 1 . 6 2 (24) +169.6(79) +112 6 (7) 0 +197 ('5) +188 ( 7 9 ) 0 0 +141 5 (28) +87 (37) +39 ('37) -15 99 (37) +54 33 (37) +14 52 (37) +84 9 (28) +40 99 (9) -9 36 (23) + l o 8 l(7) +71.5 (7) +31 l ( 2 9 )
-22.42 (72) -32.52 (72) -31.65(72) -24.44(23) -42.26(70) -42.98(79) - 0 . 5 1 (23) -38.83(23) - 3 5 . 5 (26) - 3 7 . 5 (26) -39.2b -36.50(30) - 4 0 . 0 (26) -44.0 (8) - 3 6 . 4 (26) -37.15 ( 9 ) -37.99 (23) - 4 2 . 4 (70) -47.71 (30) - 4 0 . 8 (2)
Component Hi Cl
CN CZNZ HCN
Primary Thermodynamic Data for the H-C-N Ternary System
Heot of Formation. ( A H FO ) O , Kcal./Mole
2tlolar Free Energy Function, ( F r 2000 3000
-31.88 (24) -42.21 (24) -41.10 (72) -37.67(24) - 5 6 . 3 3 (37) -61.82(79) - 5 . 3 7 (24) -52.50(23) - 4 8 . 9 (26) - 5 3 . 5 (26) -57.81 (30) -57.22 ( 7 7 ) - 6 1 . 3 (26) -69.54 ( 7 7 ) - 4 9 . 9 (26) -53.43 ( 9 ) - 56.56 (23) - 5 5 . 4 (70) - 7 3 . 6 (70) - 5 8 . 5 (2)
-33.89 (24) -44.25 (24) -43.12 (72) -40.72(24) -59.65 (6) -66.93(79) - 7 . 2 8 (24) -55.69 (26) - 5 2 . 1 (26) - 5 7 . 8 (26) -63.46(30) -64.26 ( 7 7 ) -67.7 (26) -78.39 ( 7 7 ) - 5 3 . 0 (26) -57.64 ( 9 ) -62.2b - 5 8 . 6 (26) - 8 0 . 7 2 (30) - 6 3 . 4 (2)
"C. refers to stable or metastable solid carbon (graphite) at all temperatures. cal./mole. ( H ~ g 8- Ho)estimated at 2200 cal./mole.
CONSIDERATION OF RAWMATERIALS.From a n economic standpoint. it would be preferable to use inexpensive raw materials such as CHd and .?J2 for the H C N synthesis. With a 1 to 2 feed ratio of C H I and Nz, the initial C :N : H ratio would be 0.25 : 1 : 1, which is fortuitously nearly optimum a t 4000' K. and 1000 atm., and is only slightly suboptimum a t 4000' K. and 100 atm. However, the (2:N:H ratios would change slightly as the reaction by-products were recycled. If economics dictated removal of part of the by-products-for example, acetyleneprior to recycle, the C : iY:H ratios woud be shifted still further from optimum values. Stanford Research Institute has programmed the H-C-N ternary for machine calculation of suboptimum equilibria on its Burroughs 220 computer. I t was demonstrated that the dependence of the HClK concentration on the element ratios is
Table II.
b
K.,
at
T o K.
4000
5000
6000
-35.32 (24) -45.70 (24) -44.55 (72) -42.98(24) -62.08 ( 6 ) -70.73(79) - 8 . 7 8 (24) - 5 8 . 0 4 (26) - 5 4 . 4 (26) - 6 1 . 1 (26) -67.86(30) -69.77 ( 7 7 ) - 7 2 . 5 (26) -84.3b - 5 5 . 3 (26) -60.85 ( 9 ) -66.5h -61.11 (26) -86.00 (30) - 6 7 . 0 (2)
-36.43 (24) -46.85 (24) -45.67 ( ~ -44.81 (24) -64.00 ( 6 ) -73.8h - 9 . 9 8 (6) - 5 9 . 9 1 (26) - 5 6 . 3 (26) - 6 3 . 7 (26) -70.9b -74.0b - 7 6 . 5 (26) -89.05 - 5 7 . 2 (26) -63.46 ( 9 ) -69.5b - 6 3 . 1 3 (26) - 9 0 . 2 2 (30) - 7 0 . 0 (2)
-37.33 ( 7 7 ) -47.80 ( 7 7 ) -46.60 (26 -46.34 ( 7 7 -65.60 (6) -76.4b -11.02 (6) -61.46 (26 - 5 7 . 8 (26) - 6 5 . 9 (26) -73.5b -77.3b - 7 9 . 8 (26) -93.0b - 5 8 . 7 (26) -65.65 ( 9 ) -72,Ob -64.85 (26) - 9 3 . 7 3 (30) - 7 2 . 5 (26)
Extrapolated values.
c
j
(H2@* H o ) estimated at 2050
very small unless the elements are grossly out of balance. At 4000' K., allowance for recycle of by-products and removal of acetylene (as well as for the effects of C2H and C2N) results in calculated effluent HCN concentrations of about 27 mole % a t 1000 atm., or ofabout 23 mole % a t 100 atm. COMPARISON WITH CURRENTTECHNOLOGY. The above HCN concentration may be compared with the 5.8 mole yo reported (27) for the Andrussow process, in which methane, ammonia, and air are reacted over a platinum catalyst a t about 1800' F. and 2 to 3 atm. Even the relatively low yield of 5.8 mole yoin that commercial process is far above the equilibrium value a t 1800" F.; consequently the reaction mechanism must proceed through H C N as an intermediate, with the formation reactions being much faster than the decomposition reactions to Hz, N,, carbon, water, etc. The process is made feasible
Equilibrium Constantso for the Formation of Polyatomic Products from the Ideal Monatomic Gases, at T o K.
Reaction 1. 2 H i + H z 2. 2c1-t cz 3. 3 c i + c 3 4. c1-t c, 5. 2 N 1 + N z 6. Ci Hi+ CH 7. Ci 2 H 1 + CH:! 8. C I 3Hi + CH:, 9. Ci 4Hi + CH., 2H1+ CzIHz 10. 2Ci 11. 2 c 1 4 H i -t CzIHa HI+" 12. Ni 13. Ni 2H1 -P NHZ 3H1+ NHB 14. Ni 15. C i N I + CN 16. 2C1 2N1 + CzI'JZ 17. Hi Ci N I 4. H C N
+ + + + + + + + + + + + +
a
- H o " ) / T , Cal./,Mole
2000 3.80, +5 2.63, 9 7 . 9 5 , $20 3.02, 10 1.35, 18 1.62, 3 7.07, 8 5.01, 13 1.82, 18 2.82, 23 8.91, 26 4.22, 3 7.38, 7 5.37, 12 1.15, 13 3.98, 33 5.25, 20
+ + + + + + + + + + + + + + +
3000 4.01, 1 1.11, 4 1 . 0 0 , +9 1.90, 4 5.25, 9 1.29 4.76, 1 5.85, 2 2.00, 3 8.32, 8 7.25, 6 3.35 1.25, 1 1.24, 2 2.51, 6 2.51, 15 2.63, 9
+ + + + + + + + + + + + + +
4000 3.95, 2.29, 1.04, 1.57, 3.25, 3.45, 1.18, 1.90, 6.31, 4.29, 3.90, 9.15, 4.78, 5.80, 1.38, 1.90, 5.35,
-
+ + + + -
-
+ -
+ + +
1 1 3 1 5 2 2 3 5 1 4 2 3 4 3 6 3
5000
6000
2.35, - 2 5.35, - 1 2.75, - 1 2.28, - 1 9.60, 2 3.80, - 3 7.40, - 5 6.60, - 7 1.50, - 9 1.88, - 3 2.00, - 10 1.02, - 2 4.04, - 5 2.45, - 7 1.56, 1 6.69 2.22
3.71, - 3 4.21, - 2 1.20, - 3 1.38, - 2 1.82, 1 8.50, - 4 2.51, - 6 4.37, - 9 1 . 2 6 , - 12 2.35, - 6 1 . 4 5 , - 14 2.37, - 3 1.62, - 6 1.41, - 9 7.70, - 1 1.51, - 3 1.20, - 2
+
+
+
Floating decimal notation.
VOL. 1
NO. 1 F E B R U A R Y 1 9 6 2
59
ANODE monitored by the Materials Laboratory, Wright Air Development Division, Wright-Patterson Air Force Base, Ohio.
VOL. 1
NO. 1
FEBRUARY 1962
61
