METHANE-OXYGEN FLAME STRUCTURE. 11. CONSERVATIOX OF MATTER AND ENERGY IN THE ONE-TEKTH ATMOSPHERE FLXME’ BY A. A. WESTENBERG AND R. M. FRISTROM d pplied Physics Laboratorg, The Johns Hopkins Unioersity, Silver Spring, Maryland Recezued February 18,1960
The experimental data on temperature, composition and aerodynamic profiles through a flat, premixed CE14-02flnme obtained by techniques described in paper I of this series are analyzed in terms of matter and energy conservation. The composition profiles for the seven stable species found in the flame are corrected for molecular diffusion, using diffusion coefhcients measured in this Laboratory, and the resulting flux distributions are shown to give a satisfactory balance of carbon and hydrogen through ibe flame. The fluxes of enthalpy by means of convection, diffusion and conduction are given separatcly, and summed to show the degree to which energy conservation is fulfilled by the data. The various approximations used in the treatment are critically discussed, and it is shown that the general reliability of the results has been improved considerably over previous laminar flame structure analyses.
Introduction The dcvelopinent of experimental techniques for the measurement of temperature, composition and aerodynamic profiles through laminar flame zones haE; been reported in earlier publications of a series from this L a b o r a t ~ r y . ~ JThis work culminated in a set of data obtained in a stoichiometric, premixed, propane-air flame of conical geometry at ‘/4 atm. pressure. Paper IV of that series4reported the analysis of these data in terms of material transport. The experience gained up to that time pointed the way to various refinements and changes in the experimental techniques, and also to the desirability of studying a flame system which was chemically simpler insofar as the number of stable species present is concerned. The changes in technique were described in detail in paper I of the present series6 In brief summary, these included (a) A fiat-flame stabilized on a screen burner was used instead of the conical flame as in the previous work. This brought about some simplification in the geometrical handling of the data, and in the physLcal manipulation of the apparatus. (b) Thci operating pressure was lower (0.1 instead of 0 25 atm.) which gave a thicker flame and hence eased the requirements on spatial resolution. (c) Gas sampling and mass spectrometer analyses were done in a continuous flow system instead of batch-wise. This afforded much better precision, arid circumvented wall adsorption difficulties. In particular, this system permitted good analyses for water to be realized. (d) Temperature profiles were obtained with a fine, silica,-coated Pt-Pt, 10% llh thermocouple rather than by particle-track photography (which was used only as a supplementary technique). Considerably better precision thus was attained. (e) Improvements in controlling and monitoring the flow of gases to the burner were introduced which led to bebter flame stability. A monitoring (1) Supported by the Bureau of Ordnance, U. 3. Navy, under contract NOrd 7386. (2) (a) R. hZ. Fristrom, W. H. Avery R. Preseott and A. J. M a t tuck. J. Chem. Phys , 22, 106 (1954): (b) R. M. Fnatrorn, zbrd., 24, 888 (1956). (3) R. M. I ristrom, R Freecott and C. Grunfelder. Combustion & i lame. 1, 102 (1957). (4) R. M. Fristrom and A. A. Weatenberg, kbzd., 1, 217 (1957). ( 5 ) R M. Friatron~C. Crunfelder and S. Favin THIB JOURNAL64, 1386 f l Y b 0 ) .
thermocouple was mounted just downstream of the screen, which allowed the flame position to be monitored a t all times. The chemically simpler flame system finally decided on was a mixture of methane and oxygen. It was thought that this represented a reasonable compromise between chemical simplicity, ease of handling, and some degree of general interest as a common combustible mixture. ;\is shown in reference 5, this flame contained five major stable species (methane, oxygen, carbon monoxide, carbon dioxide and water) and two minor ones (hydrogen and formaldehyde) for whim analyses mere made, which is considerably simpler than the twelve components found in the propane-air flame. S o other species (other than impurities) a t a eoncentration greater than 0.01% were found. One other important improvement incorporated in this new work should be rnentioncd. This is that experimentally determined molecular diffusion coefficients were used in the data analysis to be described. In view of the pronounced-in some cases the predominant-effect of diffusion on the flux profiles of the various flame constituents, this is a decided gain in the reliability of this general approach to laminar flame studies, particularly in the derivation of chemical kinetic information from the data. In the previous work on propane-air fiames it was necessary to use values of the molecular diffusion coefficients calculated from kinetic theory and empirical low temperature viscosity parameters, so that the reliability of the diffusion Coefficients a t flame temperatures was quite uncertain. Since then a new method of measuring diffusion coefficients up to moderately high temperatures (-1200°K.) has been developed in this and used specifically to measure the pertinent coefficients for the methane-oxygen flame.g The present paper describes the nnalysis of the data on the methane-oxygen flame from the viewpoint of the transfer of mass and energy. It is believed that the various changes and refinements noted above have contributed to making the analysis of this flame considerably more reliable than was possible before. ( 6 ) R. E. Walker and A. A. Westenberg, J. Chern. P b v ~ 29, , 1139 (1958). (7) R. E. Walker a n d A. A. Westenberg, zbzd., 29, 1147 (1958). ( 8 ) R. E. Walker and A. 4 Westenberg, zbkd.. 31, 519 (1959). (9) R. E. Walker and A. A. Weatenhrrg, rbtd. 31, 136 (l9GO).
A. A. WESTENBERG AND R. M. FRISTROM Prvfai =
TEMPERATURE (OK).
350
500
1000 1500 1750
1850
1900
VOl. 64 ma
=P ~ / R T
-*-
0.1
0.2
0.3
0.5
0.4
t (cm)
Fig. 1.-Concentration (f) and flux fraction (G) profiles of methane through flame zone. TEMPERATURE (‘(0
12350
500
to00
1500 1750 I
I
1850
1900
I
I
n?
p, 1950 2000
0.5 0.7 0.9
Z (cm)
Fig. Z.-Concentmtion ( f ) and flux fraction (G) profiles of water through flame zone. TEMPERATURE ( O K ) -
350 4
500 2
r
IO00
r
1500 1750 -
1850 7
p
1950 2000
1900
0.5 0.7 0.9 ~
t (em)
Fig. 3.-Concentration (f) and flux fraction (G) profiles of carbon dioxide through flame zone.
(1)
where p is density and a is the cross-sectional area of a streamtube, and the equation of state (2)
where A 7 is the mean molecular weight and the other symbols are conventional. Since the thermocouple temperature profile was much smoother and more reproducible than the particle-track velocity profile, it was felt that this procedure of deriving the velocity from the temperature by fitting at the measured point where the particle-track data were most reliable was preferable. Note that this is the reverse procedure to that used previously4 where the temperature profile was derived from particle-track velocity measurements. The problem then arises as to how best to superimpose, spatially, the temperature profile (as discussed above, the gas velocity and area ratio profiles were coupled to the temperature, and thus not independently variable) and the composition profiles determined by independent means. In paper I it was pointed out that the fact that temperature and composition are determined with different devices (thermocouple and sampling probe) leads to an uncertainty in referring both to a common spatial origin even though the positions of both are measured relative to a k e d point on the burner (the monitoring thermocouple). Since the pneumatic (sonic flow) probe temperature measurements were taken with a probe similar to that used in sampling, presumably a temperature read in this way would coincide automatically with the appropriate composition point. Thus the method used to determine the absolute origin was to superimpose the thermocouple and pneumatic probe temperature “knees,” ie., the point of intersection of straight lines extrapolated from the hot gas region and the region of most rapid rise in the temperature profiles. The composition profile was then fixed relative to the thermocouple temperature profile. Additional discussion of this problem is included in the next section. The distance coordinate z was taken to be zero a t the monitoring thermocouple just downstream of the screen. Conservation of Matter With the primary data on composition, temperature and mass average gas velocity available, the first step in the analysis was to take account of diffusion effects. The quantity Gi is the fraction of the total mass flow a t any point in the flame which is due to chemical species i, and is given by
Preparation of the Data As described in detail in paper I of this series15 the flame used in this study was flat, and held a t a pressure of 7.60 cm. The initial mixture G, = f t ( u + v,)/u (3) composition (mole fractions) aside from traces of where fi is the concentration expressed as mass impurities totaling less than 1% (argon, nitrogen, fraction a t any point and Vi is the diffusion velocity. carbon dioxide and water) was It is a net flux variable which includes a positive ZCH, = 0.0785; 50% = 0.914 contribution from diffusion if the concentration of The data finally used in the subsequent analysis i decreases downstream, or a negative contribution consisted of a set of concentration profiles for the in the opposite case. As in the previous work,* stable species present, a thermocouple temperature the diffusion velocity Vi was calculated by assumprofile, a streamtube area ratio profile, and a mass ing first, that each species i could be regarded as 5~ average gas velocity profile. The latter was ob- trace component in the mixture and, second, since tained from a measurement of the final (hot bound- oxygen is present in large excess everywhere, each ary) gas velocity uf by mans of particle-track species i could be treated as being in a binary mixphotography and the temperature profile, making ture with oxygen (see Appendix A). Under these conditions the approximate relation use of the continuity relation
Oct., 1960
CONSERVATION OF MATTER AND ENERGY IN Vi =
- (Di/~i)(d~i/dz)
(4)
may be used, where Di is the binary diffusion COefficient with oxygen. (This also neglects the effect of thermal diffusion, a point which is discussed in Appendix B.) Equation 4 was used to compute the Vi for d l the flame species (except oxygen, of course) a t each point throughout the flame. The diffusion velocity for oxygen was then obtained from the required normalization condition (Ni is the NiMiVi = 0
OXYGEN-METHANE FLAME
THE
6350 N
500 I
'
TEMPERATURE ( O K ) 1500 1750 1850
1000 i
l
l
1
I
(10) J. 0. Hirschfelder, C. F. Curtis8 and R. B. Bird, "Molecular Theory of Gases and Li.quids," John Wiley and Sons, Ino., New York, 1Y54.
Fig. $.-Concentration (f) and flux fraction (G) profiles of carbon monoxide through flame zone. TEMPERATURE (OK.).
0.10
350
500
1000 1500 1750
1900 1950 2000
1850
i
?J 0
X
0.05
z
243 0.04
'.
I
v)
0.1
I
I
I
I
0
0.4
0.3
0.2
i
The diffusion coefficients D i used in eq. 4 were measured :is a function of temperature in this L a b ~ r a t o r y . ~The point source technique used permitted measurement of the gas pairs C02-Oz and HzO-C12 up to about 1100"K., while CO-02, H2-02, and CH4--02were limited to slightly lower temperatures because of self-ignition. In all cases, however, the temperature range covered was enough to permit fitting the data to the appropriate kinetic theory formula^,^ and reliable extrapolation to the highest temperatures needed in this flame (2O0O0I5.). Diffusion coefficients for the CH20-02pair were not measured. For this minor component, t,he necessary values were obtained from kinetic theory,1° using the Lennard-Jones (6-12) potentia,l and viscosity parameters. Since the latter are unavailable for formaldehyde, the values for methanol mere used, this being a closely related molecule of similar size and mass. Table I lists the values of D i cs. temperature. The underlined values were ext,rapolated using the Lennard-Jones 65-12) pot'ential with parameters fitt,ed to the lower temperature data. Having all the diffusion velocities V i a t each 0.02 em. interval throughout the flame, the mass flux fractions Gi were computed from eq. 3. These are shown as the broken curves in Fig. 1-7. The great importance of diffusion is obvious in all cases. It will be noted that some of the Gi curves (water, carbon dioxide, carbon monoxide and hydrogen) have regions of negative values, which would indicate a net upstream flux of these species. While there does not amppearto be any a priori reason why this is not possible, the negative gradient dGi/dz which exists upstream of these minima also implies tha,t these species are undergoing a net disa,ppearance due to chemical reaction. I ' .
'IF---
t (crn).
molar density of species i, and Mi its molecular weight) which must be fulfilled in view of the definition of diffusion velocity (relative to the mass average gas velocity v). The concentration gradients required in eq. 4 for each species were obtained by numerical differentiation of the smooth curves drawn through the experimental dat.a, such as are shown as the solid curves in Fig. 1-7. The numerical process was supplemented by graphical differentiation a t those portions of the curve where the slope changed rapidly. The internal consistency of the differentiations was checked using the requirement that (dzi/dz) == 0, since xi = 1.
X.
1900 1950 2090
I
(5)
i
i
1395
~
W
0.5 0.5 0.7 0.9
t (crn)
Fig. 5.-Concentration (f) and flux fraction (G) profiles of hydrogen through flame zone. TEMPERATURE 350
C'O.61I
500
1000
1
I
(OK)
1500 1750 I
1850
1900
I
I
I
:I X
t (crn)
Fig. B.-Concentration (f) and flux fraction (G) profiles of formaldehyde through flame zone. TEMPERATURE 98350
500
I t
1000
I
I
I
I
0.1
78'
1500 1753
0.2
,
(OM)
1850 I
' l i19502( '
1900
I
0.3
'E
2 (crn),
Fig. 7.-Concentration (f) and flux fraction (G) profiles oxygen through flame zone. _. .
. .
-
IO
_.
.. .
04
Since it is diflicult to see how this could happen, it seems likely that the negative Gi regions are not real and should be regarded as errors in the overall treatment. By the same token, the positive
A. A. WESTENBERG AND R. M. F’RWPROM
13‘36 I
Conservation of Energy It is of interest next to examine the data in terms of energy considerations. Since the flame is an
1
Fig. 8.--Conservation of carbon and hydrogen (atom balances) through flame zone.
maximum in the GO,probably is not real since it is a direct consequence of the negative G values for the other species, by the normalization procedure used to obtain the oxygen diffusion velocity. TABLE I BINARYI)IFFCrSION
T.
-
D(cm.*/seo.)
CHcOn
COrOn
300 500 700 900 1100 1300 1500 1700 1900 2100
0.226 0.581 1.05 1.63 2.29 323 3.86
0.161 .419 .;ti7 1.19 1.68 2.23 2.84 -
c75
5 2
Ha0-On
0.288 0.692 1.22 1.85 2.58 3.41 __ 4.32 5.32 _ _ 4.21 _ _6.40
4.98
~
CO-02
0.821 2.09 3.76 5.79 8.14 1- G 13.7 _. _16.9 _ 20.3
0.224 .542 .956 1.45 2.03
7.55 24.0
i
n,Gi/Mi = constant
-
+
=0
(I)
(7)
-c
where v is the mass average velocity vector, H is -+
the specific enthalpy of the mixture, and q is the heat flux vector given by (ref. 10, p. 717) q =
- Xvl’ +
-+
iV,H,T‘,
(8)
i
if the inverse thermal diffusion (Dufour) effect is neglected. X is the mixture thermal conductivity, 4
HrOa
CHzO-
On
0.180 .422 ,739 1.12 1.57 2.68 ~2.07 3.40 2.63 4.18 3.24 __ 5.03 3.91 __ 5.94 4.61 ~
As :in the previous propane-air flame,4 it is important to examine the data in terms of conservation of atomic species. If mi is the number of atoms of a particular element in a molecule of species i, it was shown that the relation
c
-*
V*(pZ”
FUNCTION O F TEM-
Underlined values are extrapolated; CH20-02 values computed from theory; pressure = 1 atm. OK.
essentially constant pressure system, the convenient energy variable to use is the enthalpy. The energy continuity equation appropriate to a quasi-one-dimensional flow with area change such as is found in the flat flame must first be derived. The basic energy equation for a steady-state system with no viscosity, radiation, or external forces may be written
-.r
COEFFICIENTS AS PERATURE
1701.64
(6)
Vi is the diffusion velocity vector, and Hi the absolute molar enthalpy of species i. The enthalpy per unit mass I? is related to the Hi by i
i
Making use of the theorem (ref. 10, p. S13) which 4
states that, if F is a vector which is tangent to the surfacef(z,y) = z, then
Equation 7 may be converted to J ( p a v y) dx dy = coii3tnnt (10) where v and q are the z-components (ie., normal to the flame front) of their respective vectors. This may be written as
+
puaa
+ pa = constant
(11)
must hold throughout the flame, since atoms are neither created nor destroyed. In the methane- the quantities p , 21, ?i and p now represeiiting suitoxygen flame, carbon and hydrogen are the two ably averaged values across the streamtube area a. elements whose conservation is to be examined, Combining the z-component of eq. 8 with eq. 11, the oxygen heing present in such excess in the form and using the quasi-one-dimensional over-all conof 0 2 that its constancy is practically assured. tinuity relation in the form Results of applying eq. 6 for carbon and hydrogen POVO = paA (E) to the Gi data given in Fig. 1-6 are shown in Fig, 8. where A = a/ao and the subscript “ o J 1 refers to The data are given as percentage deviation from the cold boundary ( z k , the screen), eq. 11 becomes the initial value of the summation, L e . , the cold finally gas composition upstream of the screen. (Because po’pB - AX(dT/dz) + A S,H,T’, = (13) of diffusion, .the probe composition just downstream z of the screen at z = 0.03 em. is not quite equal to the true cold gas composition.) The balances are assuming that gradients in temperature and comconsidered quite good, and are definitely better position are essentially zero at the screen. than those in the earlier propane-air work. The This equation represents the enthalpy conservntion through the flame zone in terms of the flux worst deviation is -12% for carbon and -9% for hydrogen, while in most of the flame the balances of enthalpy per unit of inlet area at the screen. are considerably better (average deviations through The first term on the right side is the flux due to the flame are about -3%). While the atom convection, the second is that due to conduction, balance is not a very sensitive test of the sampling and the third that due to diflusion. These terms data and the diffusion corrections, the fact that it were evaluated for the experimental methaneis reasonably good certainly indicates there are no oxygen data. The specific enthalpy was obtained large errors in the data as a whole. from eq. 9 using tabulated molar eiithalpies from
o c t., 1960
C(OKSI~liVAT1ONO F MATTER AND
ENERGY IN THE
1397
OXY GEN-1IETHANE F L A M E
standard sources. l1,l2 The enthalpies for formaldehyde were obtained from the heat capacity data of Stevenson and Reach. l 3 The thermal conductivity was taken 1,o be that of pure oxygen, rather than attempting the exceedingly laborious computations for mixtures (for which all the necessary data are not avitilable anyway). Because of the preponderance of oxygen, this approximation was adequate (3ee Appendix C). The thermal conductivity of oxygen has not been measured up t o the temperatures required here, so it was calculated W , by a semi-empirical procedure : the translational , -A (or monatomic) thermal conductivity Xmon was obtained from the KBS tabulation’l of viscosity (7) Fig. 9.-Conservation of energy (enthalpy balance) and enthalpy fluxes through flame zone. by means of the rigorous theoretical (first approximation) relation vection term itself indicates that the sign of the hmnn = (15/’4)(R/iW(~) latter is not reliably established in this case. With no absolute criterion or prior data to comThe improved E d e n - t y p e correction of Hirschpare, it is difficult to say how good this energy balfcider14 then was applied, i.e., to account for the ance result is. It might well be that the neglect X/X,, = 0.4G9 0.354 (CJR - 1) of free radicals (which show up as stable products effect of internal degrees of frcedom. The tempera- in the sampled gas, of course) is more serious from ture gradicnt was, obtained by numerical differen- an energetic point of view than in the material tiation of the temperature profile, and the other balances. At any rate, the results given in Fig. 9 quaiititieb in eq. 13 were already available. seem reasonable, and there are no gross violations The various eiy,hnlpy fluxes are shown in Fig. 9. of energy conservation. As noted in Appendix The conduction term IS, of course, negative, since C, the actual mixture thermal conductivity is it al~vaysrepresents a flux of heat (positive en- probably greater than the pure oxygen value asthalpy) upstream. The diffusion term would sumed, and this would tend to made the total be expected t o be positive relative to the inlet flux energy balance somewhat better. as it is, since the reactants of high enthalpy diffuse Acknowledgment.-The authors are indebted to downstream and the products of low enthalpy Mr. Stanley Favin far performing the numerical diffuse upstream, both effects constituting a net computations reported herein. positive m,halpj flux. (It seems unlikely that Appendices the effects of intermediates, which diffuse in both A. Binary Mixture Approximation for Diffusion. directions depending on which side of their maximum in coilcentration one considers, would alter -The use of rigorous, multicomponent diffusion this statement. ‘They have enthalpies lower than coefficients in a mixture even as relatively simple as the reactanl s and higher than the final products.) dealt with here is completely impractical, and (forWhether the convection term, i.e., the specific tunately) not necessary either. For any species enthalpy prqfile, (.onstitUtes a positive or negative i present in small concentration in a mixture, it flux depends up01 the relative magnitudes of the can be shown” that the effective diffusion coefficonduction snd diffusion terms, as has been noted cient of species i is closely approximated by by Lewis and von Elbe.I5 These terms depend upon their rixspective transport coefficients. In the special case (the theoreticians’ favorite) that all j#i thc binary Idiffusion coefficients are equal to each This relation has been verified experimentally. 18,1g other and t o the thermal diffusivity X/pC (all If, in addition, one species k is present in such Lewis numbers unity), the conduction and difexcess that all the other components may be refusion fluxes cancel and the convection flux is constant through the flame. This has been dis- garded as traces, then the above simplifies still cussed receiitly b,v €Iirsclifelder.l6 In the data of further to DI-mia = Di E D i k (‘4% Fig. 9, the caoiwection term shows a small positive maximum, but 1 he present authors attach no which is the approximation used in eq. 4. This general significance to this. The sum of the three is certainly justified. I n the flame considered here, fluxes shonn as the dotted curve would ideally in no case did the diffusion coefficient Di-oo, be constant throughout the flame. The fact that differ from the calculated from eq. A1 by the sum shows a maximum greater than the con- more than 3%, which is about the experimental error of the diffusion coefficient measurements. (11) J Hilserrath. et a2 “Tables of Thermal Properties of Gases,” NBS Circular 584 1955 B. Neglect of Thermal Diffusion.-For any ,12) b. D. Ro3sin1,et d.,”Selected Values of Physical and Thermotrace component, the expression for the diffusion d, nnmic P-opri’res of H>drocarbons and Related Compounds,” (17) 3. 0. Himchfelder and C. F. Curties, “Third Symposium on AmerTcan Petiolenm Institute. Carneqe Press, Pittsburgh, 1953.
3L
-J_--I02
03
0.
0,
I ,om,
+
13) D P. Stwenson and J. Y Beach J Chrm P h y s , 6 , 25 (1938). (11) J. 0. Hirschfeide- t b d., 26 274 ( 1 5 ) B. Lerris and G r o n Flbe, ‘Combustion, Flames and Explosions of Gaseii ’* 4rademic Presa New York, N. Y , 1951, p. 345 (16) I. 0 IIirwhfrldei Phys Fluzda, 3 , 109 f
(1957).
(1960).
Combustion, Flame and Explosion Phenomena,” Williams & Wilkins, Baltimore, Md.. 1949, p. 124. (18) D. Fairbanks and C. R. Wilke, Ind. Eng. Chem.. 42,471 (1950). (19) N. deHaaa, R. E. Walker and A. A. Weetenberg, J . Chem. Phys.. 3’2, 1314 (1960).
R. R. IRANI A N D C. F. CALLIS
1398
velocity including thermal diffusion may be written lo
v,E - 5 X*
[z I.!!?] &
1' dz
(B1)
where the F ositive sign holds if the trace i is heavier than the II sin component, and the negative sign if the trace is lighter. k~ is the thermal diffusion ratio given by kT
S zk D,T/NIM,D,
(B2)
DIT being the trace thermal diffusion coefficient, and N the total molar density. In most cases, DiT itself is positive if the trace is heavier and negative if it is lighter than (in our case) oxygen, so that k T is generally positive. Therefore, the common situation is for a heavier trace species to thermally diffuse upstream and a lighter species downstream. The thermal diffusion correction to the diffusion velocity was carried out for the case of HzO, for which it probably would be as large as for any of the major species. The necessary thermal diffusion data were computed from our concentration diffusion coefficients and viscosities as out-
Vol. 64
lined by Amdur and Mason. 2o At most , the thermal diffusion contribution to VH*O was about 10%. Thus, while the effect is not always as small as one would like, the error caused by its neglect is a t worst probably no larger than others, and the simplification this neglect brings to an already complex analysis is most welcome. C. Pure Oxygen Approximation for Thermal Conductivity.-The use of XO, instead of the true mixture thermal conductivity was occasioned primarily (as with the other approximations) by the great simplification it afforded. The actual flame mixture was composed throughout of roughly 80% oxygen, with the remaining 20% mostly lighter components (except for COZ) which might be expected to increase the thermal conductivity over that of pure oxygen. To get some idea of the error introduced here, an approximate ca1culation2l was made of X for a mixture composed of 85% oxygen and 15% water a t 1500'K. This gave a value about 15% higher than the pure oxygen value. Such an increase in X would improve the enthalpy balance of Fig. 9 somewhat, (20) I. Amdur and E. A. Mason. P h y s F l u i d s , 1, ,370 (1958). (21) R. S.Brokaw, J . Chem Phya., 29, 391 (14581.
METAL COMPLEXING BY PHOSPHORUS CORIPOUNDS. I. THE THERMODYNAMICS OF ASSOCIATION OF LINEAR POLYPHOSPHATES WITH CALCIUM' BY R. R. IRAXI AND C. F. CALLIS Research Department, Inorganic Chemicals Division, Monsanto Chemical Company, St. Louis 66, Missotcri Received February 19, 1960
The stabilities of calcium complexes of the linear chain phosphates have been evaluated, from nephelometric titrations in the presence of an added precipitating agent, as a function of pH, temperature, ionic strength and length of the phosphate chain. At high pH values the number of phosphorus atoms that are in equilibrium with one calcium ion was evaluated and found to be 2, 3, 4,4 and 5 for linear phosphates with average chain lengths of 2, 3, 6, 14 and 60, respectively. The free energy change a t 25' accompanying the association of calcium with P z O T - ~HPzOT-~, , PgOla-5,HP301a-4 and HzP301p-a was found to be -7.6, -4.9, -9.5, -5.3 and -5.3 kcal., respectively. For the longer chain phosphates the corresponding free energy changes were found to be -10.2 f 0.2 kcal. and independent of chain length. For CaP301~-3 and CaP20T-2 the enthalpies of association were found to be -3.2 and 4.6 kcal., respectively, whereas for the long chain phosphates the values were negligibly small. A large positive entropy change (21-46 e.u.) was found to accompany association in all cases. This positive entropy change is attibuted to the release of waters of hydration upon association. The frer energy, enthalpy and entropy of formation of aqueous pyrophosphate and tripolyphosphate anions are evaluated from published data.
Introduction (1) to check and extend by an indepcndent method The ability of the polyphosphates to form soluble the results of Watters, et al.,2 and thereby test the complexes with calcium ions has been known for validity of both methods; ( 2 ) to investigate the about a century. Several investigators have re- effects of pH, total ionic strength and temperaported evaluation of complexity constants. How- ture on the stability constants in order to evaluate ever, as indicated by Watters, et aLlZmost of the the thermodynamic formation constants and the evaluations were carried out in the presence of related free energies, enthalpies and entropies of alkali metal ions that are well known to form com- complex formation; (3) to investigate the effect of plexes of their own with the polyph~sphates.~the chain length of the polyphosphates on the stah review4 on this subject appeared as recently as bility of their calcium complexes: and (4)to use the resulting thermodynamic quantities to te3t 1958. The purpose of this study is fourfold, namely recent proposed theories5-' 011 entropy changeq 7 accompanying association reactions in solution. (1) Prvsented before the Division of Inorganic Chemistry, 137th meeting .,f the American Chemical Society, Cleveland, Ohio, April, 1960. (2) J. 1. Watters and 8. M. Lambert, J . Am. Chem. Soc., 81, 3201 (1959). (3) U. P. Strauss and P. D. Ross, ibid., 81, 5295 (1959). (4) J. R. Van U'azer and C. F. Callis, Chem. Reus., 68, 1011 (1958).
(5) E. L. King, J . Chem. Educ., 30, 71 (1953). ( G ) J. W.Cobble, J . Chem. Phys., 21, 1446 (1953). (7) W. J. Hamer, "The Structure of Electrolytic Solutions," J o h n Wiley and Sons, Inc., New York, N. Y., 1959, Chapter 2 4 by J. & I , Austin, R. A. Matheson and H. N. Parton.
