Formation of Engine-Deposit Compounds bySolid-State Reactions X-Ray Dijgraction Study FK4NCES W. LAIIR
4ND
LEONARD M. NIEBYLStiI
Ethyl Corp., Detroit, .Mich. In making an x-ray diflraction study of the inorganic: lead compounds occurring in engine deposits, the importance of their formation by solid-state reactions was recognized. A study of numerous solidstate addition and replacement reactions between inorganic lead salts was undertaken. I t was learned t h a t all the compounds commonl>-found may be produced as a result of addition reactions w-hich take place in the solid state between various lead salts and lead monoxide when mixtures of these are heated a t temperatures well below their melting points. The resulting or surviving products of the solidstate reactions are determined only by the temperature and by the mole ratio of the lead monoxide to the normal lead salts. A one-to-one correspondence is shown between the temperatures which produce specific compounds on a thermal plug in a n engine and the “reaction” temperatures required for production of the same compounds by solidstate reaction. In a solid-state replacement reaction between a basic lead salt and a normal lead salt the reaction temperature is determined not by the relative stability of the reactants, but by the temper-
T
~
H E interpretation of results obtained in various studies of engine deposits has been handicapped by the limitations imposed by chemical analysis. Quantitative analyses were routinely obtained for the major elements known to be presentnamely, lead, chlorine, bromine, and sulfur-and were ordinarily expressed in weight percentages of lead chloride, bromide, and sulfate, with the balance of the lead accounted for as lead monoxide. Information on the actual compounds present was not obtainable, although it is of fundamental importance in automotive engineering and chemical studies concerned with engine deposits. The crystalline compounds which exist in engine deposits may be identified by x-ray diffraction if a library of powder patterns or tables of the interplanar spacing values of all the compounds a r c available. However, a search of the literature and a preliminary study of lead compounds revealed that the x-ray diffraction data reported in the literature are not adequate. If semiquantitative analyses are to be made, it is necessary to have preparations of each of the compounds for use in preparing synthetic standard mixtures. For these reasom, a systematic study of pure lead compounds and of their binary systems has been made by x-i ay diffraction and thermal analysis. Work on the lead chloridelead bromide (3)and lead monoxide-lead bromide ( I S , 14) systems has been completed, and studies on several other systems (lead monoxide-lead chloride, lead monoxide-lead sulfate, lead monoxide-lead carbonate, and lead monoxide-lead peroxide) arr nearing completion. During the course of these studies, several synthetic mixturrs of lead salts and basic lead salts were heated a t temperatures below their melting points. A n x-ray diffraction examination revealed that replacement reactions had taken place. The temperatures a t which the new basic lead salts appeared were known to be reasonably close t o the temperatures of the wall sur-
ature required for the solid-state addition reaction of the released lead monoxide and the normal lead salts. The crystalline form of PbO.PbCl.Br, produced from the solid-state reactions between 2Pb0 .PnBr! and lead chloride and between 2Pb0. PbCL and lead bromide is dependent on the parent structure of the monobasic lead halide formed by the initial addition reaction between released lead monoxide and the original normal lead halide. Examples are given of increased reactivity due to the abilitj of metastable yellow lead monoxide to form a reacti\e red lead monoxide when heated in the presence of a second compound with which lead monoxide will readily form an addition product. This property is believed to be important in the mechanism of the solid-state reactions studied, and its possible relation to engine conibustion phenomena is suggested. Interplanar spacing values are given for the major reflections of inorganic lead compounds commonly occurring in engine deposits: PbO.PbBr2 (two forms), PbO.PbCl2, Pb0.PbC1.Br (two forms), 2PbO.PbBr, 2PbO.PbC1, 2PbO.PbCl.Br, Pb0.PbS04, and 4PbO.PbS0,.
-
fttcea in a combustion chamher on nhich these same compounds were found. Consequently, the inipoi tance of solid state reactions in formation of compounds found in engine deposits nas recognized, and the present study of addition and replacement reactions of lead compounds in the solid state was undertaken. Examples of reactions in the solid state are common, a nuinher of them being of considerable industrial importance in the fields of metallurgy, catalysis, sintering, explosives, and the nianufacture of cement. In spite of the many practical applications and the numerous technical studies of solid-state reactions, the phenomenon and mechanism by which they occur is not well understood. It may be said, however, that diffusion is definitely the most important factor in determining both the rate and the mechanism of such reactions. This is true because the reactions are known to take place a t the boundary layer between the tn-o reactants by diffusion of one component or of the two components a t different rates within the boundary product. Regardless of the number of reactants, the reactions in the solid state are limited to reactions between two components only, because chemical combination is possible only a t the phase boundary betwern adjacent phases. Addition reactions such as A B +A B and replacement reactions such as A B CD & A D BC mav occur. Diffusion frequently occurs in solid salts and in systems of solid salts a t temperatures from a few hundred degrees be lo^ their melting points up to the melting points of the salts. Tamiiiann ($3, 24) observed that solid-state addition reactions showed a pronounced increase in activity a t the temperature of measui able self-diffusion of one of the reactants. A fundamental concept is that diffusion and conductivity of crystals, as me11 as reactions in the solid state, are performed by the disordered fraction of the lattice particles. The theory and kinetics, including type of lattice disorder, have been established quantitatively for a
+
1388
+
+
V O L U M E 23, NO. 10, O C T O B E R 1 9 5 1
1389
number of the simpler ionic crystal reactions in studies by Schottky and Wagner (21, 27) and Frenkel ( 7 ) . These authors 1i:ive shown that an ideal crystal at finite temperatures is in rvluilibrium only when a deiinite fraction of lattice particles has l ( 2 t t the normal sites and is occupying certain positions of disolder. These theoretical studies, as me11 as those of other investigators, have been carrfully considered and integratrd by ( 'ohn (6) in an extensive review article on reactions in thr solid .t:Lte. Other useful revielqq of the suhject are given by Thorwaldson (W5),by Riley (19), and in a report of a Symposium on ~'hemicalReactions Involving Solids (22) held a t the University o f I3risto1, England, April 1936, which gives the views of the leadi n xorkers ~ in the field at that time. It is extremelv difficult t o establish the diffusion and reaction r:ites of the majority of systems hecause of the complexity and il,rqIrodurihility of the phase boundary processes, n-hich are :iffrrteti by nat,ure of the surface, part,icle size, degree of contact, I t may therefore br said that most solid-state reactions are I: ructure-sensitive and that an investigation of the mechanism by i t 1iic.h they occur must he essentially of an empirical nature.
LIost solids contain sufficientnonequilibrium lattice disturbances at temperatures well below their melting points to have a considerable effect on their chemical behavior. The energy required for motion of lattice defects or of particles influenced o r created by lattice disturbances is lower than thr migration energF of equilibrium particles. EXPERIMENTAL METHOD
Mechanical mixtures of the reactants listed in Tables I, 11, and I11 were prepared. After specific heat treatments, which ale desclibed in detail below, the resulting were analyzed x-ray diffraction for the appearance of new phases and for their identification.
h Sorelco x-ray diffraction Geiger-counter spectrometer, Model 12021, was used for t'hese studies. The methods used for eter have Preparation sliecitnen been described and(5 for ). angular calibration of the goniom-
The primary lead compounds, lead monoxide (both yellow orthorhombic and the red tetragonal forms), lead chloride, lead hromide, and lead sulfate, used in the above mixtures n-ere .4CS reagent grade chemicals. Their identity and purity were checked by x-ray diffraction. The basic lead __ ~ . _ _ salts, 2PbO.PbBr2, 2PbO.PbCl2, PbO.PbSO1, and ~4Pb0.PbSOn, were prepared by fusion from t,he appropriate amounts of the primary lead comTable 1. Comparative Temperatures o f Solid-state Reactions pounds. The two hydrates, Pb0.PhRr2.H20and Ilatio Pb0.PhC12.H20,were prepared by addition of 0.5 ol W ammonium hydroxide dropwise to 3 liters of Threshold T l i r ~ s l i - ReacTemp. to carbon dioxide-free, 80" C. distilled water containold tion h l . p , of XI. p . ing approximately 25 grams of the respective lead C'oinpoiind Temp, Temo., tonipound (Both halide until precipitation of the yellow-white hyRrartant." Formed 0 C.h 0 C.b Formed, C.' Ahs.; drates ceased to he visible. The precipitates m-ere I'hO + P h h PbO.PbBX 160 275 1 4 7 (I.?) 0.56 filtered, washed with 95y0 ethyl alcohol, and ( R forin)d {Peritectirj I'hO + Pl,CI? PhO.PbC'lc 17.5 300 626 ( f , SO) 0 , Ji, dried in an oven a t 70" C. for 24 hours. Chemi(Peritectir) ( S 1orrn)d cal analyses of replicate preparations of thew hy2 P h 0 + PlrC'I? PPhO.PhCI? 210 350 69.5 ( 1 ) 0 44 drates showed a purity of 98% or better. 2PhO + PbBrz 2PhO.PhRrl 2.70 io0 709 (1.9) 0 53 PhO I'hSOg PhO.PhSO4 325 000 975 ( 1 ; ) 0.48 Thermal plug deposit studies were conducted It'hO t PhSO4 4PhO.PhSOd GO0 $9-5 ( 1 6 ) under conditions of cont,rolled temperahre and '' Coln1,arahle results oiliainpd lor Ilotli red irtraponal and FrllobY orthorhonibic furni.: oi fuel-air ratio. Deposits were obtained on the sur1 'I a, face of an air-cooled thermal plug inserted in the' Tenilwrc+tnrrs are considered reliable t o z5' C. for temperatures below 200' C.. combustion chamber of a Labco 17.6 engine. For +.loo C., for ZOOo t o 3OO0 C . . and zt l 5 O C . for higher temperatwen. ' Roiirreb o f melting ~ i o i n tdata a r c indicated hy reference nuinhers f o l l o ~ i n temperatilre g the present studies, the engine n-as operated at \ XI\lPS. 1800 r.p.m., wit,h wide-open throttle, 100" F. in11 Pol>-niorphic form. o f inonohnsic lead halides discussed belon-. ( s t ? .
~
-
I
.
Table 11. Solid-State Replacement Reactions
-
Compounds Resulting a t Tetni)eraturra" 01 \Iiut,iire
Reactant;
1-0.
1'hO.PhSOr
T
+ I'hRrr
+ +
Phrl!
+ + +
+
+
+
+
''
11
,f
5000
c.
600' and 700° C
PbO.PbSO: PbO.PhS0r PhO.PhCl>h PbO.PbSO4 PhO.PhSO4 2 PbO.PbBrz PhO PhSOi PbCI? PhO.PhSOa PhO.PbSO4 x PhO.PhCI? I'hO PhSOr PhBr? PbO.PbSOrc PhO.PbSOr 4 PbO.PhBn I'bO.PhCl?.li?O PbO PbSOI PhSOI4 PhO.PhC'I? .5 PbSOd PhO PhSO, PhO.PbBr2.HzO PhS0le PbO.PhSOic 6 PbO.PbBrz 2PhO.PhClz 4PbO.PhSO~t PhCI: 4PbO.PhSOa. PbO.PbClz 7a PbO.PhSOr 2PhO.PbCI?. PhO.PbSO1 4PhO.PhSOr t 2PhClg PhO.PhCln(h). ?PhO.PhCI? ib PhO.PhSO4 4PhO.PbSO4 C ~ P I I C I ? PhO.PhClz(h), PPbO.PbCI? IC PhO.PhSO4 4Ph0.PhS01, PhO.PhBr?' 2PhO.PhBra 4PhO.PhSO4 PhBr! Sa PbO.PhSOi ZPhO.PbRr?. PhO.PhSOa ..... 2PhO.PhBrz .Il'hO.PhSO< PPhRrr 8h PhSOd Ph0.PhBr2h. PPbO.PhBri 1PhO.PbSOr -C 4I'bBrz RC PhSOI PhO.PbSO; PhO.PbSOr 2PhO.PhClz t PtJbOd !?a ZPhO.PhCI> PhO.PhCl? PhO.PhSO8 PhO.PhRO1 :'PhO.PlrCI? 2 2Pb.504 1-o reaction Yh PbCl? 2I'iiO.PhBr? PhSOa S o reaction PbO.PbSO4 PhO.PhSO1 103 2PhO.PhBri 2PbO.PhBrz 2PbO.PhBrr PhO.PbSOa PPhPO4 S o reaction PhO.PbSOa 1Oh PhBr? 0.2. t o 1-gram rnixiiirri h e a t ~ dfor 2 iroiirs, crcel,t 7b, 7c. 8h. and Sc which were .?-gram mixtures heated for 24 hours. s form. K form. Po1ne PPhO.PhCI? produced in mixture 3 a t i0O0 C. and in mixtiire 7a a t 300O C. Some 2PbO.PbBrr produced in mixture 8a a t N O o C. llydrates used as source of PhO.PhClz and PhO.PhBrz. 1
PhO.PhSOr
230° C. PhO.PbClzb PbSOl PbO.PbBrzC PbSOI PbO. PbCl,h*d I'hSO4 PhO.PhBrrC PbSOi PhO.PhClzf PhSOI PbO.PbBrt9 PhSO4 PhO.PbSOid PhO.PhCl?td PhO.PbC12 PhSO4 PbO.PbClib PbSOa PhO.PbSOid PbO PhBr2Cjd PhO.PbBrrC PhSOd PbO.PbBr2 PhSOi S o reaction
i 31 form. I. form a t ZOOo C., L and S forins a t 260'
C., and R form a t 300' C.
..
ANALYTICAL CHEMISTRY
1390 Table 111.
Solid-state Replacement Reactions Involving Solid Solution
Compounds Resulting a t Temperatures" of 600" a n d 700' C. 11 PbO PbO.PbC1.Rrb PbO.PbC1.BrC PbC1.Br 12 PbO.PbClz.Hz0 PbBrr PbO.PbCI.Brb PbO.PbC1.BrC PbCI.Br 2PbO.PbCI.B: 13 PbO.PbBrz.Hz0 PbCIz PbO.PbC1.Brh PbO.PbC1.Br PbC1.Br 2PbO.PbCl.B; 14 2PbO.PbBrz PbClz PbO.PbC1.BrC PbO.PbCI.Br 2PbO.PbCI.Br 15 2PbO.PbClz PbBrz PbO.PbC1.Brd PbO.PbCI.BrC 2PhO.PbCl.Rr 0.5- t o 1-gram mixtures heated 2 hours. Mixture of N and R forms. N form. R form.
hlix t ure SO.
+
Reactants PbCIz PbBrz
+ + +
250' C.
+ +
a b C
d
let-air temperature, 180' F. jacket-coolant temperature, and a t approximately maximum-poiver ignition timing. The mean t,emperaturesof the thermal plug tips were controlled to &lo0 F. during the course of a run, which was normally of 6 hours' duration, This uniformity was obtained by cont,rolling the flow of the air coc>laritto the thermal plug by means of a Brown Elect,ronik controller ( M c del 152CIP). SOLID-STATE ADDITION REACTIONS
predicting the temperatures a t which a solid-state reaction might occur. These experimental values are close to the average value of 0.57 reported by Tammann (23, 24) for solid-state addition reactions of inorganic substances. He observed that the reaction temperatures were often the temperatures a t which appreciable selfdiffusion occurs for one of the reactants. From a survey of a large number of solid-state reactions he concluded that in an addition reaction the ratio of the temperature of measurable self-diffusion of one of the reactants to the melting point of the compound formed (both in degrees absolute) is approximately 0.3 for metals, 0.57 for inorganic substances, and 0.9 for organic compounds. -411 the compounds listed in column 2 of Table I were readily prcduced in a relatively pure state, with the exception of 4Pb0.PbS04, which required the highest reaction temperature and was always accompanied by some PbO.PbSO4. Attempts to prepare 2PbO.PbSOa by solid-state reactions on heating a t temperatures to and including 700" c'. were not successful. At teniperatures up to 400' C. the resulting products were mixtures of lead sulfate, lead monoxide, and lead tetroxide. At 500' and 600' C. some PbO.PbSO4 is formed and at 700" C. a mixture of Ph0.PbSOd and 4Pb0.PbS04 is produced. A preparation of 2Pb0.PbSOd obtained by heating a 2 to 1 mole mixture of lead monoxide and lead sulfate above the melting point of 961' C. (16) and cooling rapidly was found to decompose on heating for 24 houis at temperatures of 400", 500", and 600' C. into a mixture of I'hO PbSOa and 4PbO.PbSO4. The fact that the dibasic sulfate decomposes a t these temperatures may account for the inability to prepare it by solid-state reaction and for its apparent absence in engine deposits. Polymorphism of Monobasic Lead Halides. From a study involving the dehydration and subsequent heat treatment of the hydrates, PbO.PbCI,.H,O and PbO.PbBr,.H,O, it has been learned that the monobasic lead halides may exist in several polymorphic forms. The thermal relationships of the several forms are indicated in Equations 2 and 3, in which the letters L, AT, N, and R are used to designate the individual forms.
In thc study of the mechanical mixtures of lead monoxide and various lead salts indicated in Table I, one series of experiments was performed in which 1-gram mixtures were heated a t successively higher temperat'ures in open magnesium oxide crucibles for a constant heating time of 2 hours. These conditions were selected to cover those which might exist in an engine, in order that the reactmiondata obtained might then be applied to studies related to the mechanism of the formation of engine deposits, These conditions were selected also because preliminary experiments had 9hoM-n that heating a 1-gram sample for 2 hours gave data which were reliable and useful for following the coursc of the reactions and for making a comparative study of the temperatures required for production of specific compounds. ifter the respective heat treatments, the requiting mixtures ivere e\A 4 amined by x-ray diffraction for the appearance of new Pb0.PbBr2.H20-+-PbO.PbBrp (I, form) + Pb0.PbBr2 ( S form) 125O to 210° C. 210' t o 260' c. phases. The temperature a t which a new phase was well - HzO defined in the powder patterns has been designated thci A ?r +Pb0.PbBr2 (R form) +PbO.PbRrp ( N form) (2) ',reaction" temperature. 260' t o 450" C . 4500 c. A second series of experiments was performed in which 5-gram mixtures were heated at higher Pb0.PbC12.H20 PbO.PbC1, (I, form) Pb0.PbC12 ( A I form) Deratures in open magnesium oxide crucibles for a con90' t o 150' C. 150' t o 326' C . HzO stant time of 48 hours. The lowest temperature a t which 1 the formation of a new phase was detected by x-ray diffraction +PbO.PbC1, ( N form) (3) has been designated the "threshold" temperature. For the re325' C. actions studied, it hss been observed that, in general, the longer Material balance elperiments and chemieal analyses have the heating time the lower the temperature required for initishown that in each case one molecule of water is lost nith the ation of the reaction. The reaction and threshold temperatures formation of the first, low-temperature L form. No furthei lost as defined here are for convenience in making a comparative study of water oocurred on heating to produce the higher temperatui e of the temperature requirements of the specific reactions. forms. The I, forms of the two halides have isomorphic strucThe threshold and reaction temperatures are given in Table I tures, and the N forms are also isomorphous. A crystalline f o r m for production of the compounds, PbO.PbBrz, PbO.PbCI2, of Pb0.PbBr2 isomorphous Hith the U ! form of PbO.PbC12 has 2Pb0.PbC12, 2Pb0.PbBrz, PbO.PbSO1, and 4Pb0.PbS04. A not been observed, and a rry5talline form of PbO.PIiC12 isomorgeneral equation for these solid-state addition reactions may br phous with the R form of PhO PbBr2 has not yet been produced. stated as: Equation 2 s h o w that the R form of PbO.PbBrz resulting nPbO PbA -+- nPbO.PbA from the heat treatment of the hydrate may be converted to thc in which A is bromine, chlorine, or sulfate. N form by heating a t 450" C. for several hours. I n a drterTable I shows the comparative temperatures required to initiate mination of the phase diagram of the lead monoxide-lead bromide the solid-state reactions which are listed in columns 1 and 2, in system both by thermal analysis and by x-ray diffraction (13, f4), order of increasing energy requirements. In the last column, it has been found that the N form is the high temperature form, values are given for the ratios between threshold temperatures and the R form is the Ion temperature form. I n a study of the and melting points (both in degrees absolute) of the compounds lead monoxide-lead chloiide system, the N form of PbO.Ph('l: ic: formed (peritectic temperatures for PbO.PbBr, and PbO.PbC1,). the only form so far observed from fused preparations. These ratios range from 0.48 to 0.56; although they do not establish an infallible rule, they are of value as a useful criterion for In this discussion of the polymorphic monobmir lead halides,
2
I
+
&-
V O L U M E 23, NO. 10, O C T O B E R 1 9 5 1 it is important to note that in solid-state addition reactions the R form of Pb0.PbBr2 and the N form of PbO.PbCl2 are those regularly prcdnccd at low temperatures (Table I). The R form of Pb0.PbBr2 resulting from solid-state reaction is converted to the S form if heated a t 450' C. for several hours, as is indicated in Equation 2 for the R form resulting from the hydrate. The conversion of the 1%form of Pb0.PbBr2to the r\; form on heating a t higher temperatures and also the above thermal relationships for the polymorphic forms resulting from the hydrates are pertinent to an understanding of the results o h e r v e d in studying the solid-state replacement, reactions report,cd helou. Relation to Engine Deposits. 411 the inorganic Irad compounds commonly found in engine deposits are included in the lists given in Table I, column 2, and Table 111, columns 3 and 4. It has been shown (Table I) t,hat the products formed from the primary compounds are determined by the temperature and the mole ratio of the lead monoxide to the normal lead salts. Comparable results have been observed in thermal plug studies i n which fuel containing G ml. of tetraethyllead per gallon with ~i definite proportion of ethylene dibromide was used (crinimercial 1-T 3lix). In one series of studies the temperature was varied from 450' F. (238" C.) to 1200" F. (650" C.) while the fuel-air rat,io was held constant. I n other studies the fuel-air ratio was varied from 0.063 to 0.116 while the temperature was held constant. In general, the higher the kmperature and the lower thr fuel-air ratio, the greater the production of those compounds listed in Tahle I which required the higher reaction temperatures. For example, using a fuel-air ratio of 0.063 and a temperature of 450" F. (238" C.) thc deposits Rere chiefly lead bromide with some I'hO.Phl3r2 (R form); at 650" F. (343' C.) the deposits were ehirfly PbO.PbBrt (R form) with lesser amounts of lead bromide and 2PI)0.PbBr2;a t 900" F. (482" C.) the deposits wei'e entirely 2PbO.PbBr2; and at 1200" F. (650" C.) an appreciable amount of PbO.PbSO4 and 4Pb0.PbS04 was formed, the source of the pulfur twing t,he 0.01 1% sulfur present in t h r bo-octane (2,2,4t rimethylpvntane) used a s the fuel. .in important obsrrvation to he made from the thermal plug ticposit study is the almost perfect correlation between the teniperatures which produced each of the specific compounds and thr reaction temperatures listed in Table I required to pr(:duce the same compounds by solid-state reaction. To produce t'hese compounds by fusion would require temperatures almost twice as high. These data, therefore, strongly indicate that the inorganic, lead compounds present in combustion chamber deposits are tht. result of solid-state rwctions. The mechanism of solid-state reactions is such that they must occur a t the boundary between binary mixtures. If a third component is involved, the reaction must take place as a hinary reaction a t the boundary between the initial prodnet and the third component. It is believed that the relative simplicity found for the oonipc sition of most engine deposits is the result of this requirement of tiinary solid-state reactions and, also, of the fact that t h r resulting products are temperature-determinrd. SO LID- STATE REPLACEMENT REACTIOK S
It has been shown that all the basic lead salts commonly found in engine deposits may be produced by solid-state addition reactions from the primary compounds, lead monoxide, lead chloride, lead bromide, and lead sulfate. The next question of interest is: Do these basic salts interact with each other and with the primary compounds? No evidence has been found of interaction between the basic lead salts, with the exception of solid-solution reactions hetween the isomorphic chloride and bromide compounds. Evidence has been found, however, of replacement reactions between t'he basic lead salts and the normal lead salts. Consequently, the replacement reactions of the 15 mixtures listed in Tables 11 and I11 were studied. For this phase of the investigation, 0.5- to I-gram mixtures (unless otherwiv noted) were heated in open magnesium oxide
1391 crucibles for 2 hours :it temperatures of 200", 250°, 300°, 400", 500°, 600", and 700" C. These conditions were chosen to hr romparable to those used for the determination of the reaction temperatures of the addition reactions. Mixtures 1 through 10 were selected to present conditions for replacement react'ions hetween a lead basic sulfate and a lead halide (chloride or hromide) and between a lead basic halide (chloride or bromide) and lead sulfate. Mixtures 11 through 15 present conditions for replacement reactions followed by a type of solid-soh.hon reaction hetween the basic lead bromides (or chlorides) and lead chloride (or bromide), respectivrly. Mixtures of Lead Monoxide and Lead Sulfate with Lead Chloride or Lead Bromide. An x-ray diffraction study of the heat-treated mixtures of a lead basic sulfat,e and a lead halide, and of a lead basic halide and lead sulfate, has shown that re~ilacement,rractiom occur in the solid state. These reactiom i , c w l t in the formation of compounds having lattice structures (Jntirely different from thosr of the starting compounds. The powder patterns show that the monobasic lead sulfate and the monobasic lead halides do not have isomorphic structures and that there are no instances of solid-solution reaction betn-ec,n the sulfate and halide compounds. A summary of the replacemriit reactions for the respective mixtures, given in Table IT, shows the compounds which predominated following heating for 2 hours a t 250°, 500°, 600', and 700' C. These temperatures were selected because they cover the most pertinent observations of this study. However, it' i s generally true that many. of the compounds listed under the 250' C. temperature column were present to a small extent in the powder patterns of the mixtures heated a t 200" C.; and that, for the most part, the reactions forming these compounds showed completion a t 300" C. With few exceptions (footnote d to Tahle 11) there were only minor changes in composition at 300" :ind 400" C'. from those noted at 250" C. The replacement rrrirtiona t)etween monobasic lead sulfate and :t lead halide to produw the respective basic lead halides and lead sulfate at 280" C. (mixtures 1 and 2) are surprising when one considers the stability of Pb0.PbS04 and its high melting point of 975" C. (Table I). PbO.PhSOa is present in the mixtures heated a t 500", 600", and 700" C. At these temperatures appreciable amounts of the lead halides are volatilized before t,hey have had an opportunity to react with the monobasic lead sulfate. The presence of unreacted PhO.PbSO1 shows that it S stable a t these higher temperatures and that the presence of some second compound which n-ill rcact with lead monoxide, such as lead chloride, is required i n cirtlrr to c a u ~ it to release reactive lead monoxide. Similar observations were made for the replacement reactions lietween 4PbO.PbSOa and the lead halides (mixtures 7A, B, C and 8.4, €3, C). As for the above mixtures, the respective monobasic lead halides were formed a t 250' C. These reactions were not rn simple as those involving the monobrasic lead sulfate, because of the higher mole ratio of lead monoxide to lead halide. In mixtures 7A and 8A, equimolar amounts of 4PbO.PbSOI and the lead halide, the dibasic lead chloride is formed a t 300' C. and the clibasic lead bromide at 400' C. The results obtained on these six mixtures, in which the mole ratio of lead monoxide to lead halide is varied, show that the higher the mole ratio of lead monoxide to lead halide the higher is the relative amount of the dibasic lead halides formed and t.he lower is the temperature a t which they are formed. In mixtures 5 and 6, as well as in mixtures 12 and 13 (Table III), it was desired to use the monobasic lead compounds, PbO.PbC1, and PbO.PbBr2. At the time this work wm started these two compounds had not been completely characterized and had not been prepared with certainty by direct fusion of lead monoxide and the respective lead halide. Considerable work had been done, however, on the preparation of the two hydrates and their subsequent heat treatment to form the monobasic lead halides. For these reasons, the hydrates were used as a source of PbO.PhCln and PbO.PhRr?.
1392
ANALYTICAL CHEMISTRY
Heating mixtuies 5 and 6 at 200", 250", 300", and 400" C. simply resulted in dehydration of the hydrates and formation of the previously mentioned polymorphic forms of the respective monobasic lead halides. At 500" C., hotFever, a replacement reaction takes place with the formation of Pb0.PbS04. In the solid-state replacement reactions between the dibasic lead halides and lead sulfate (mixtures 9A, B and 10A, B), the formation of PbO.PbSO4 is also noted to occur a t 500" C. I n the three-component mixtures (Kos. 3 and 4) of lead monoxide and lead sulfate with lead chloride or lead bromide, the addition reaction between lead monolide and the lead halide takes place a t 250' C. to form the monobasic lead halide. At 500" C. the addition reaction between lead monoxide and lead sulfate takes place to form the monobasic lead sulfate. The presence of a third compound does not interfere nith the binary nature of the respective solid-state reactions. An interesting observation \vas made in this connection. I n the study of the solid-state addition reaction between lead monoxide and lead sulfate (Table I) it n-as found that 1-gram mixtures heated a t 500' C. for 2 hours produced PbO.PbSO4, whereas those heated a t 400'C. showed a mixtureof lead sulfate and lead tetroxide(Pb304). I n the above three-component mixture, however, it was noted that the oxidation of lead monoxide to form lead tetroxide is prevented because the lead monoxide preferentially reacts nith the Irad chloride to form PbO.PbCl2. From these observations it is concluded that the following pi inciple governs the temperature a t tvhich the solid-state replacement reactions covered by this investigation occur: The temperature a t which the solid-state replacement reaction PbO.PbY
+ PbA +PbO.PbA + PbY
(4)
ciccurs is determined not by the stability of the basic lead salt, I'hO.PbY, but by the temperature of the solid-state addition I eaction between the primary compounds, lead monoxide and I%A, to form PbO.PbA (in this general statement, A and Y I rpresent bromine, chlorine, and sulfate). Using equimolar mixtures of 4PbO.PbSOa and lead chloride or lead bromide (mixtures 7A and SA) as examples, the mechanism of the solid-state replacement reactions may be considered to be as followve: (I) When an intimate mixture of the two compounds is heated, the lattice units of 4Pb0.PbS04 and of the lead halide arrange themselves in close proximity to one another; (2) as the temperature is increased, the interfacial attraction between the halide and the lead monoxide portion of the lattice unit of 4Pb0.PbS04 becomes greater and the bonding between the lead monoxide and lead sulfate portions of the lattice unit of 4Pb0.PbS01 becomes weakened; (3) the release of active lead monoxide and its solid-state reaction with the lead halide then occur a t the same temperature as would produce the same solidstate addition reaction from the primary substances; (4) the presence of an excess of lead monoxide to lead halides promotes the formation of some of the dibasic lead halides at 300" to 400' C. and at higher temperatures; and (5) a t 500" C., the excess lead monoxide and the more or less inactive lead sulfate formed as the result of steps (l), (2), and (3) react to form PbO.PbSO4. This is the temperature a t which it would be formed by a solidstate reaction from the primary substance. I n mixtures 7C, SB, and 8C, heated at 500' C., the tendency to form the dibasic lead halides predominates over the tendency to form PbO.PbSO4 There is no reaction below 500" C. between equimolar amounts of the dibasic lead halides and lead sulfate (mixtures 9-4 and 10A). At this temperature (the reaction temperature for formation of Pb0.PbS04 from the primary compounds lead monoxide and lead sulfate), both PbO.PbSO4 and the respective monobasic lead halides are produced. Thus, a t temperatures up to 500" C. there is no breakdown of the lattice of the dibasic lead halide to form the monobasic lead halide and lead monoxide, and this reaction is permitted to take place a t 500' C. simultaneously R ith and only because of the reaction between lead monoxide and lead sulfate.
Mixtures of Lead Monoxide, Lead Chloride, and Lead Bromide. Mixtures 11 to 15 (Table 111) involve compounds consisting of lead monoxide, lead chloride, and lead bromide and present conditions for solid-solution reactions between isomorphic compounds as well as solid-state replacement reactions. A4summary of the results obtained is given in Table 111. The reactions which took place for mivture 11 may he represented as folloa~s: PbO
+ PbClz + PbBrz +
PbO.PbC1 Br ( N and R forms)
+ PbC1.Br
(5)
A 250' t o 400' C.
2 hours
PbO
+ PbCl, + PbBrzPbO.PbC1.Br + ( N form) + PbC1.Br t
(6)
C.
A 500' t o 700'
2 hours
The two forms of PbO.PbC1.Br shown in Equation 5 are due to the fact that in the initial reaction between lead monoxide and lead bromide the R form of Pb0.PbBr2is established and this is then followed by a solid-solution reaction in which half of the bromine ions are replaced by chlorine ions to form PbO.PbC1.Br (R form). Similarly, the initial reaction between lead monoxide and lead chloride produces the N form of PbO.PbCI,, which is also followed by a solid-solution reaction in which half of the chlorine ions are replaced by bromine ions to form PbO.PbC1.Rr (X form). In mixtures 12 and 13 the form of the monobasic lead chlorobromide is influenced by two simultaneous solid-state reactions: (1) the reaction between the normal lead halide and released lead monoxide to produce the crystalline form characteristic of the halide (with lead bromide the R form is produced, and with lead chloride the N form), and (2) the dehydration of the hydrate and its further heat treatment to produce its normal sequence of polymorphic forms L, MI N, and R. It would appear that the dehydration process is the major factor in determining the forms produced a t 200" C. and a t 250Oto 400' C. The N form at 500" C. could result either from a reaction between lead chloride and released lead monoxide, or from the heat treatment of the R forni to produce the high temperature PI' form. The presence of some PbC1.Br was noted for all temperatures except 700" C. Some of the dibasic lead chlorobromide was formed a t 600" C., and an increased amount was produced a t 700" C. The reactions which took place for mixture 14 may be represented as follows: 2Pb0.PbBrz
+ PbClz 300' --+ t o 2(PbO.PbCI C. Br) N form 500'
A
(7)
2 hours
2(2Pb0 PhBr,)
+ 2PbC1,600'+ t o 700' A
2 hours
S(PbO.PbC1.Br) N form
c
+ 2PbO.PbCl.Br + PbC1.Br t
(8)
The patterns obtained for the mixture heated a t 200" and 250' C. were diffuse and did not show the presence of a new phase. At 300' C., however, the N form of the monobasic lead chlorobromide was formed, and a t 600' and 700" C. an appreciable amount of the dibasic lead chlorobromide was formed. The reactions for mixture 15 were the same as for mixture 14, except that the R form of PbO.PbC1.Br was initially produced a t 300" and 400" C., instead of the N form, as indicated in the, following equation: 2PbO.PbClz
+ PbBrz + 2(PbO.PbCI.Br) R form A 300 t o 400' C.
(9)
O
2 hours
At 500" C. the R form was converted to the high temperature S form.
+
Mechanism of Reaction, 2Pb0 PbX', PbX",. The results obtained for mixtures 14 and 15 are of particular significance in giving further evidence of the mechanism by which the solid-state
. 1393
V O L U M E 23, NO. 10, O C T O B E R 1 9 5 1 replacement reactions occur. The reactions shown by Equations 7 and 9 %erechecked several times; the same results were always obtained. The data obtained show that the N form of Pb0.PbCI.Br is produced in the reaction between 2Pb0.PbBr2 and Imd chloride, whereas the R form is initially produced by the rc,action between 2PbO.PbClz and lead bromide. This is particularly interesting when one considers that the S form of Pb0.I’bCl? is consistently produced when a binary mixture of lead monoxide and lead chloiide is heated and that the R form of PbO.PbHrz is produred when a mixture of lead n i o n o d e and lead bromide is heated a t lo\$ temperatures. Thus, because of the fortunate circumstance that the t x o low tempei ature solid.tate 1e:iction compounds PbO.PbCI2 and Pb0.PbBr2 do not have isomorphic ciystal structures, a unique means is provided lor observing the mechanism of these solid-state reactions. From these observations, it has been concluded that vhen a solid-state reaction occurs betxeen 2Pb0.PbXt2 and P b S ” , to form Z(PbO.PbS’.X”), the crystalline form of the resulting solid solution compound is determined by the initial reaction, ahich in turn is that of the primary compounds lead monoxide and PbX”2 to form the parent cr~stallinecompound PbO.PbX”2 (in these formula., S’and X” are used as alternate symbols for chloiine and bromine). This means that in these rolid-state reactions the initial 1 paction takes place between the noimal lead halide and the actiw lead monoxide released in some niannei from the dibasic lend hdide. This initial reaction determines the cr? stalline form of the monobasic lead halide produced and is then followed by a type of solid-solution reaction in Khich half of the initial halide iow of the parent lattice are replaced by an equal number of the other halide ionq The resulting monobasic lead chlorobromide niaintains the same crystalline form as established by the initial bolid-state reaction. For the initiation of these reactions, the solid-state mechanism must be one in nhich the ionic lattice of the normal lead halide comes in contact a i t h the lead monoxide units of the dibasic lead halide arid, a t the same time, the lead halide portion of the dibasic lead salt loses its contact with the lead monoxide units and becomes isolated or barred from the ensuing solid-state reaction. All data obtained indicate that these solid-state replacement reactions do not iesult in a collapse of the 2PbO.PbX’z lattice structure to form the lattice structure of PhO.PbX’, and active lead monoxide
PO0
P0CLI
,
d E b Pa0
PSO
200-300.C 2 HR ____L_
PBO PBCLZ
PBCLz
PBO
PBcq
PBCC,
-0
Pno
pso
9F PBO
+
A
Po0
PlERp
-0 /RBRz
PBO P S c c p pas*
PSO PSBR
I
PBCL2
I 21
PBO
Faccz
PB BQ PBO
-
RO
PSO
PBO PsBnZ
A graphical presentation of a mechanism for the solid-state reaction is shown in Figure 1 for the reaction between 2Pb0.Pb(’12 and lead bromide, using four molecules of each. It is postulatcd that when an intimate mixture of the two components is made and heated a t 200’ to 300’ C. the lead bromide molecules becomc. very reactive, owing to the thermal vibration of the planes in their ionic lattice, and that they are able to position themselves iri close proximity to the lead monoxide units within the lattice of 2Pb0.PbClz in some such manner as illustrat’ed by the box diagram in Figure l, A . The boundaries of the intact lattice units (figuratively speaking) of 2PbO.PbC12 and lead bromide arcs outlined by heavy lines. Because of the close proximity of the lead bromide units and its stronger or preferred attraction for the lead monoxide units, the bonds holding the lattice units of 2PbO.PbCl2 become weakrr and weaker until a state represented by Figure 1, B, exists, in xhich t,here are no loriger intact lattice units of 2PbO.PbC1,. This results in leaving the reactive lead monoxide and lead bromide units in close proximity to each other and also in leaving the. lead chloride units grouped together in a more or less inactivt. and isolated state a t the center of the reaction unit. The reactive lead monoxide and lead bromide then react as they normal11 would t,o produce lattice units of PbO.PbBr2 of the R forni. This step is shown as C in Figure 1, in which the lattice units of PbO.PbBrz are outlinrd in heavy lines. This step of the niechanism establishes the form of the monobasic lead chlorobromidv whicli is to result from the reaction. Following this, t,he solidsolution reaction takes place between the PbO.PbBr2 (R foriii) and an additional lead monoxide and lead chloride unit t,o forni two molecules o r crystal units of PbO.PbCI.Br of the R form, tis illustrated by D in Figure 1. In case the starting materials are 2Pb0.PbBrz and lead chloride, the solid-state reaction mechanism proceeds in the sanic manner: in step A the lead bromide units will be oriented to th(. center and the lead chloride will take up the corner positions in close proximity to the lead monoxide units, The reaction determining the parent lattice a-ill then take place between lead monoxide and lead chloride and, as would he expected, t,he K form of PbO.PbC1z will be produced, Thus the polymorphic form of th(. resulting monobasic lead chlorobroniide is established in step C‘. Folloa-ing this, the solid-solution reaction illustrated by step D takes place, and PbO.Pbfi.Hr (Tu’ form) is produced. The two reactions discussecl above have been consistent]) observed and the relationship between the starting materials and the crystalline form of thc. resulting product has been definitely established by repeated experiments. I n no case, ho\T ever, have patterns been ohtained from mixtures 14 and 15 which show the parent nionobasic halide prior to its solidsolution reaction to form the monobasic lead chlorobromide. It is not known, therefore, how rapidly the four steps illustrated in Figure 1 take place. No patterns have been observed having a line shift intermediate between that required by the products of steps C and D. The data, therefore, support the probability of a preferential replacement compound, in which half of the chlorine ions of the PbO.PbCI? lattice are
PBO PB 812
A N A L Y T I C A L CHEMISTRY
1394 replaced by bromine ions. I t is planned to follow the course of these reactions at 5-minute intervals using a high temperature specimen mount similar to the one described by Birks and Friedman (d), in an effort to obtain evidence of the formation of the parent compound indicated in step C, and also to determine if any intermediate solid-solution compositions are formed between steps C and D. Mono- and Dibasic Lead Chlorobromides. I n a study of the reactions of mixtures 11 through 15 it ha9 been noted that there are two forms of PbO.PbC1.Br: thc R form a hich is isomorphouz with the R form of Pb0.PbBr2, and the hT form which is isomorphous with the N form of PbO.PbBrz and PbO.PbClz. Thc c( nvistency with which the 28 values of the reflections are repeated in the powder patterns of the numerous preparations of the R and N forms of PbO.PbCI.Br, produced in this investigation, leads one to postulate that each of these forms has a preferential replacement composition conforming to an equal number of chlorine and bromine ions in the lattice. In a study of the lead chloridelead bromide system (3) it wac shown that a preferential replacement compound, PbCl.Br, exists which is stable at room temperature and is isomorphous
with lead chloride and lead bromide. I n this investigation, a discontinuity in the lattice expansion-composition relationship a t the 50 mole % composition was established by a detailed study of several intermediate compositions. In the present study, interplanar spacing values (Table IV) are available for only three compositions of the S form of the monobasic lead halidesnamely, Ph0.Pt)C12, PbO.PbCl.Br, and PbO.PbBr2. The lineshift data for several reflections are shown in Figure 2. These indicate a discontinuity in the lattice expansion-composition relationship exactly analogous to that observed for PbCI.Br and give support to the existence of the preferential replacement compound, PbO.PbC1.Br. The interplanar spacing values (Table IV) for the R form of PbO.PbBrz are larger than those for corresponding reflections of the R form of PbO.PbCl.Br, indicating a replacement of some (probably half) of the bromine ions with the smaller chlorine ions, which permits a contraction of the lattice. So far, a form of PbO.PbCl2 having a lattice structure isomorphous with the R forms of PbO.PbBrz and PbO.PbC1.Hr has not been produced. Consequently, it is not possible t u show a discontinuity in the latire expansion-composition relationship for the R form similar to that observed for the S form.
Table IV. Interplanar Spacing Values PbO.PbBr2 (R form) do, A . I/Ilb 8.61C 0.10 6.20 0.30 6.00 0.30 4.58 0.30 4.16 0.25 3.88 0.35 3.67 0.26 3.32 1.00 3.15 0.95 2.91 0.87 2.89 0.55 2.84 0.65 2.80 0.31 2.74 0.68 2.64 0.38 2.60 0.42 2.47 0.30 2.41 0.46 2.35 0.29 2.05 0.22 1.95 0.56 1.89 0.10 1.87 0.24 1.84 0.15 2PbO.PbBrp 7.55e 5.15 4.88 3.87 3.58
(Copper K, PbO.PbC1.Br ( R form) d. A. I/Ii 8.50C 0.10 6.11 0.25 0.30 5.95 4.53 0.30 4.13 0.15 3.85 0.35 3.64 0.30 3.29 1.00 3.12 0.88 2.89 0.76 2.86 0.58 2.82 0.64 2.79 0.37 2.72 0.58 2.63 0.30 2.58 0.35 2.46 0.20 2.40 0.42 2.34 0.20 2.03 0.17 1.94 0.53 1.88 0.12 1.86 0.20 1 83 0.08 2PbO.PbCl.Br 7.38e 5.02 4.78 3.80 3.56 3.10 3.08 2.92 2.82 2.75 2.67 2 , .i4 2.31 2.42 2.33 2.21 2.19 2.12 2.03 1.90 1.95 1.90
0 70 0 22 0 06 0 15 0 18 0 38 1 00 0 26 0 48 0 17 0 38 0 08 0 16 0 13 0 03 0 20 0 59 0 20 0 04 0 15 0 07 0 23
Radiation, Xw.sr. = 1.5418 -4.) PbO.PbBr2 PbO.PbC1.Br (Nform) ( S form) d , A. I/I. d , A. I/II 7.65d 0.20 7.50d 0.40 6.12 0.20 6.05 0.25 4.05 0.14 3.99 0.20 3.83 0.16 3.76 0.25 3.60 0.15 3.53 0.12 3.41 0.11 3.35 0.15 3.33 3.27 0.13 0.15 3.13 0.15 3.18 0.30 0.20 3.13 .. .. 0.10 3.06 2:94 0.40 2.97 0'30 2.91 0 55 2.86 0 45 2.86 1.00 2.81 1 00 2.83 0.43 2.80 0 45 2.79 0.18 2.76 0 15 2.72 0.25 2.67 0 15 2.55 2.47 0.10 0 12 2.51 0.15 2.24 0.25 2:io 0:io 2.20 0.20 2.17 0.35 2.15 0.13 2.12 0.22 2.09 0.13 2.06 O,l5 1.84 0.12 0.10 1.83 2PbO.PbClt 7.31e 4.97 4.70 3.77 3.48 3.08 3.05 2.89 2.78 2.70 2.64 2.51 2.48 2.37
0.81 0.27 0.12 0.18 0.25 0.28 1.00 0.25 0.75 0.27 0.48
PbO.PbSOa 6.27 6.15 5.88 4.39 4.22 3.78 3.69 3.32 3.21 2.99 2.95 2.85 2.76 2.70 2.62 2.47 2 42 2.40 2.27 2.23 2.06 2.03 1.97 1.91 1.85
d , A.
I/II
7.40J 6.00 3.94 3.74
0.80 0.40 0.30 0.40
3.24 3.10 3.04 2.98 2.92 2.81 2.79 2.74 2.71 2.65 2.43
0.30 0.25 0.50 0.20 0.35 0.60 1.00 0 60 0.30 0.30 0.30
2:i7 2.14 2.10 2.02 1.82
o:i5 0.25 0.20 0.25 0.15
{E E 3.33 0.25
4PbO.PbSO4
8.23 0.15 7.38 0.05 0.30 6.22 0.05 0.12 5.78 0.11 0.05 5.45 0.17 0.05 5.17 0.05 3:i4 4.28 1:oo 0.11 3.24 2.93 1.00 0.16 3.12 2.85 0.45 0.37 3.08 2.78 0.24 0.31 2 89 2.72 0.35 0.37 0.11 2.68 2.59 0.37 0.10 2 59 2.56 0.29 0.26 0.08 2.35 2.45 0.20 0.10 0.05 2.23 2.37 0.06 0.06 2.15 2:21 2.27 0 :i4 0.14 0.05 2.06 2.17 2.25 0.47 0.71 0.05 2.10 0 11 2.14 1.97 0.31 0.20 1.95 2.04 0.23 0 09 1.87 1:98 o:i5 0.05 0 08 2.00 1.84 1.94 0.09 1.96 0.12 0.10 1.73 1.88 0.34 0 15 0.15 1.94 1.70 0.08 1.66 0.10 1.62 0.10 1.60 0.10 1.59 0.05 4 Interplanar spacing ( d ) values are accurate t o *0.05 A. for values of 4 A. or greater, t o kO.02 A. for values of 2 t o 4 -&.,,and t o +O.Ol A , , for values less t h a n 2 . 4 . b Relative intensity ( I l I i ) values obtained by dividing heights of various reflections by t h e height of strongest reflection. C Respective interplanar spacing ( d ) values are given in adjoining columns for corresponding reflections of isomorphic R forms of PbO.PbBrz a n d PbO.PbC1.Br. d Respective interplanar spacing ( d ) values are given in adjoining columns for corresponding reflections of isomorphic N forms of PbO.PbBfz, PbO.PbCl.Br, and PbO.PbC!z. e Res ective interplanar spacing ( d ) values are given in adjoining columns for corresponding reflections of isomorpiic compounds, ZPbO.PbBrs, PPbO.PbCl.Br, and 2PbO.PbCIs. O,59
0.40 0.38 0.22 0.15 0.29 0.14 0.51 1.00 0.25 0.39 0.93 0.28 0.17 0.20 0.13 0.17 0.54 0.30 0.28 0.21 0.57 0.25 0.19 0.18 0.28
PbO.PbCls (Nform)
V O L U M E 2 3 , NO. 10, O C T O B E R 1 9 5 1
1395
Relation to Engine Deposits. The replacement reactions observed for the 15 mixtures (Tables I1 and 111) of basic lead salts and normal lead salts are useful in showing which compounds are compatible a t a given temperature. If this information is applied to the solid-state reactions which may take place in an automotive engine, the resulting picture is as follows:
1 lie 3.17
-
116
2
2.98
3.15
M I
.
E86
2 97
285
296
2 84
2 95
2 83
294
rn
5
2
> V
z n V
< a K < ltY z
2 82
2 91
2 81
2 9r?
309
/I-
Firqt, it must be assumed that the primal? compounds, lead mono\ide, lead chlorobicmide, and lead sulfate are available a8 a result of the combustion process. These compounds have been found in engine depobits, although the proress by which they are produced has not been fullv established. These primary compounds will then form addition compounds depending on the temperature of their location in the combusQon chamber. Also, the basic lead salts formed may participate in replacement reactions with the normal lead salts. The reactants and products formed at spwifir temprratures ale given in the following tabulated equationa:
2ea
Temp..
a
2 7 9
*
278
250-300 350-400 500
