RONALD T. PFLAUM AND LESTER c. HOWICK
Vol. i S
It was found that the KBr-K2MoC16 mixture de-
coniposed at 450” in a current of nitrogen, and Mo-
Cls was deposited at the end of the reaction tube.
Sirice excess bromine at 450” can change KCl to
KBr, the equation for the over-all reaction of Kj-
MoCls and Brs at 430’ can be expressed as
KIR.loC1, + 1 jRr2 = 3KRr + RIoCl? 4- l.5C12
[CONTRIBUTION FROM THE DEPARTMENT
The Chromium-Diphenylcarbazide Reaction1
OF CHEMISTRY, STATE UNIVERSITY OF IO\I’A]
BY RONALD T. PFLAUM
AND LESTER C. HOWICK~
RECEIVED APRIL 6, 1956
A study of the nature of the chromium-diphenylcarbazide reaction was carried out. Absorptimetric data for the reac-
tions of chromium( VI), chromium(II1) and chromium(I1) ions with diphenylcarbazide and dipheriylcarbazone were com-
pared. The stoichiometry of the various systems was determined together with the efTects of pH and the extractability of
the colored reaction product into non-aqueous media. The behavior of the colored complex under the influence of an electric
field was observed. The nature of the highly absorbing complex formed in the reaction of chromium and the organic rc-
agents was postulated.
The color reaction between diphenylcarbazide
and chromiuni(V1) has long been used for the colori-
tnetric determination of chromium.3 Today it is
one of the most widely used reactions for this par-
ticular analy~is.~ The colored system enjoys this
popularity due to the sensitivity, selectivity, and
simplicity inherent in the reaction. In addition,
the organic reagent is readily available in a state of
purity sufficient for analytical work.
In spite of the above situation, little is known of
the actual nature of the red-violet species formed in
the reaction. A survey of the literature reveals
many inconsistent and contradictory statements, as
well as many unexplained observations. The pres-
ent investigation was undertaken in order to resolve
certain of these factors and to gain a better insight
into the nature of the color reaction.
Various formulations for the colored species
formed in the reaction have been advanced in the
50-odd years since Cazeneuve first reported his ob-
servation~.~~~ He proposed that an organo-metal-
lic compound was formed in the reaction of diphen-
ylcarbazide and chromium. Babko and Paulii7
and Feig18 have concluded, however, that the col-
ored material is merely an oxidation product of the
reagent. Moreover, the oxidation must be very
selective since none of the other common oxidizing
agents, i.e., ceric salts, permanganate, persulfate,
etc., give similar results. The most recent work
was carried out by Boseg who postulated that it is
highly unlikely that chromium(V1) should possess
a unique oxidizing ability but that, however, some
(1) Presented before the Division of Physical and Inorganic Chemis-
try at the 127th Meeting of the American Chemical Society, Cincinnati,
(2) An Abstract of a thesis submitted by Lester C. Howick to the
Graduate College of the State University of Iowa. 1955, in partial
fulfillment of the requirements for the Degree of Master of Science.
(3) M. A. Moulin, Bull. snc. chim., S1, 296 (1904).
(4) F. D. Snell and C. T. Snell, “Colorimetric Methods of Analysis,”
Vol. 11, 3rd Ed., D. Van Pl‘ostrand Co., Inc., New York, N. Y., 1949, P.
(5) P. Cazeneuve, Bull. soc. chim., 23, 701 (1900).
(6) P. Cazeneuve. ibid., 26, 758 (1901).
(7) A. K. Babko and L. A. Paulii, Zhur. And. Khim., 6,272 (1950).
(8) F. Feigl, “Spot Tests,” Vol. I, 4th English Ed., Elsevier Pub-
lishing Co., New York, N. Y.. 1954, p. 159.
(9) M. Bose, Anal. Chim. Acta, 10, 201, 209 (1954).
type of oxidation-reduction with subsequent co-
ordination must be involved in the reaction. He
performed absorption, migration, extraction and
magnetic susceptibility studies and concluded that
the colored species was a neutral monodiphenylcar-
was based in part upon the observation that chro-
mium(II1) ion did not react with the reagent.
The present investigation became imperative
when it was learned that the diphenylcarbazone
used in the above study was in reality a 1:1 mix-
ture of diphenylcarbazide and diphenylcarba-
and when it was observed that chro-
mium(II1) did react with the reagents. The work
described herein is intended to clarify some CJf the
unresolved factors in the chromiuni-diphenylcar-
condensation of urea and phenylhydrazine at 15j0.12 The
pure white compound with a melting point of 170’ (on re-
peated recrystallization from ethard) m s used LIS the pure
reagent. Diphenylcarbazone was prepared by the oxidation
of crude diphenylcarbazide with 3y0 hydrogen peroxide in
alcoholic potassium hydroxide.1° On neutralization and re-
crystallization, the red-orange mixture of the two reagents
was obtained. Treatment of this product with sodium car-
bonate in hot ethanol, extraction of the diplienylcnrbazide
with ether and acidification of the aqueous solution with hy-
drochloric acid yielded a red powder melting at 1%:’.
material is pure diphenylcarbazone.”
Dimethylformamide was obtained from the liohm and
Haas Company. Purification wxs effected by treatment
with barium oxide for a period of 24 hr. with subsequelit
rectification in an all glass system. The fraction boiling ,it
151 f 1” was used as the purified solvent. All otlier tech-
nical grade solvents were distilled before use.
Solutions of chr~imiurn( 11) ion were prepared according
to the method of Hatfieltl‘3 and stored under nitrcigcii.
Standardization WLLS carried out titrimetrically with st:iudar~l
ceric and ferrous sulfates. XI1 otlier chemicals used were of
reagent grade quality.
recording spectrophotometer and a Becknian Model B spec-
trophotometer were used to obtain absorptiirietric data.
All measurements were made in matched 1 .OO zt 0.01 CUI.
cells at room temperature of approximately 25”.
was prepared by the
Gary Model 11
(10) K. H. Slotta and IC. R. Jacobi, 2. A?ial. Chem., 71, 344 (1933).
(11) P Krumholz and E. Krumholz, Monafsh., 70, 431 (1937).
(12) 0. L. Barneby and S. R Wilson, THIS
JUL’RNAL, 36, lr,7
(13) M. R. Hatfield, “Inorganic Syntheses,” Vol. 111, 1st Eil.,
McGraw-Hill Book Co., Inc., New York, N. Y., 1950, p. 148.
Oct. 5, 1956
The Color Reaction.-The
and diphenylcarbazone with chromium( VI), chromium( 111)
and chromium(I1) ions in aqueous and in non-aqueous
media were studied spectrophotometrically. Solutions of
chromium(V1) were prepared by the dissolution of potss-
sium dichromate in dilute solutions of sulfuric acid. Solu-
tions of hydrated chromium(II1) ion were prepared by the
dissolution of chromium(II1) perchlorate hexahydrate in
dimethylformamide. Solutions of anhydrous chromium
(111) ion were prepared by the dissolution of anhydrous
chromium( 111) chloride in dimethylformamide. Anhy-
drous chromium chloride dissolves in the solvent upon heat-
ing in the presence of traces of zinc dust. The anhydrous
salt dissolves readily in organic solvents in the presence of
catalytic amounts of reducing agents.14 The solutions were
cooled, filtered and allowed to stand in a dry-box to ensure
anhydrous conditions with no possibility of the presence of
chromium( 11) ion. Chromium( 11) solutions were prepared
as described above.
Determination of the Effect of pH.-The
the above systems and on solutions of the reagents was de-
termined. Measurements of pH were made on a Beckman
Model G pH meter. The effects of changes in pH were de-
Determination of Formulas.-Formulas
species in the various systems were determined by the
method of continuous variations.'s
10-6 Jf chromium ion and the reagents were prepared and
aliquots were mixed in the appropriate ratios. Absorption
measurements were made at selected wave lengths. Cor-
rected absorbance values were obtained by subtracting the
absorbance for zero reaction from the observed readings.
Formulas were determined from plots of absorbance against
the mole fraction of chromium ion.
Extraction Studies.-A study on the extractability of the
colored material formed in the reaction into non-aqueous
solvents was carried out. Common solvents immiscible with
water were added to aqueous solutions containing the colored
material. The effects of the addition of soluble salts to
the aqueous systems were studied. The colored extracts
were evaporated and analyzed for chromium content.
Migration Studies.--A Hittorf type transference cell with
platinum electrodes was used to study the migration of the
colored species under the influence of an electric field. The
colored reaction mixtures were introduced into the middle
compartment of the apparatus while the electrode compart-
ments were filled with 0.1 N sulfuric acid. An average
current of 0.5 amp. was applied for 30 min. The tris-1,lO-
phenanthroline-iron( 11) complex was studied under identical
conditions as a reference system.
Results and Discussion
The Color Reaction.-Spectrophotometric
aminations of solutions of diphenylcarbazide and
diphenylcarbazone with chromium in its three
oxidation states reveals some very interesting re-
lationships. For clarity, systems of the two re-
agents will be treated separately. Absorption
curves for the two systems are shown in Figs. 1 and
Diphenylcarbazide reacts with chromium(V1) in
acidic solution to produce an intense red-violet
coloration. The absorption curve for the aqueous
system is shown in Fig. I, curve 4. The absorp-
tion maximum occurs at 540 mp. In solutions of
@H 1.3, the molar absorptivity of the colored spe-
cies (based upon the concentration of chromium) is
26,000. This value is somewhat lower than the
value of 31,000 reported by Ege and Silverman.16
The addition of diphenylcarbazide to green solu-
tions of anhydrous chromium(II1) chloride or to
chromium(II1) perchlorate hexahydrate in dimeth-
ylformamide does not cause an immediate forma-
(14) N. V. Sidgwick, "The Chemical Elements and Their Com-
pounds," Val. 11, Oxford University Press, London, 1950, p. 1012.
reactions of diphenylcarbazide
effect of pH on
for the colored
Stock solutions of 8 X
(1.5) P. Job, Comfit. rend., 180, 928 (1925).
(16) J. Ege and L. Silverman, And. Chcm., 19, 693 (1947).
WAV E LE N G T H
spectra for diphenylcarbazide sys-
M reagent in H20 at pH 1.5; 2, 8.0 X
tems: 1, 1.0 X
10-6 M Cr(II1) and reagent in dimethylformamide;
4.0 X lod6 M Cr(V1) and reagent in HzO at pH 2.09; 4,
4.0 X 10-5 M Cr(V1) and reagent in HzO at PH 1.30.
tems: 1, 1.0 X
M reagent in dimethylformamide; 3, 8.0 X 10-5 M
Cr(II1) and reagent in dimethylformamide; 4, 4.0 X 10-6
M Cr(I1) and reagent in HzO.
spectra for diphenylcarbazone sys-
Mreagent in H20 at pH 1.5; 2, 1.0 X
tion of a purple coloration. Color does develop,
however slowly, and the degree of color is depend-
ent upon several factors. The addition of small
amounts of water or acid interferes in the color de-
velopment. An increase in temperature from 25 to
50' causes approximately a fivefold increase in the
rate of the reaction. Traces of base, added in the
form of solid anhydrous lithium hydroxide, greatly
increase the rate of color formation. Treatment
with oxygen at elevated temperatures, in the pres-
ence of traces of base, causes immediate color
formation. It was found also that diphenylcarba-
zide readily could be oxidized to diphenylcarbazone
under these latter conditions.
The absorption curve for a dimethylformamide
solution of hydrated chromium(II1) ion and di-
Vol. i S
phenylcarbazide is represented by curve 2 in Fig. 1.
The absorption maximum of the red-violet solu-
tion occurs at 550 mp. Addition of water after
color formation shifts the maximum to 545 mp.
The absorption of the reagent itself in the solvent is
similar to that shown for the reagent in water as
represented by curve 1.
Chromium(I1) ion does not react with diphenyl-
carbazide. This same observation has been made
previo~sly.~ Color does not develop even under
every variation in the reaction conditions.
It was found that pure diphenylcarbazone does
not react with chromium(1‘1) ion. This observa-
tion clarifies much of the difficulty reported with
this reagent.g Solutions of the reagent and chro-
mium(V1) did not shon7 any color change even after a
period of standing. Little oxidation of the red-
orange colored diphenylcarbazone to the colorless
diphenylcarbadiazone takes place.
Red-violet solutions (curve 3, Fig. 2) are obtained
on reaction of diphenylcarbazone with chromium-
(111) ion in dimethylformamide. (The absorption
spectruni of the reagent itself in the solvent is rep-
resented by curve 2.) The effects of added water or
acid are similar to those described above for the
diphenylcarbazide system. Oxygen appears to
have little effect on the system. Color develop-
ment is rapid on the addition of traces of base to an
anhydrous system of chromium(II1) ion. The
rate of reaction is immeasurably fast on heating an
anhydrous solution with base.
Diphenylcarbazone, contrary to diphenylcarba-
zide, does react with chromium(I1) ion. Reaction is
immediate and the absorption of aqueous solutions
(curve 4) is identical in all respects to that for the
chroniium(V1) diphenylcarbazide system.
solutions show a great stability after reaction and
after the addition of acid to pH of 1.5.
The results of the above study show that the
same absorbing species can be obtained by the re-
action of three oxidation states of chromium. These
data are summarized in Table I. It can be seen
that the color formed in the reactions is not due to
either reagent alone. Likewise, color is not due to
a higher oxidation product, diphenylcarbadiazone,
which is known to be colorless and non-reactive
toward metal ions.’’
-A complex between the rea-
gent or reagents and a species of chromium ion
must be responsible for the intense coloration ob-
SUMMARY OF ABSORPTIMETRIC
Ijiphenylcarbazide (PH 1.5)
Diphenylcarbazide (pH 12)
Diphenylcarbazone (pH 1.5)
Diphenylcarbazone (pH 9)
Cr(V1)-Diphenylcarbazide ( HzO)
Cr( 11)-Diphenylcarbazone (HzO)
‘I Time dependent.
It is postulated that the reaction of chromium-
(VI) in acidic solution with diphenylcarbazide in-
(17) 1’ Feigl and F. Lederer, Munntsh., 46, 112 (1024)
volves an oxidation of the reagent to diphenylcar-
bazone by the dichromate with simultaneous re-
duction of chromium(V1) to chromium(II1). Coni-
plexation between the newly formed products ac-
counts for the intense color in the reaction. In di-
methylformamide solutions of chromium(II1) ion.
diphenylcarbazide is air oxidized to diphenylcarba-
zone in the basic solvent. Subsequent complexa-
tion of chromium(II1) and diphenylcarbazone gives
the same species as observed for the chromium(V1)
reaction. Reaction in the presence of oxygen, as
described earlier, precludes the forination of a
chromium(I1) complex. In the reaction of chro-
mium(I1) ion with diphenylcarbazone, a portion of
the reagent may be reduced to form diphenylcarba-
zide and chromiurn(II1) ion. Reaction of chro-
mium(II1) and the remaining diphenylcarbazone
again results in the formation of the colored coni-
The Effect of pH.-The
with the various chromium systems, were studied
over a range of PH values to determine the effect
of changes in acidity. The effects were deter-
mined spectrophotometrically as shown in Figs.
1 and 2.
Considering diphenylcarbazide firstly, an in-
crease in pH greatly increases the absorption of the
reagent. A t low pH, 1.5 (curve 1, Fig. l), the
reagent shows a molar absorptivity of 200 at 540
mp. In basic solution, pH 9.4, a molar absorptiv-
ity of 1525 mp is observed at the same wave length.
It is evident that the absorbance due to the reagent
at low pH is negligible.
Diphenylcarbazone likewise shows a molar ab-
sorptivity of about 200 at 540 mp at pH 1.5 (curve
I, Fig. 2). Again at pH 9.0, the value is about
1500. h’either reagent shows the higher molar ab-
sorptivity observed for the chromium complex.
,A study of the effects of changes in pH shows
that maximum color formation for the chromium-
(VI) diphenylcarbazide reaction occurs in a CH
range of 1.0-1.4. Color fades very rapidly in solu-
tions of higher pH. KO color is observed on addi-
tion of the reagent to a neutral or basic solution of
chromium(V1) ion. The addition of a small
amount of acid results in the immediate formation
It is known that the reagents react with a num-
ber of metal ions to form inner complex salts of
the metal ion and diphenylcarbazone.ls Metal
ions, such as copper, mercury, nickel, react to pro-
duce purple colored species. These compounds
exhibit very little stability in solutions of low pH
and are, in fact, dissociated at approximately pH 4.
Chromium compounds show a behavior dissimilar
to that for these inner complex salts. Thisindicates
that the chromium complex is probably not an inner
An inner complex salt of chromiuni(I1)-diphenyl-
carbazone has been postulatedg for chromium on the
basis of extraction, migration and magnetic obser-
vations. The postulate necessitates the reaction of
diphenylcarbazone in its enolic form in order to
lose two protons and thus preserve the electroneu-
trality of the complex. The occurrence of such a
two reagents, together
(18) H Pischer, Mzkiochern , 30, 38 (lY42)
Oct. 5, 1966
THE CHROhfIUM-DIPHENYLCARBAZIDE REACTION
reaction in strong acid solution is a distinct im-
Determination of Formulas.-The
diphenylcarbazide and -diphenylcarbazone systems
were examined by the method of continuous varia-
tions. Plots of the data obtained are shown in
The data for the chromium(V1)-diphenylcarba-
zide reaction at 540 and 600 mp are shown as plots
4 and 1, respectively. Maxima are found at 0.4
mole fraction of chromium. Values for absorbance
at several selected wave lengths indicate that only
one primary absorbing species is present in solution
and that it is formed by the reaction of 3 moles of
reagent with 2 moles of chromium ion. This ratio
was also found by Boseg and is in agreement with
the reduction of two moles of chromium(V1) to
chromium(II1) and the oxidation of three moles of
diphenylcarbazide to diphenylcarbazone.
Continuous variations data were obtained for
the chromium(II1)-diphenylcarbazide and -di-
phenylcarbazone reactions in dimethylformamide.
Absorbance measurements at 550 mp were made
for solutions after reaction times of 4.5> 10.0 and
20.0 hr. Data for the diphenylcarbazide reaction
after 10.0 hr. are represented by curve 2 in Fig. 3.
Curve 3 results from a plot of the data from the di-
phenylcarbazone reaction after 20.0 hr. In both
cases, the 3:2 ratio of reagent to metal ion is evi-
A continuous variations study of the chro-
maximum at 0.3 mole fraction of chromium. A value
of 0.33 would be expected on the oxidation of 2 moles
of chromium(I1) to chromium(II1) and the reduc-
tion of one mole of diphenylcarbazone to diphenyl-
carbazide with subsequent reaction of the two moles
of chromium(II1) and 3 additional moles of diphen-
ylcarbazone. This result is at variance with the
1 : 1 ratio obtained by B o ~ e . ~
the reagent he used as diphenylcarbazone (a I :1
mixture of carbazide and carbazone), a continuous
variations study with equimolar solutions was not
carried out and the results obtained do not neces-
sarily indicate the stoichiometry of the reaction. l5
A11 of the data obtained prove conclusively that a
complex species is responsible for the absorption
observed. The formula of this species may be
something different from the ratio found. However,
the conformity of all systems to essentially one
pattern indicates a singular species. The analysis
on this isolated entity might prove useful in assign-
ing a formula. All attempts toward the isolation of
a solid colored product from the various systems
formed in the reaction of diphenylcarbazide or di-
phenylcarbazone with chromium in its three oxida-
tion states is not readily extractable out of aqueous
solutions into non-aqueous media. Only a frac-
tion of the color is extracted into benzene, isoamyl
alcohol, chloroform or carbon tetrachloride. Ex-
traction was forthcoming when an excess of acetate,
chloride or perchlorate ion was added. These ob-
servations are in agreement with Bose9 who found
that the colored material was extracted into ben-
system showed a
However, in view of
MOLE FRACTION CHROMIUM.
Fig. 3.-Continuous variations study of the chromium
systems: 1, Cr(V1)-diphenylcarbazide at 600 mp;
Cr(II1)-diphenylcarbazide at 650 mp (DMF) ; 3, Cr( 111)-
diphenylcarbazone at 550 mp (DMF); 4, Cr(VI)-diphenyl-
carbazide at 540 rnp.
zene, chloroform and cyclohexanol in the presence
of acetate ion.
It was found on analysis of an isoamyl alcoholic
extract of the colored material from aqueous chlo-
ride solution that chloride ion and chromium were
present, These two ions were not extracted under
identical conditions in the absence of the organic
reagent. The results of this study show that the
colored material is a complexed chromium species.
Furthermore, the species is not an inner complex
salt such as the copper salt which is readily ex-
tracted into benzene. Rather, the species is a
charged cation which is extracted together with
an anion as a neutral molecule.
determine the charge on the complexed chromium
ion were carried out using a Hittorf transference
cell. It was found that the colored complex
migrated to the cathode under the influence of an
electric current. Migration was reversible on re-
versal of the polarity of the platinum electrodes.
showed identical behavior.
The results of this study indicate that the colored
complex is in reality a charged cation and not a
neutral species as reported by one worker.$ The
migration supports the view that the chromium
complex is not an inner complex salt.
Several factors pertaining to the chromium-di-
phenylcarbazide-diphenylcarbazone reaction can
be concluded from the study. These can be formu-
lated in the following manner. 1. Diphenylcarba-
zide reacts with Cr(V1) and Cr(II1) ions to form a
singular red-violet complex. No reaction is forth-
4866 R. L. LIVINGSTON
coming with Cr(I1) ion. -3.
reacts with Cr(II1) and Cr(I1) ions to form the
same complex as observed above. No reaction
occurs with chromium(V1) ion. 3. The stoichiom-
etry of the reaction of chromium and the rea-
gents is in a ratio of three moles of reagent to two
nioles of the metallic ion. 4. The highly absorb-
ing chroniium coniplex exists as a cationic species
in aqueous solution. 5. The chromium complex
is extracted, together with an anion, into non-aque-
AND G. VAUGIIAN
ous media as a neutral nlolecule. 6. X chromiuin-
(111)-diphenylcarbazone complex is postulated as
the colored species in the reactions.
The above conclusions are the result of all of the
experimental data obtained. This situation is
unique in studies of the systems under considera-
tion. Such a situation serves to clarify much of
the unsatisfactory nature of the existing literature
on the subject.
[CONTRIBUTION FROM THE DEPARTMENT OF CHEMISTRY AND THE PURDUE RESEARCH
The Molecular Structure of Perfluorotrimethylamine by Electron Diffraction1
BY R. L. LIVINGSTON
AND G. VAUGHAN
MARCH 15, 1956
The molecular structure of perfluorotrimethylamine has been investigated by electron diffraction using the visual coi-rcla-
The$ructural parameters, as determined by this investigation, are as follows: C-F = 1.32 f 0.0% .&.,
C-N = 1.43 =t 0.03A., LFCF = 108.5 = I = 2.0", and LCNC = 114 d~ 3".
Previous investigations of the structures of
hexafluoropropene2 and octafluorocyclobutane3~4
in this Laboratory indicated, for these molecules,
that the closest approach of fluorine atoms which
are bonded to different carbon atoms is about 2.70
A. or twice the van der Kaals radius of fluorine.
Preliminary calculations on perfluorotrimethyl-
amine indicated that if a similar F..F distance pre-
vailed in this compound, then rather unusual struc-
tural parameters would be encountered ; hence an
investigation of the molecular parameters of this
compound was undertaken.
The sample of perfluorotrirnethylarnine was supplied by
Dr. W. H. Pearlson of the Minnesota Mining and Manu-
facturing Company. In the absence of any comparative
data, their estimate of a purity greater than 98 niol per cent.
was based on the constancy of the boiling point and the
molecular weight over successive distillations. No known
compounds were observed as impurities in the infrared
The diffraction photographs were obtained in the usual
way6 using a camera designed and constructed by Professor
H. J. Yearian of the Purdue Physics Department. The
camera distance was about 107.1 mm., and the electron
wave length, as determined from a transmission pattern
of ZtiO, was about 0.05SS a. The recorded diffraction
pattern of pcrfluorotriinetliylaInine extended to a q value of
Interpretation of the Diffraction Pattern.-The
visual correlation n i e t h ~ d ~ . ~
tribution i n e t h ~ d ~ , ~ were used in interpretation of the
diffraction pattern. The measurements of the
and the radial dis-
(1) Contains material from the Ph.D. thesis of G. Vaughan, Purdue
Research Foundation Fellow in Chemistry, 1951-1953.
(2) F. A. M. Buck and R. L. Livingston, J . Chem. Phys., 18, 570
(3) IT. P. Lemaire and I<. I,. Livingston, ;bid., 18, 569 (1950).
(4) €1. 1'. Lemaire and I<. L. Livingston. L IS JOURXAL, 74, 5732
(6) L. 0. Brockway, Rev. Moderiz Phys., 8, 231 (1936).
(ti) L. Pauling and L. 0. Brockway, J . Chcm. Phys., 2 , 867 (1934).
(7) L. Pauling and I,. 0. Brockway, THIS JOURKAL, 67, 3684
(8) P. A. Shaffer, V. Schomaker and L. Pauling. J . Chem. Phrs., 14,
diffraction features on three of the best plates are
summarized in Table I. These values are based on
measurements of each feature by two observers.
The visual curve shown in Fig. 1 was based on in-
dependent interpretations of the patterns by three
observers. The interpretations were in close agree-
ment on all features except as noted below in the
case of the eighth maximum and the ninth minimum.
The portion of the curve in the interval q = 0 to
p = 20 was copied directly from the most accept-
able model as is customary.
Due to the diffuse nature of the eighth maximum
and the ninth minimum, there was some doubt as
to the exact shape of these features. However, it
was the opinion of all observers that the maxiinuin
was asymmetric to the outside and that the in-
dicated shapes of these features are approximately
correct. Due consideration was given to this uii-
certainty in selecting acceptable models.
The radical distribution curve appearing in Fig.
1 was calculated using the equation8
The values I(q)o were read from the visual curve,
Fig. 1, and the radial distribution curve was cal-
culated on I.B.M. tabulators.* The peak at 1.37
A. correspoqds to the C-I? and C-N distances
and at 2.23 A. corresponds to the N
and the F
liminary calculations of models showed quantita-
tive incompatibility with the curve with respect to
these two peaks, further investigations of these
models were abandoned. It was later demon-
strated that none of these models was within the
range of acceptability. In view of the complex
nature of the vibrational problem for this molecule,
as indicated later, a complete quantitative inter-
pretation of the radial distribution was riot at-
The structural determination of perfluorotri-
methylamine involves the evaluation of four param-
* F distance
. F distance in the CF3 group.