grams were dipped or sprayed with this reagent.
Neutral silver nitrate was a highly sensitive reagent for detecting phenolic compounds, I n studies with gallic acid, this reagent was comparable with ultraviolet light in sensitivity and much more sensitive than diazotized sulfanilic acid, which is commonly used in the detection of phenolic compounds (3). It was also possible t o detect reducing sugars and phenolic compounds separately on the same chromatogram, as the sugars did not give positive responses untii after the silver nitratetreated paper was dipped in a 0.5N sodium hydroxide in methanol. Many aromatic nniines also gave distinctive color reactions with silver nitrate in acetone. -1 particularly striking example was the brilliant magenta color given by p-amino-N,N-diethylaniline.
The colored spots obtained with the silver nitrate reagent range from light pink t o deep green (Table I). Although several spots are referred t o as t a n or brown, they often appear different when viewed together, as would be done in comparing a n unknown compound n i t h a known, under identical conditions. The development of distinctive colors gives this method a decided advantage over earlier procedures (8-4) utilizing silver nitrate. The colors changed to a conimon brown on contact with water or bases. Phenolic compounds which can be converted t o 1,2-or 1,4-benzoquinones appeared to give the most intense colors, although both complex formation with silver ion (1) and oxidation are possibly involved, Certain of the ether derivativesdevoid of free phenolic hydroxyl groups did not give a color reaction with neutral silver nitrate.
ACKNOWLEDGMENT
The authors are indebted to the National Polio Foundation for financial
support and t o George B. Rice for the synthesis of several of the phenolic compounds used in this study. LITERATURE CITED
(1) Andrews, L. J., Chem. Revs. 5 4 , 713 (1954). (2) Block, R. J., Durrum, E. L., Zweig, G., “Manual of Paper Chromatography and Paper Electrophoresis,” p. 228, Academic Press New York, 11955. (3) Lederer, E. hderer, M., Chromatography, A keview of Principles and A plications,” 2nd ed., pp. 163-4, Eievier, Sewl)iork, 1957. (4) .Smit$ I., Chromatographic Tech. niques, p. 196, Interscience, Sew York, 1958. W. J. BURKE A. D. POTTER R. M. PARKHURST Department of Chemistry University of Utah Salt Lake City, Utah 1 Present address, Stanford Reeearci Institute, Menlo Park, Calif.
The Mathematics of Single-Explosion Gas Analysis SIR: I n the single-explosion method of gas analysis computations are usually based upon the assumption that GayLussac’s law of combining volumes holds within the limits of accuracy required. Four equations may be written and a maximum of four components may be determined. However, a system of four components may be indeterminate, or it may be determinate with respect to only one, two, or three components. The problem of judging determinacy was examined at length by de Voldere and de Smet (1). They classified gases arbitrarily &s hydrocarbons with n and K values to fit the formula C,HZ, 2K and formulated rules based upon such classification. Kobe (8) has demonstrated that any gas mixture can be proved to be determinate or indeterminate by applying the mathematical theory of determinants.
However, it is believed that adequate and much simpler rules than those formulated by de Voldere and de Smet for distinguishing between determinate and indeterminate systems can be formulated. Any equation which can be expressed in terms of the other equations in the system is not an independent equation. Conditions which nullify the independence of one or more of the equations which express the volumes of nitrogen, oxygen, and carbon dioxide and the contraction in volume necessarily reside in the coefficients of the equations. The true criteria of independency or dependency are, therefore, to be found in the relationship between volume coefficients. Illustrative volume relationships are shown in the table. The term “nitrogen indes” is defined as the sum of the volume coefficients in the equations
+
Illustrative Volume Relationships I. Absence of Nitrogen
Gas + Vol. in mixt. Vol. O2 used Vol. GO2formed
Contraction Gas -P
Vol. in mixt. Vol. 02 used Vol. CO2,formed
Contraction Nitrogen index 728
C&o CzH4 CzHa d 9 P 0.5~ 3.5b 5c 6.5d 3q 2.5~ . o a 2b 3c 4d 2q 2p 1 . 5 ~ 2a 2.5b 3c 3.5d 2q 1.5~ 11. Presence of Nitrogen or Nitrogen Compound N2 N*0 XO NHs HCN XzHd CHsNOi N A B C D E F 0 -0.5A -0.5B 0.75C 1.25D E 0.75F 0 0
N
Hz
CH4
CzHe
C3Ha
X
a 2a
b
C
0
0
0
-0.511 A
D
0
l.25C 0.5C
0.76D 0.5D
ANALYTICAL CHEMISTRY
0.5B
0 E E
E!
0.25F 0.5F
expressing (1) volume of sample an( (2) volume of 02 consumed, minus thc sum of the coefficients expressing (3 volume of C 0 2 formed and (4) contrac tion in volume. I n the absence of nitrogen or a com pound which yields nitrogen in t h explosion reaction, any one of thl relationships numbered (1) to (4) ma! be expressed in terms of the other three I n such cases, therefore, a maximum o only three components may be deter mined by the single-explosion method If one component is nitrogen or a com pound which yields nitrogen up01 oxidation, its volume is expressed a 2 nitrogen index X ,; where n is t h number of atoms of nitrogen in thl molecule. This is true irrespective o the total number of components. Heno no system is indeterminate with respec to a single component of free or com bined nitrogen. Similarly no system it indeterminate with respect to a sing1 carbon compound. Equations which express the volum of 02 consumed, volume of CO1 formed contraction in volume, and the nitrogei index are independent equations unles there is a constant difference in th volume coefficients (or identity of th nitrogen index VI hich represents a dif ference) or identity of coefficients be tween the components taken separatel: or in pairs. Reference to the table shows that fo a series in which successive member differ in composition by CH2, thi volumes of O2 used and C0, formed, an(
the contraction in volume for any member differ from the values for adjacent members by 1.5, 1.0, and 0.5, respectively. Adding to or subtracting from an equation the amount by which the equation differs from a second equation does not yield a third independent relationship. Hence only two independent equations can be written for the system CH;, C211~,CS&. Similarly, for nitrogen and nitrogen compounds, if no carbon compound is present and the nitrogen indexes are the same, only two independent equations can be written. The system Nz,NzO, N?HI, for example, is indeterminate. Identity of coefficients is apparent for isomers and for compounds which differ in composition by H20. Identity of paired coefficients exists when one or two of the components are expressible in terms of the other components without changing the number of molecules, not counting water (which is condensed). Reference to the table shows that this is the case, for example, in the systems 2 C a h = CdHlo CzHc and c2& N:O = CZH, N, HpO.
+
+ +
+
The relationships pointed out may be conveniently summarized in the form of rules aa follows. RULES FOR CLASSIFACATION
SUMMARY.
Rule 1. I n a system of three (or more) components, if the composition of the reactants differs by a constant group, or multiple of such group, the system is indeterminate. Examples:
Rule 2. If the number of nitrogen atoms per molecule is the same in each of four components (three in the absence of a carbon compound), the system is indeterminate (except for a single carbon compound), Examples: NO, CHsNOr, H C N , "8; Nz, NZO, NZH4; N H z O H , NO, NHa, H C N (determinate for H C N only). Rule 3. Isomers and compounds which differ in composition by Ha0 are indeterminate. Examples: (CHa)zO, CHaCHzOH; (CH2)20, CH8-
CHO; (CHz)s, CHaCHCHz; CZHI, CzHsOH; CzHz, CHaCHO; (CHJzO, CZH4. Rule 4. If the composition of a component can be expressed in terms of other components without changing the number of molecules, not counting water, the system is indeterminate with respect to these components. Examples: 2CpH4 = CpHs CZHZ; 2 H C K = CrH2 Nz; (CHr)zO X2 = C*H+ NzO; C2H4 NzO = 2HCX HZO.
+
+
+ +
+
+
LITERATURE CITED
(1) de Voldere, G., de Smet, G., 2. anal. C h a . 49, 661 (1910). (2) Kobe, K. A., Im. ENG.CHEM.,AXAL.
ED.3, 262 (1931).
J. H, ROBERTSOX
Department of Chemistry University of Tennessee Knoxville 16, Tenn. Division of Physical Chemistry, Southeastern Regional Meeting, ACS, Gainesville, Fla., December 1958.
190. Zr0,.3TeO R. P. AGARWALA, E. GOVINDAN, and M. C. NAlK Chemistry Division, Atomic Energy Establishment, Trombay, India
and tellurium, taken in the ratio corresponding to one atom 3f Zr to three atoms of Te, were heated in air a t 750' C. for 48 hours and yielded 3, compound (Zr02.3Te0) which is not reported in literature. The synthetic sample so prepared was chemically analyzed: ZrO, required 22.23%, found 21.65%; Te required 69.10%, oy difference 69.20%. The crystal parameters were deduced by indexing a powder photograph by the graphic nethod.
Z
IRCONIUM OXIDE
X-RAYDIFFRACTIOH DATA Celldimensions. a = 7.985 A,, c = 5.589 A., c / a = 0.70 Molecules per unit cell. 2. Density. 5.176 grams per cc., 5.156 crams per cc. (calculated). Crystal symmetry. Tetragonal Space group. Possibly P4/mmm, P422, or P 4 / m The x-ray ponder diffraction data were obtained using CuKa radiation with nickel filter and a 143.2-mm.
~~~
~~
~~
~
Table I.
X-Ray Powder Diffraction Data for ZrOp. 3 T e 0 dcalcd. 17.1 SO. hkl dobld dc,iod 1 101 4.575 4.580 M 17 402 1.627 1.624 2 201 3.241 3.248 VS 1.598 1.597 3 211 3.000 3.009 W MS 19 510 1.570 1.566 4 201 2.817 2.823 5 102 2.645 2.636 M 2o 1.540 1.535 6 221 2.516 2.520 VW 7 320 2,209 2.211 M 21 511 1.512 1.508 I'W 22 521 8 321 2.056 2.059 1.439 1.433 1.395 1.397 9 400 1.994 1,996 S 23 004 10 410 IT 1.374 1.369 1.934 1.936 24 530 25 114 11 003 1,866 1.863 VVW 1.355 1.356 12 411 1.829 1.830 w 26 413 1.336 1.343 13 331 1.784 1.783 YM' 27 204 1.317 1.318 IT' 28 214 14 322 1.743 1.736 1.296 1.301 15 421 1.702 1.701 S 29 611 1.279 1.278 16 231 1.665 1.657 n. 30 620 1.266 1.263 OVS, Very strong. S, strong. ITS,medium stlong. M, medium. PVIW, weak. W, weak. Vu', very weak. TT'R, very very weak.
NO. hkl
dobad.
t:;}
diameter camera, and using the xray d iff ractometer
.
ACKNOWLEDGMENT
The authors thank C. T. Mehta of
Ire]a
w \T'
VW bfW MK AIS
Vu'
11
MW TIT
VIT' TV
VW IV
medium
this division for the chemical analysis. CRYSTALLQQRRAYHIC data for publication in this section should be sent to W. C. McCrone, 501 East 32nd St., Chicago 16,
111.
VOL. 32, NO. 6, MAY 1960
729
