1184
ANALYTICAL CHEMISTRY
Table I. Effect of Molten Sodium Peroxide on Bureau of Mines Zirconium (50 grams of NazOz in 168-gram Zr dish heated over open flame) Chemical” Tieatment Lose of Weight of Dish Analysis Mg. % M g . / g . NazOz
dish, which is directly subject to the open flame, was made 0.25 inch thick. I n Table I are given the results obtained by fusing 50-gram amounts of sodium peroxide in the zirconium dish. The melts after cooling were easily removed by inverting the dish and striking it sharply against a flat surface. The dish was washed with concentrated hydrochloric acid before each weighing. The dish after each fusion showed a white film of zirconium oxide on the inside where the molten sodium peroxide came in contact with the dish and on the bottom where the direct flame of the burner was applied. If the fusion were performed in a muffle at the lowest temperature necessary for fusion, and if the more corrosion-resistant de Boer process zirconium were used, the losses would be appreciably lessened. The disadvantage of the de Boer type metal is its expense, more than ten times the cost of the vacuum-cast metal. The studies conducted by Seelye and Rafter (d, 3) in platinum should also be of value in determining the optimum condition for fusions in zirconium. Zirconium metal is rapidly attacked by hydrofluoric acid, and appreciably by phosphoric and sulfuric acids. Nitric and hydrochloric acids have little effect.
M$af6p*
Ka?Oz heated 15 minutes until molten and then 2 minutea more 188 0.11 3.8 2.6 2. 1 repeated with 50 grams more of Sa202 217 0.18 4.3 2.1 3. 2 repeated 205 0.12 4.1 2.9 4. 2 repeated but heated for about 25 minutes 360 0.22 7.2 5.7 a Sodium peroxide,melt dissolved i n water and HC1. Zr precipitated with IiHbOH, filtered, ignited. and weighed as ZrOn. 1.
crucible without showing an appreciable attack. A4few tests have shown a crucible loss of about 5 mg. for each gram of sodium peroxide, whereas fusions carried out similarly in nickel, iron, and silver lost twenty to fifty times as much. Moreover, as both nickel and iron were to be determined, the use of zirconium for the fusions was ideal, giving no interferences. The zirconium crucibles were machined from both the de Boer process zirconium bar and the Bureau of Mines vacuum-cast metal. The high purity de Boer metal is more corrosion-resistant and is less attacked during the fusions. The crucibles are approximately 1.375 inches long, ‘5/,e inch in diameter a t the top, tapering to 1 3 / 1 6 inch at the bottom, and 3 / 6 4 inch thick, A 3-inch diameter, round-bottomed 3/64 inch thick zirconium dish weighing about 168 grams was also machined from the Bureau of Mines metal. However, because zirconium is converted to the oxide a t elevated temperature, the bottom of the
LITERATURE CITED
Muehlberg, W.F., I n d . Eng. Chem., 17, 690 (1925). Rafter, T. A., Analyst, 75, 485 (1950). Rafter, T. A , , and Seelye, F. T., “Low Temperature Decomposition of Inorganic Materials by Sodium Peroxide,” Dominion Laboratory, Dept. Sci. Ind. Research, Wellington, New Zealand, 1948. (4) Rafter, T. A., and Seelye, F. T., Nature, 165, 317 (1950). RECEIVED October 20, 1950,
Analysis of Ruaternary Mixtures .4pplication of a Graphical Solution of Four Simultaneous Linear Equations JAMAL TADAYON The Metal Box Co., Ltd., Acton, London W.3, England S &UAKTITAITIVEanaljsis of quaternary mixtures it is
I usual to determine four independent physical properties for each of the pure components and the corresponding properties for the mixture; then
if
PRINCIPLE OF METHOD AND PROCEDURE
the linea1 mixture law holds
+ a22J + + ajtc = B biz + bly + b l + b4v R c1x + c*y + cai + = c d i + ~ d22~ + dgt + D
aix
a32
CIIC
d4ul
s + y + z + u = l
computation, depends on the scale used and the care with which the lines are drawn and measured.
(1) (2) (3)
(4) (5)
n here A , B , C, and D are the measured values of the four physical
properties for the mixture, and a,,b,, c l , and d, (i = 1, 2, 3, and 4) are the corresponding values for the four pure components X, Y , 2, and W , whose fractional concentrations in the mixture are x, y, 2 , and w , respectively. Equation 5 is normally used for checking the results of the analysis obtained from the simultaneous Equations 1, 2, 3, and 4. I t is equally possible to solve four equations composed of Equation 5 and any three of the four Equations 1, 2, 3, and 4. The remaining equation is then used for checking purposes. Whichever procedure is adopted, the problem is one of solving four simultaneous linear equations. The speed and the degree of accuracy evidently determine the method of solution, which is usually carried out by successive elimination of the variables or by the use of determinants. As an alternative to these methods, the folloLying simple graphical method has been developed. Its accuracy, as with all other graphical methods of solving mathematical problems ( I ) or other graphical aids to
A quaternary system expressed by Equations 1, 2, 3, and 5 may be represented geometrically as a pyramid shown in Figure 1, ahere points X, Y , Z, and W represent the four pure components in space. Each point is defined by plotting the coefficients a,, b,, and c 2 for the particular pure component and therefore can be Iegarded as fixed with respect to the orthogonal axes, a, b, and c. If the mixture law holds, a point representing a binary mixture of X and Y will plot on line XY,that representing a mixture of Y and 2 will lie on line YZ,and so on. Similarly, a point
Figure 1. Geometrical Representation of a Quaternary Mixture
V O L U M E 23, NO. 8, A U G U S T 1 9 5 1
1185
representing a ternary mixture of, say, X, Y , and Z will lie inside triangle X Y Z . Finally, a point such as P, representing a quaternary mixture of X , Y , Z, and W , will fall in the space bound by the four surfaces of the pyramid. If line X P intersects the plane of triangle YWZ a t 0, the fractional concentration of X will be given by
x
=
OP/OX
mixture of Y , 2, and Wand the solution is carried out as described and given by the expressions 7 , 8 ,and 9. Because coefficients a,, b,, and cI are constants characteristic of the pure components, points x', y', z', w',x , y, z, and w can be plotted permanently on a convenient and constant scale and used for the solution of any mixture composed of X , Y , 2, and TV The points that characterize a particular mixture are p ' and p and only these are freshly plotted. When x , y, z , and IC, are not given as fractions-Le., when Equation 5 is not valid-the following transformation of Equation 4 may be carried out.
Putting X = d l x / D , Y = d n y / D , Z = d,z/D, and W = d , u / D , and substituting, results in: (11) I
112)
k
Figure 2. Graphical Solution of Four Linear Simultaneous Equations
(13)
X + Y + Z + W = l
Point 0 can now be considered to represent a ternary mixture of Y , Z, and TV, the fractional concentration of each of which may be given by
(14)
The equations are now in a convenient form for graphical solution. The values of x, y$z , and 2c can be obtained from X, Y , 2, and W ,respectively.
y = (SO/NY)(l - 2)
(7)
PROOF
z = ( M O / . ! ! Z ) (l 5)
(8)
w = (RO/RW)(l - x)
(9)
The fractional concentration of X can be given by 0PjO-Y (Figure 1). As points X and P are defined, it remains to locate point 0 at which X P intersects the base, YZW. Project the pyramid on the vertical plane containing axes a and b and on the horizontal plane containing axes b and c to obtain Figure 3, where the vertical plane is rotated anticlockwise through 90 O to lie in the horizontal plane.
Figure 3. Vertical and Horizontal Projections of Pyramid Representing a Quaternary Mixture
The graphical procedure, the proof of which is given below, is as follows : In Figure 2 let z', y', z ' , and w' represent plots of a, against b, (i = 1, 2 , 3, and 4) in Equations 1 and 2; and x , y, 2, and w
represent plots of ci against b, in Equations 3 and 2 for each of the four pure components, respectively. Similarly, by plotting A, and C against B from Equations 1, 3, and 2 we obtain points p and p , respectively, for the quaternary mixture, P. Let x'p' intersect any two sides of triangle y'w'z', such as y'w' and y'z', a t f ' and g . Produce f'jand g'g a t right angles to axis b and drawfg. (Pointsf and g are easily obtained by inspection if the figure is drawn on graph paper.) Produce x p to intersect fg a t 0. The fractional concentration of X is then given by z = op/ox. Point o is now regarded as representing a ternary
,
,
1186
ANALYTICAL CHEMISTRY
A plane containing X P and a t right angles to the vertical plane will project on the latter as z'p'. This line cuts the sides of triangle y'w'z' a t f' and g'. f'g' is therefore the projection 011 the vertical plane of the intersection of plane YWZ and that containing X P . Because points f' and g' belong to y'w' and y'z', t,heir projections on the horizontal plane, f and g, should lie on yw and yz, respectively. Point 0 is the intersection of X P and plane YWZ; therefore rp is &ended to intersectfg a t point 0 .
respectively (Figure 4). Points p and p' are similarly obtained b y plotting 49 and 83.5 against 44.5. Produce x'p' t o obtain points f' and g'. Transfer these points vertically down onto the corresponding sides, 2/t and IW, t o obtain f and g. Extend x p to intersect fg at o. The tractional concentrations of the ronipoueutq %rethen given by x
In the graphical solution described for simplicity, the vertical plane containing a and 6 is rotated clockwise so that the t m planes are superimposed (Figure 2). It is evident that the chnngr of scale by addition or multiplicat,ion does not alter thr solution.
2
( o p o x ) = 22 88
IJ = ( n o n y ) ( l - x ) =
22 110
025
=
x
0 75
=
0.13
21.2 x 80
o.;j
=
0.20
Example.
+ 401) + -102 + 60w = 49 20x + lo!/ + 702 + 50w = 44.5 90r + 8 0 ~+ 90z + 65w = 83.5 1'+ !/ + r + w = 1 601
(i)
/('
=
(ro h ) ( l - I) =
(ii) LITERATI'RE CITED
(iii)
(iv) Plot coefficients of I, IJ, 9 and w in ( i ) and (iii) against tlie corresponding coeficient~in (h) to obtain points x', y', ?'. arid w ' ,
(1
l l e h n i k e , Rudolph. "Leitfadeii z u ~ i iGraphiwhrii Hechneii," p. 12. Leipzig arid K i e n . F r a n z Deuticke. 1924,
K w m r 8 : n July 21. 1S.W.
Colorimetric Determination of Vanadium with Benzoylphenylhydroxylamine SUDHIH C H C W R A SfIOhfE' Indian Institic tr of Scierrre. Rnngulore, India
ANADIUhI, as vanadate, has been determined colorinietriVenlly using various organic reagents. The uses of strychnine (6, l b ) , diphenylamine ( 7 , I s ) , and aniline hydrochloride ( 1 4 ) have been reported for the colorimetric determination of the metal. Montequi and Gallego (9) have prepared the conipounds of vanadate ions with 8-quinolinol (8-hydroxyquinoline) and have found the violet-black precipitate obtained from a slightly acid solution to be (CsH8ON)4V2O3. The same workers have separated vanadium from chromium by rstractirig the 8-quinolinol compound with chloroform. Bach and Ti,elles ( 1 ) have determined vanadium in water by ext,racting the quinolate with isoamyl alcohol. Molland (8) employed 8-quinolinol-5-sulfonic acid instead of 8-quinolinol. Chervyakov and Ostrouniov (3) determined minute quantities of vanadium in uranium preparations using p-dimethylaminoaniline. Szebell6dy and Ajtai (1.3) studied the catalytic effect (which was activated with pyrocatechol) of vanadiuni upon the reaction between p-phenetidine and potassium bromate, and determined as little as 0.0006 microgram of vanadium. Findlay and Furman (dq 6 ) extracted vanadium even in microgram amounts from dilut'e sulfuric acid solut,ion by cupferron and ether prior to its estimation by eolorimetric methods. series of allied organic compounds was investigated ( 1 1 ) in order to improve upon the defects of cupferron (ammonium salt of nitrosophenylhydroxylamine). The use of henzoylphenylhydroxylamine, which was first prepared by Bamherger ( 2 ) , as an analytical reagent for the gravimetric determinat'ion of copper, iron, aluminum, and titanium, has recently been described by the author (10). Benzoylphenylhydroxylamine, like cupferron, gives a mahogany red precipitate tyith vanadate ions. The precipitate is soluble in organic solvents such as ethyl alcohol, benzene, and acetic acid. This new organic reagent is not' suitable for the gravimetric determination of vanadium, because a portion of the complex remains in the colloidal condition and passes through the filter paper (Whatman No. 42). In the present investigation benzoylphen?-lhydroxylamine was employed for the colorimetric determination of vanadium. A\
1
Present address. Sational Institute of Sciences, Delhi 8 . India.
APPARATUS AND SOLUTIOYS
.\bsorpt,ion measurements a t various wave lengths were Inade visually with a polarizing spectrophotometer (Gaertner), using a solut,ion thickness of 1 cm. Colorimetric comparisons n-ere carried out using a Duboacq colorimeter. Sensitivity tests were performed in 50-nil. Sessler tubes. pH values of the solutions were measured with a glass electrode. Benzoylphenylhydroxylamine Solution. A 0.2mc solution of I)enzoylphenylhydroxylamine in ethyl alcohol was used in tlie spectrophotometric work. Vanadium Solution. -4. vanadate solution was prepared by dissolving sodium vanadate in distilled water and the vanadiuni content ivas determined by precipitating with cupferron in icecold solutions. A portion of the stock solution was diluted so that the final solution contained 0.05 mg. of vanadium per nil. Diverse Ion Solutions. Standard solutions of ferric alum and titanium sulfate were prepared separately by the usual methods. The other solut'ions were made by dissolving weighed amounts of salt! in distilled water, each milliliter containing 2.5 mg. of the ion in question. Solutions of the anions were prepared from thr alkali nietd salts: sulfates were used for the solution.; of tllr rations. -411 the eheniicals used %yereof analytical rragriit quality. SPECTROPHOTOMETRIC STUDY OF COLORED SOLCTIOIS
In preparing the colorimet,ric solutions used in thi:: stlid!. t h e following procedure was adopted. -4.known amount of vanadium solution ( 1 to 15 nil.) was introduced into a 50-ml. volumetric flask and suitable quarititiee of di1ut.e sulfuric acid were added to adjust the pH of t,he final solution to t,he required value. -4preliminary experinipnt was ear' to regulate the pH of the solutions. ine sollti?n (10 i d . ) was then added and the contents were thoroughly mixed. The resulting solution was dilut,ed with ethyl alcohol (15 nil.) and made to volume with distilled water. After 10 minutes, the absorption due to the solut,ion was measured with the spectroIJhotoineter. Effect of pH. The orange-red color formed by benzoylpheriylhydroxylamine with vanadate ions was influenced by the pH of the solutions. The variation of absorbancy (log Io/Z) of the colored solution, containing 10 mg. per liter of vanadium, with pH is shown in Figure 1. A s the field of view was not very bright at 480 mp, it was convenient to take thp readings at 510 nip. The
