ANALYTICAL EDITION
262
.
efficient was measured a t a wave length of 550 millimicrons using a 3-cm. layer of solution. At this wave length it was found that the extinction coefficient of tartrazine is negligible. This value was then divided by 1.87, the extinction coefficient of pure amaranth a t this wave length, and multiplied by 100. This gave the per cent amaranth present. When there was only a small per cent of amaranth present, it was found advantageous to use a dye concentration greater than 20 mg. per liter and reduce the reading by direct proportion to a basis of 20 mg. per liter. Curve 2, Figure 1, which represents measurements on a dye mixture composed of 60 per cent amaranth and 40 per cent tartrazine, illustrates the basis of the calculation just given. Between wave lengths 550 and 590, the altitude of any point on curve 2 is very nearly 60 per cent of the altitude of a corresponding point on the amaranth curve. For example, in Figure 1, at a wave length of 550, the distance AB = 59.4 per cent of AC. Results obtained by this method are shown in Table 11. Knowing the per cent of amaranth present, the per cent of tartrazine can be calculated from the volume of standard titanium trichloride solution necessary to titrate a given weight of the dye mixture, For example, 0.25 gram of the above dye mixture required 34.84 cc. of 0.05 N titanium trichloride solution. On the same basis, one gram of the dye mixture would require 69.68 cc. of 0.1 N titanium trichloride solution. As determined above by the spectrophotometer, there is 59.4 per cent of amaranth present, or 0.594 gram in one gram of dye mixture. This quantity of amaranth would require 0.594/0.01511, or 39.31 cc. of 0.1 N titanium trichloride solution, The difference between 69.68 cc. and 39.31 cc., or 30.37 cc., represents the quantity of reducing solution
Vol. 3, No. 3
required for the tartrazine. The percentage of tartrazine then equals 30.37 X 0.01336 X 100, or 40.47. This calculation is analogous to that performed in estimating the am+ ranth by the selective reduction method given in this paper and may be summarized in the following equation: , A - X 0.01336 X 100 = % ' tartrazine 0.01511 When A = cc. of 0.1 N titanium trichloride required by 1 gram of dye mixture b = gram amaranth present in 1 gram of dye mixture Conclusion
Of the two methods presented in this paper the selective reduction method is perhaps the better. It has the advantage of being more uniformly accurate and it does not take any special equipment. Both methods have the advantage of being rapid, requiring only a few minutes for each determination, and, as shown by the tables included, give fairly consistent and reasonably satisfactory results. Literature Cited (1) Ambler, J. A,, Clarke, W. F., Evenson, 0. I,., and Wales, H., U. S. Dept Agr., Bull. 1390, 26 (1927). (2) Evenson, 0. L., and McCutchen, D. T., IND.ENG.CHEM.,20,860 (1928). (3) Evenson, 0. L , and Nagel, R. N., I b i d , Anal Ed., S, 167 (1931). (4) Holmes, W. C., A m . Dyesluf Reptr., April, 247 (1926). (5) Holmes, W. C , Ibid., March 22, IS9 (1926). (6) Jablonski, C. F., J . Assocn. Oficial Agr. Chem., 12, 354 (1929); 13, 412 (1930). (7) Mathewson, W. E , "Allen's Commercial Organic Analysis," p . 500, 5th ed., Vol. 5, Blakiston. (8) Wales, H., A m . Dyestuf RReptr., 12, 751, 791, 855, and 863 (1923).
Analysis of Three Hydrocarbons by Combustion' K e n n e t h A. Kobe SCHOOL OF CHEMISTRY, UNIVERSITYOF MINNESOTA, MINNEAPOI,IS, MI".
OMBUSTION data in gas analysis are generally used to determine hydrogen and a hydrocarbon, or two hydrocarbons, and it is not generally recognized that it is possible to determine three hydrocarbons in one combustion. DeVoldere and deSmet (9, 3) have divided gases into three classes, and deduced relationships between these classes, and series within the classes, which show when it is possible to determine three hydrocarbons by a single combustion. Much simpler relations can be deduced from the general formulas of any three hydrocarbons by the use of determinants, avoiding the necessity of fixing the class and series of which the gas is a member. It is not necessary that the gas be a hydrocarbon, since values for other gases can be inserted into the formula with the same result. Table I gives the equivalent values for other gases.
C
Table I-Eouivalent Values for Other Gases a b GAS,CaH b 0 2 Hydrogen Hz 1 -2 Carbon rnbnoxide, CO 1 -4 Carbon dioxide, COz 0 -4 Oxygen, Oz 1 0 Formaldehyde CHz0 2 4 Dimethyl ether, (CHa)zO
Thus the term "hydrocarbon" as used here will also include these gases. Determination of Three Hydrocarbons
If nitrogen is not present in the mixture or is determined by actual difference, the calculations can be made from the 1
Received February 13, 1931.
volume of gas used, the volume of carbon dioxide f o r m l , and the contraction in volume occurring on combustion.
V
= volume of gas used
C
volume of carbon dioxide formed contraction in volume on combustion = cc. of hydrocarbon C,Hb = cc. of hydrocarbon CcHd = cc. of hydrocarbon CeHf
U x
y z
= =
The general equation for the combustion of a hydrocarbon is C,Ha
+ (a + b / 4 ) 02 +a COa + b / 2 H20
This leads to the equations
v
= x + y + z cy ez b/4h f (1
C = ax U = (1
+ +
+
(1)
+ d/4)Y f (1 + f / 4 ) z
(2) (3)
The determinant D of this set of equations is I 1 1 1
1
D = D =
ad
1 fcd/4
1 +'b/4
1 -kef/4
+ be + cf - af - bc - de 4
The Equations 1, 2, and 3 are dependent if D case ad
+ be + cf = af + bc + de
=
0, in which (5)
Thus if Equation 5 is an equality, it will not be possible
July 15, 1931
INDUSTRIAL AND ENGINEERING CHEMISTRY
to determine the three hydrocarbons, and conversely, if the two sides of the equation are not equal, then it is possible to calculate the three hydrocarbons from Equations 1, 2, and 3. I n the case of a homologous series b =am
b
+ af - be 4
y=
+ n,d = cm + n, andf = e m + n
D
d
substituting these values in Equation 5 we find that the equality holds, that D = 0, so it is not possible to solve these equations for three hydrocarbons of the same homologous series. However, if the third hydrocarbon is of another series, the identity of Equation 5 does not hold, so it is possible to determine the three hydrocarbons. If all three hydrocarbons are of different series, the values of the subscripts must be inserted in the equation to find if the identity is true. Solving Equations 1, 2, and 3, the general values for 2,y, and z are:
- .f
263
- b + bc
+
)+
- a d ) + u(-)bc - a d
4
D
+
4
D
D = af
+ bc + de - ad - be - cf
D
4
Although there are four equations (1, 2, 3, and 6) it is not possible to determine four hydrocarbons since the equations are dependent, being related by the equation U = V + W - c
(8)
Application of Method
x =
D
The determination of carbon monoxide, hydrogen, an,] methane by this method has been known for some time ( 7 ) . The new apparatus devised by Shepherd (6) makes use of Y = D this method for the determination of these three gases. The ad - bc b-d method of manipulation for the determination of any three I / ( , - c +T) ~(7) U(c - a ) gases is the same as that used for carbon monoxide, hydrogen, z = D and methane, and may be carried out by the instructions given for either style of apparatus (6, 7 ) . It is seen that the ad be cf - a.f - bc - de D = general equations reduce to very simple ones when specific 4 values are substituted for the general terms, -so that the calculations involved are no more difficult than those of an Determination of Three Hydrocarbons and Nitrogen ordinary combustion. Not only can a gas of another series Nitrogen is usually determined by difference from the sum be determined in the presence of two saturated hydrocarbons, of all gases present. However, it may be determined from but two unsaturated hydrocarbons may be determined in the the combustion data. Its presence in the hydrocarbon presence of a third gas, an advantage since both unsaturates mixture adds one more gas so that a fourth equation is would be absorbed in the usual method. The method lends necessary for the determination of the composition. This itself t o the analysis of the products from catalytic and will be given by the volume of oxygen consumed in the pyrolytic reactions, and many other uses for specific problems combustion of the hydrocarbons. can be worked out. be
- af + c
(f9) + u(a - e)
+
+
+ +
Errrors of Method
W = volume of oxygen used in the combustion W = (a b/4)x (c d/4)y (e + f / 4 ) z
+
+ +
+
(6)
Equations 2, 3, and 6 now can be solved for x, y, and z, the volume of nitrogen being the difference between the volume taken and the sum of these gases. The determinant of these equations is
D =
D =
1
1 a
+7 bb // 44
+4 dd // 44
1 e
f/4 + f/4 af + bc + de - ad - be - cf 1
c
1
4
(7)
This reduces to Equation 5 ad
+ be + cf
= af
+ bc + de
(5)
Thus the same relationship tells whether or not the equations are dependent so that three hydrocarbons can be determined in the presence of nitrogen by the use of the volume of oxygen consumed in the combustion. The general values for 2 , y, and z are: e - c + f - d + d e 4- q f
x =
D
)+u
( V )+
The correctness of these results, as those of all methods in gas analysis, assumes that volumes of gases are additive and that the volume of carbon dioxide formed in a combustion is an exact multiple of the volume of hydrocarbon conshmed. Fuchs (4) has shown that there is an increase in volume on mixing carbon dioxide with nitrogen or with oxygen. With the former gas the maximum increase was 2.73 per cent a t 56.7 per cent nitrogen, while with the latter gas the maximum increase was 2.45 per cent a t 53.0 per cent oxygen. Also, carbon dioxide does not have as great a molecular volume as methane or carbon monoxide, so that the combustion of these gases does not produce an equal volume of carbon dioxide but a slightly smaller volume ( 1 ) . Corrections for these effects are not ordinarily applied, but in certain cases they cause appreciable error and correction should be made. In the use of this method it may be emphasized that combustion by the slow-combustion method (5) gives rise to less error than the explosion method since the sample and oxygen used are larger. The use of this method involves but one more measurement than the ordinary combustion for, after the carbon dioxide has been absorbed, the excess oxygen left from the combustion is absorbed. It is apparent that this one measurement cannot appreciably increase the error of the determination. The error calculated by Shepherd for his combustion does not give differences greater
ANALYTICAL EDITION
264
than one-tenth of one per cent for the technical method, and would be less for the exact method. Literature Cited (1) Dennis and Nichols, “Gas Analysis,’’ p. 134, MacMillan, 1929. (2) Dennis and Nichols, I b i d . , p. 123.
’
Vol. 3, N o . 3
(3) devoldere and deSmet, 2.anal. Chem., 49,661 (1910). (4) Fuchs, 2. physik. Chem., 92, 641 (1918). (5) Kobe, IND. ENG.CHEM.,Anal. Ed., 8, 159 (1931). (6) Shepherd, Bur. Standards J . Research, 6 , 121-67 (1931). (7) U.S. Steel Corporation Chemists, “Methods for Sampling and Analysis of Gases,’’ pp. 62 and 98, Carnegie Steel Co., Pittsburgh, 1927.
Determination of Organic Acids
V-Applica tion of Partition Method to Quantitative Determination of Acetic, Propionic, and Butyric Acids in Mixture1a2 0. L. Osburn and C. H. Werkman DEPARTMENT OF BACTERIOLOGY, I O W A STATE COLLEGE, AMES,IOWA
HE differential distri-
The partition method has been extended to the of partition has yielded the bution of fatty acids quantitative determination of acetic, propionic, and most satisfactory results and between two immisbutyric acids in a mixture. A nomogram has been has been chosen for the desolvents has been emconstructed from which is read the percentage of each of termination of three acids. ployed in a partition method the three acids present after two values (percentage In former publications (2, for (a) the quantitative departition constants) characteristic of the mixture have 3, 4, 5 ) the partition value termination of t w o known been determined. characteristic of the mixture fatty acids in a mixture (2,3), of acids has been called the and (b) the provisional identification of two fatty acids in partition constant (P’) and was defined as the number reprea mixture (6). The method was developed to fill a need senting the cubic centimeters of 0.1 N alkali required to neuin fermentation studies for rapid and accurate determina- tralize 25 cc. of the aqueous phase to phenolphthalein, when tions of the lower fatty acids. For a consideration of the 30 cc. of the unknown 0.1 N acid solution were partitioned principles and advantages of the partition method, the reader with 20 cc. of the immiscible solvent. It is necessary in using is referred to Behrens (1) and to previous publications in this partition constants to adjust the unknown acid solution to 0.1 N . If, instead of adjusting the acid solution to exactly series (2, 3, 4, 6). The partition method is extended in the present paper to 0.1 N and determining the partition constant, the quantity the quantitative determination of acetic, propionic, and of acid distributed in the aqueous phase be calculated as the butyric acids in a mixture. The method has yielded excellent per cent of the total acid in an equal volume of the unknown results in this laboratory and with reasonable care will give solution, it becomes unnecessary to adjust the acid solution to results with an error of less than 5 per cent for each acid. exactly 0.1 N . It has been found necessary to adjust only Its most severe test is in the case of a mixture containing a to within the limits of 0.12 N and 0.08 N . Of course, the small proportion of one or two of the acids, final adjustment must be known accurately. This percentage I n conducting the quantitative determination according is termed the percentage partition constant ( K ) to differento the partition method, the unknown acid solution is parti- tiate i t from the partition constant (P’). tioned with isopropyl ether. If the isopropyl ether is of a The two values of K employed to determine the percentages commercial grade it should be purified by adding an excess of each of the three acids in solution are: of a solution of 5 per cent sodium hydroxide. After the K1equals percentage of acid in the aqueous phase when 30 mixture is shaken, the ether is decanted and dried by adding cc. of the unknown acid solution, adjusted to a normality calcium chloride. It is then distilled and the portion coming between 0.12 and 0.08, are partitioned with 60 cc. of isoover at constant temperature is collected for use. The propyl ether a t 25” C. K z is determined by using 30 cc. of the acid solution and 15 cc. of isopropyl ether. M reprecommercial product develops an acidity upon standing. I n determining the quantitative relationships of two acids sents the number of cubic centimeters of 0.1 N alkali required in a mixture, only one partition value characteristic of the to neutralize 25 cc. of the unknown solution. M-2 represents mixture is necessary, whereas two values are necessary in the number of cubic centimeters of 0.1 N alkali required to the determination of three acids. Such partition values neutralize 25 cc. of the aqueous phase after partition. The solvents are shaken in a separatory funnel for 1minute, may be obtained in a number of ways: (1) The unknown acids may be serially partitioned, a method suggested by and 3 minutes are then allowed for the phases to separate Behrens (1). I n this method one of the phases is again when 25 cc. of the aqueous layer are withdrawn for titration. partitioned and a second value obtained. Serial partition M2 has not been found satisfactory, Its use did not yield re= -jjx 100 (1) sults of the degree of accuracy or sensitivity desired. (2) Successive partition of the acids between water and a suitable The percentage partition constants ( K , 30 cc. acid, and immiscible solvent, and water and a second immiscible sol- 60 CC. ether) established for the three acids are: vent. This method has been employed in the provisional Acetic acid Ki = 91.5 identification of two acids in a mixture ( 5 ) . (3) Two sepaPropionic acid K1 a 7 0 . 5 rate partitions of the aqueous solution of acids using one K1 = 39.8 Butyric acid immiscible solvent but in different proportions. This type
T
‘
Received February 26,1931. Supported by an appropriation from Industrial Research funds of Iowa State College, as a part of the program for the study of the use of wastes by fermentation. 1 9
I n like manner, by extracting 30 cc. of each acid with 15 a second ether at 250 “1 there is Of set of percentage partition constants:
“*
