ANALYTICAL EDITION
144
The writer has used this method for a considerable time and found that for all practicable purposes one need only consider the barium hydroxide titration for calculation of results, the other being merely a check. (cc. of blank - cc. of actual titration) X 0.0003X 100 = %carbon weight of sample
Vol. 4, No. 1
It is self-evident that absolute cleanliness is necessary in using this method. Before each series of runs, the flasks should be thoroughly cleaned with cleaning solution, washed well with distilled water, and dried in an oven. RECEIVBD
J d y 14, 1931.
Rapid Method for Fixing End Point of Potentiometric Titration FLORENCE FENWICK, United States Steel Corp., Kearny, N . J .
I
time-consuming and boresome. N THE ideal case, the end A S I M P L E M A T H E M A T I C A L formula has It is the object of this paper to point of an electrometric been developed for determining the end point of a point out an analytical solution titration is so sharply depotentiometric titration. I t is applicable only in applicable in many cases which fined by a considerable change in cases in which the electron interchange between p e r m i t s of the determination potential with the appearance of the electromotively active ions and the indicator of the end point directly from a very slight excess of the titratthe titration curve by a simple ing agent that it may readily be electrode is the same on both sides of the end calculation. located either by merely observpoint, and it assumes that a cubic equation fits ing t h e p o i n t of m o s t r a p i d the titration data accurately near the point of DEVELOPMENT OF FORMULA change in potential as the titratequivalence. Its use reduces the necessary plotThe equation ing solution is added, or by deting to a minimum, thereby shortening the time termining the position of the verE = E o - - 0.05915 log 5 tical portion covering the inflecrequired for an analysis. The formula has been N a2 tion of the curve obtained by a applied to a specific titration selected from the may be r e g a r d e d a s defining simple plot of potential versus group to which its use is theoretically least rethe potential of any indicator volume of t i t r a t i n g solution. stricted-i. e., neutralization reactions. The electrode a t 25' C. a1 and az There are, however, many factors results were found to compare very favorably in are the r e s p e c t i v e activities which tend to flatten the titraof $he electromotively a c t i v e accuracy with the exDerimental data. tion curve and thus obscure the substances. Eo is a E o n s t a n t inflection that marlrs the end point, For example, in oxidimetric reactions a relatively small fixed by the theoretical condition of unit values for both difference in oxidation potential between the oxidant and re- al and az, and N the number of Faradays passing. If the ductant has this effect; in precipitation reactions the titration electronic transfer is such that the electrode reactions on curve flattens rapidly with slightly increased solubility of the both sides of the end point for a given titration involve the precipitate; in acidimetric reactions the effect of a high same value for N , it is evident that the curve E versus V concentration of neutral salt is more noticeable under most is symmetrical with respect to the end-point inflection, conditions than in the other types of titration, and the magni- since V , the volume of the titrating solution added, may be tude of the dissociation constants of the acids and bases regarded as a measure of the ion activities concerned in the region of the equivalence point. Many of the most cominvolved determines the clarity of the end point. Figure 1 illustrates the pronounced decrease in the slope monly employed oxidation and precipitation reactions and of a neutralization curve caused by a high salt concentra- all neutralization titrations meet this requirement. It has tion. Curve 1 is the titration curve of*0.004 N sulfuric acid been found in studying the curves for a large number of such with sodium hydroxide. Curve 2 shows the same titration titrations that a cubic equation fits the curve with sufficient carried out in a solution 1.5 M with respect to pure ammo- accuracy over a fairly wide region on either side of the end nium sulfate. Crude ammonium sulfate containing consider- point. The problem, therefore, resolves itself into a quest able amounts of phenolic compounds and salts of pyridine for a rapid method of locating the point of inflection of a was substituted for the pure salt in the titration represented cubic equation. The type equation may be written by the third curve. Hardly a suggestion of an inflection remains, yet it will be shown that even in such unfavorable u V ~ bVa cV d =E cases the end point may be located with a considerable deBy successive differentiation gree of accuracy. I n the event that the titration curve is so flat as to render daE/dV== 6aV 2b uncertain the location of the end point by direct observation, it has been customary to determine from the curve the Since the value of V at the end point must be such that the change in potential, AE, for B given small change in the second derivative vanishes, it is not necessary to set up the volume of the titrating solution, AV; the maximum value complete equation to fix the inflection, as the determinaof the ratio A E / A V fixes the definitive value of V. AE/AV tion of the constants a and b suffices. If four equidistant points, VI, V z , V I ,and V,, are selected is a sensitive function, however, and is considerably affected by even slight irregularities in E. It is therefore advisable from the portion of the titration curve covering the end to plot if the highest accuracy is desired. This process is point, and if k is the constant difference between them, and
+
+ +
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 15, 1932
145
where D' is the first of the second tabular differences and D the third difference obtained by the successive subtraction of the four potentials. Substituting in the expression dZE/dV2 = GuV 2b = 0
200
+
the desired formula for V , the point of inflection, becomes V -
$! 9 s
100
(VJ)
- kD') = V n -
Td D'
D
The accuracy in V is not limited to the accuracy with which the third tabular difference can be determined, as is evident from the last form in which the equation is written. The formula is precise, and the only assumption involved in its application is that the titration curve is accurately defined by a cubic equation over the region specified. The calculation for the inflection is a matter of a very few minutes.
c
'E .f: LI
0
TABLE I. TITRATION OF SULFURIC ACIDIN PRESENCE OF CRUDE AMMONIUM SULFATE -100
.
Per Cent Neutralization FIGURE1
E,, Ez, Ea, and E4 are the corresponding potential values, the following four simultaneous equations must be valid: V'ib + VlC + d = El +++ [Vi Vi + k)2b + (VI + k ) + ~ d = E2 + 2k)% + (vi + 2k)c + d = Ea + (Vi + 3k)% + (Vi + 3 k ) ~+ d = Ec
V31u (Vi k)'~ (Vi 2k)'u (Vi f 3k)%
+ +
From these equations it may be shown that 6~
and
2b =
0
(Quinhydrone eleotrode; NaOH, 0.098476 N) EXPIURIMENTAL DATA INTIURPOLATED DATA NaOH E NaOH E AE/AV X 108 cc vozts cc. Vdt8 0.9 0.1482 0.00 0.1635 1.00 0.1461 21 0.10 0.1599 1.10 0.1439 22 0.20 0.1588 1.2 0.1410 29 0.40 0.1571 1.3 0.1380 30 0.60 0.1542 1.4 1.5 1.6 1.7 1.8 45 1.9 2.00 2.10 2.2 2.3 0.0772 2.4 0.0912 40 2.82 2.5 0.0876 36 3.50 0.0640 0.0335 2.6 0.0841 35 4.50 0.0120 2.7 0.0812 29 6.50 2.8 0.0782 30 2.9 0.0760 22 3.00 0.0735 25 End point graphio method): 2 .O oc. NaOH End point [anslytio method): 1.955 cc. NaOH
I
D
k3
(kD'
- V2D) ka
2 3 4 V o l u m e N a OH in c c
FIGURE 2
5
6
APPLICATION OF FORMULA Perhaps the most commonly encountered titrations presenting end points difficult to determine involve the neutralization of slightly acid but very concentrated salt solutions. For this reason the titration represented by Curve 3 of Figure 1 was selected to demonstrate the applicability of the proposed method, A small amount of sulfuric acid was added to a solution of 24.5 grams of crude ammonium sulfate, the concentration adjusted to about 1.5 M with respect to the salt, and the free acid neutralized with 0.1 N sodium hydroxide. The saturated quinhydrone electrode was used as the indicator electrode. All potentials were referred to a silver-silver chloride, 0.1 m potassium chloride electrode. Figure 2 shows both the titration curve and its derivative. It will be observed that the slope of the E versus V curve decreases as the end point is passed and then increases again. This is due to a t least two causes. The sulfuric acid is really titrated in a mixture of acids. Being by far the strongest acid present it is titrated first, but after it has been neutralized the effect of the reaction of the weakly acidic compounds pyridine sulfate and phenol with the base may be observed in the increased slope of the curve. Another factor in determining the course of the far end of the curve is the decomposition and oxidation of quinhydrone in alkaline solution. The measured potentials are much less certain as the solution becomes distinctly alkaline, and therefore the lower end of the curve is less accurately defined than the upper. The symmetry of the curve for this particular titration may thus be affected somewhat.
ANALYTICAL EDITION
146
The first two columns of Table I contain the experimental data for Figure 2. The last three columns were obtained from a careful large-scale plot of these data. Application of the above to from the third and fourth columns of the table results in the following: FIRST POTJDNTIALSDIFF. EL 0.1482 VI 0.9 0.7 -0.0214 Vz = 1 . 6 E% 0.1268 0.7 -0.0316 E3 = 0.0952 Vs 2.3 0.7 -0,0217 Ed = 0.0735 V4 = 3 . 0
-
VOLUMES
SnCOND DIFF.
k;
-
THIRD DIFF.
E
I
v = V?DD- kD‘
E
-0.0102 = D’
+o. 0099
[1.6 X (O.OZOl)]
+0.0201 = D
- [0.7X (-0.0102)l
0.0201 0.03216 0.00714 0.0201 = 1.955 CC.
+
the determined for 1‘ 1.955 cc., with the point of maximum rate of change of E with Ti as fixed by a carefully drawn plot of the derivative, 2.0 cc., shows that the difference is well within the accuracy of the titration. A number of exactly silnilar titrations were made, differing only in the amount of acid added initially, and the end points determined by both methods. The results are listed in Table 11. The analytic results were rounded to the nearest 0.1 CC. for computing the last column. The differences rarely exceed the probable error in drawing the AE/AI‘ Of
Vol. 4, No. 1
versus V curve and are never greater than 0.2 cc. of 0.1 N solution.
II. CoMPARIsoN OF GRAPHIC AND ANALYTIC FOR DETERMINING ENDPOINT OF ELECTROMETRIC TITRATIOS TITRATION VOLUMEOF 0.1 N NaOH Graphio Analytio Diff.
TABLE
cc *
la Ib 2a 2b 3a 3b 30 3d4
7.6 7.6 4.0 4.0 4.6 4.7 4.65 4.7
cc .
7.671 7.647 3.880 3.867 4.617 4.752 4.593 4.545 4.775 4 1.25 1.181 5 7.7 ’ 7.576 0 11.3 11.394 7s 2.0 1.965 7b 2.1 1.923 8a 0.8 0.705 8b 0.8 0.722 9a 3.9 3.930 9b 3.9 3 938 5 Titration ourve visibly unsymmetrical so that two selected for analytic solution.
-0.1 0.0 $0.0
$0.1 0.0 -0.1 +0.06 io.2 -0.1 +0.07 +0.1 -0.1 0.0 +0.2 $0.1 +0.1 0.0 0.0
sets of points were
If the indicator f?htrode is highly reversible, as is the quinhydrone electrode except in appreciably alkaline solution, and comes quickly to equilibrium with the solution, by exerting some care in making the titration the four necessary equidistant Points may be obtained directly without recourse to any Plotting. I n this case it is safest to calculate from at least two sets Of points* R=Q=IV=DAuguet 4, 1931,
A New Microanalytical Test for Carbon Disulfide NATHANIEL TISCHLER, Iowa Staie College, Ames, Iowa
A
REVIEW of the literature shows only three tests for that the test is possibly applicable to double-bonded sulfur carbon disulfide sufficiently sensitive to be considered compounds generally. A series of colorimetric standard concentrations of chemimicroanalytical tests: Feigl and Weisselberg’s (3) tests with Hector’s base and nickel acetate and with formaldehyde and cally pure carbon disuKide precipitated by equivalent amounts plumbate; Feigl and Chargaff’s (8) iodine azide test. These of the reagents has been prepared wherever quantitative detests, however, present certain disadvantages. Hector’s base terminations of traces of carbon disulfide in solution were is not readily available; the formaldehyde-plumbate test made, but it is undoubtedly possible to make more exact requires undue precautions of procedure; sodium azide is ex- quantitative measurements by the use of a colorimeter. The ,writer has applied this microanalytical test to toxicotremely explosive; and the test itself is not sufficiently rapid. A new microanalytical test, based on the formation of the logical studies, and has found it well suited to them; a few brown copper salt of diethyldithiocarbamic acid from carbon drops (as littletas 0.1 cc.) of insect blood showed the presence disulfide, diethylamine, and copper acetate, suggested itself of carbon disulfide when the insects were exposed to saturated to the writer on noting a brief resume (4) of Mayer and Fehl- vapors:of the fumigant for 2 minutes. man’s patented method of precipitating carbon disulfide from gas by absorption with a mixture of amines and metallic ACKNOWLEDGMENT oxides (5), and on recalling Callan and Henderson’s recent Grateful acknowledgment is made to Dr. Ralph M. Hixon use of diethyldithiocarbamic alkaline salts as microcoloriand to Dr. Charles H. Richardson who offered helpful sugmetric reagents for copper (1). Thereagentsused are as follows: 1% (by volume) diethylamine in absolute alcohol; gestions and criticisms, and to Rohm & Haas Company for a fellowship grant for the physiological investigation of the 0.05% (by weight) copper acetate C. P. in absolute alcohol. To test for the presence of carbon disulfide, 1 cc. of diethyl- insecticidal toxicity of carbon disulfide. amine solution and 5 drops of copper acetate solution are LITERATURE CITED added to 1cc. of the solution to be tested. Colorless solutions in acetone, chloroform, ether, and alcohol give a golden-yellow (I) Callan, T., and Henderson, J. A. R., Anal&, 54,650 (1929). color a t a carbon disulfide concentration of 1 to 100,000, a (2) Feigl, F.,and Chargaff, E., Z.anal. Chem., 74,376-80 (1928). (3) Feigl, F., and Weisselberg, K., Ibid., 83,93-104 (1931). pronounced yellow at 1to 500,000, and a faint but perceptible (4) Holta, J. C..and Huff, W. J., Proc. Am. Gas Assocn., 1436-9 tinge a t 1 to 1,000,000. I n aqueous solutions, a precipitate (1927). is formed, but the sensitiveness is the same. ( 5 ) Mayer, M., and Fehlman, A., German Patent 216,463 (Jan. 19, 1908); British Patent 174 (Jan. 4, 1909). Dimethylsulfide and ethyl mercaptan, pure and 1 to 100, failed to give the reaction. However, pure thioacetic acid June 12,1931. gave a similar reaction to carbon disulfide, and it is suggested RECEIVED
