It can be readily seen that Equation 10 is quite correct, but Equation 11 is only an approximation because the response shape is not actually Gaussian. Substitution of the above expressions and t,, = tR 4 2 into Equation 6 yields
I
I
I
I
+
H H
L(U*' z
- s2//12)tR2
H * - LS2/ L2tR2
(12)
Thus, the true plate height, H , can be approximately calculated from the apparent plate height, H *, by first determining the value of H * and then subtracting from it the value of h2/12tR2, which might conveniently be termed the sample plate height, H " , for a plug. It is important to realize that Equation 12 is an approximation only because of the approximate measurement of the variance of the response and not because of a non-Gaussian sample input shape nor because of any inapplicability of Equation 6. The error resulting from this approximation is considerably larger than might be anticipated after a qualitative inspection of Figure 1. Figure 5 shows that the relative error in the approximate plate height (calculated by Equation 12, using method a, b, or c evaluate u * ) as a function of H P / H * , which equals S ~ / ~ ~ C,\gain, T*~. tie lines are included in the figure to
I
0
I
I
0.2
I 0.4
I
LITERATURE CITED
0.6
HP/ H" Figure 5. Relative error in approximate plate heights, calculated by Equation 12 and methods a, b, and c Hp
the sample plate height, H P ,is less than about one fourth of the apparent plate height, H*. On the other hand, the usefulness of Equation 12 can be demonstrated by comparing Figures 3 and 5. For example, a t s/2a = 1.0, the initial error of about 40y0 in the apparent plate height is reduced to about 5y0 by subtracting the sample plate height.
S2/12tR2
facilitate comparison a t equal values of input plug width. Figure 1 shows that the response appears roughly Gaussian 2.5, a t plug widths , u p to 4 2 0 whereas Figure 5 shows that the Gaussian approximation (and method a) gives a 4% error in plate height when s / 2 u is only 1.0-with the error increasing rapidly for larger plug widths (at 4 2 0 = 2.5, the error is 4301,). Hence, Equation 12 is useful only when
-
(1) Hildebrand, G. P., Ph.D. dissertation, University of North Carolina, Chapel Hill, N. C., 1963. ( 2 ) Peniston, Q. P., Agar, H. D., McCarthv. J. L.. ANAL. CHEW 23. 994
(1951j.' (3) Purnell, H., Sawyer, D. T., Ibid., 36, 668 i 1964). (4)Re'illey,'C. N., Hildebrand, G. P., Ashley, J. W., Jr., Ibid., 34, 1198 (1962).
J. W. ASHLEY,JR. G. P. HILDEBRAND~ CHARLES N. REILLEY DeDartrnent of Chernistrv Unheraity of North Carolina Chapel Hill, N. C. Present address, Plastic Department, E.I. du Pont de Sernours & Co., Experimental Station, Wilmington 98, Del. RECEIVEDfor review March 19, 1964. Accepted April 6, 1964. Information developed during work supported by the Advanced Research Projects Agency, Contract No. SD-100.
Coulometric Titration of Organic Acids in Acetone SIR: Although acidic species have been generated electrolytically in nonaqueous solvents for the coulometric titration of organic bases (3-6), the only recent reference in the literature to a similar electrolytic generation of base for the titration of acids is a paper by Crisler and Conlon ( I ) . These men used a 1 : l mixture of benzene and methanol containing lithium chloride as the electrolyte. d n antimonyglass electrode. pair was used as the detection system. KO clear inflection points were obtained in the titration curve. Coulometry as a technique offers the advantage of precision in the detection of small quantities of materials; nonaqueous solvents are useful for the determination of acids and bases not readily determined in water either because of insolubility, low ionization in that solvent, or other reasons. The analytical interest in nonaqueous solvents over the past decade attests t o their utility. During the past yc'ar we have attempted to generate a basic species in a
nonaqueous medium containing a minimum quantity of water. The initial choice of solvent was acetone. It has a reasonable dielectric constant ( e = 21.3), dissolves a variety of organic acids, and is readily available commercially in a high degree of purity. Fritz and Yamamura (2) have demonstrated the analytical possibilities of this solvent for the titration of carboxylic acids and phenols as well as other weak organic acids. In the current work two methods were used. EXPERIMENTAL
Apparatus. A Sargent Model IV coulometric current source was employed for both methods. Using this, a current of 9.65 ma. was applied to two platinum generating electrodes immersed in separated half cells. I n one method the cells were electrically connected by a salt bridge consisting of two sintered glass filter sticks ( E , Ace Glass Co., Vineland, N. J.) joined together to form a U-tube containing 10% aqueous potassium nitrate. One end of the bridge was immersed in a
half cell containing 10% aqueous potassium nitrate and a generating electrode. The other end was protected by Whatman KO.44 filter paper, glass wool, and a second sintered glass frit and was placed in the sample half cell. The latter compartment contained a generating electrode, a calomel reference electrode, and a glass indicating electrode all surrounded by a n acetone solution which was 0.05M to tetrabutylammonium perchlorate (Southwestern dnalytical Chemical Co., Austin, Texas) and 0.lM to water. h magnetic stirrer was placed under the sample compartment. The calomel reference electrode was filled with a saturated solution of tetramethylammonium chloride in acetone. The reference and indicating electrodes were connected to a Leeds & Northrup Model 7401 pH meter. .I Model 152 voltmeter (Accurate Instrument Co.) was connected across the terminals of the coulometric current source. The second method made use of the same apparatus described above except that tetrabutylammonium bromide was employed as supporting electrolyte, and the water content was 0.5%. The salt bridge in this case consisted of a glass VOL. 36, NO. 7, JUNE 1964
1371
Accuracy and Precision of Coulometric Titrations Using 75 rnl. Acetone Containing 3.75 rnrnoles BudNCI04 and 0.75 rnrnole HzO
Table I.
Acid Toluenesulfonic Kenzoic 2,4-Dinitrophenol
Amount, peq. Added Found. 20.1 20.2 20.8 20.5 19.7 19.8
70
Rel. std. dev.
0.50 1.4 0.51
0.00
Error
0.23 0.29
Average of 3 determinations. Table II. Accuracy and Precision of Coulometric Titrations Using 75 rnl. Acetone Containing 7.50 rnrnoles BuaNBr and 21 rnrnoles HzO
Acid p-Toluenesulfonic Benzoic 2,CDinitrophenol a
Amount, peq. Added Founda 20.0 20.4 20.2
19.5 20.5 20.5
%
Error 2.5 0.5 1.5
Rel. std. dev. 0.41 0.29 0.24
Average of 5 determinations.
U-tube containing 1% aqueous potassium nitrate and 2% agar. Procedure. I n the first method the solvent to be titrated was used to standardize the p H meter at a potential of -700 mv. initially. Next t h e solvent was titrated with coulometrically generated hydrogen ion until the decrease in potential was negligible. At this point the generating electrodes were electrically reversed and the solution was titrated with coulometrically generated base. The potential of the solution was recorded 50 seconds after each addition of base. When the solvent was fully titrated a n accurately known quantity of acid (approximately 20 heq.) dissolved in 2 ml. of solvent was added. The mixture was titrated a second time as was done previously. The quantities of base generated were plotted us. the respective potentials obtained and the equivalence point of the added acid
1372
ANALYTICAL CHEMISTRY
graphically determined. The amount of base generated a t this point minus the solvent blank a t the same potential was used to determine the quantity of acid present. The procedure above was also employed for the second method except that only base was generated. I n this method the equivalence point of the solvent before and after the addition of acid was taken as a measure of the acid present . RESULTS AND DISCUSSION
To test both coulometric methods, p-toluenesulfonic acid, benzoic acid, and 2,4-dinitrophenol were employed as standard reagents. The accuracy and precision of the procedure using tetrabutylammonium perchlorate in acetone is shown in Table I. The e.m.f. across the two generating electrodes varied
between 60 and 90 volts during the course of a titration. If the end of the salt bridge placed in the sample compartment was not separated from the second glass frit by filter paper and glass wool, the e.m.f. would often rise to 120 volts. This was probably due to the formation of insoluble potassium perchlorate which clogged the outer frit. The accuracy and precision obtained when acetone containing tetrabutylammonium bromide was employed is given in Table 11. Poor results were obtained when a platinum indicating electrode was substituted for the glass electrode. The e.m.f. across the two generating electrodes using the agar salt bridge was 125 volts. This can be reduced to 70 volts if the agar bridge is replaced by the aqueous bridge used in the perchlorate system. The aqueous salt bridge is also more convenient since it is more easily prepared and cleaned. Other nonaqueous solvents that we are currently investigating are tertbutyl alcohol, n-butanol, dimethylsulfoxide, and dimethylformamide. LITERATURE CITED
(1) Crisler, R. O., Conlon, R. D., J . A m . Oil Chemists SOC.39. 470 (1962). ( 2 ) Fritz, J. S., Yamamura, S. S., Ibid., 29, 1079 (1957). (3) Hanselman, R. B., Streuli, C. A., Ibid., 28, 916 (1956). (4) Mather, W. B., Jr., Anson, F. C., Zbid.. 33. 132 (1961). (5) Ibid., p. 1634: (6) Streuli, C. A,, Zbid., 28, 130 (1956).
Central Research Division Stamford Laboratories American Cyanamid Co. Stamford, Conn.
C. A. STREULI J. J. CINCOTTA D. L. MARICLE K. K. MEAD
RECEIVED for review February 6, 1964. Accepted March 26, 1964.
