a specified “calibration line” is used for a series of determinations, the temperat,ure of each of the two solutions involved (the unknown per se, on the one hand, and the reagent per se, on the other hand) must be the same. The zero intercept of curve 11, Figure 2 , indicates that heats of dilution were indeed negligible-- i.e., AH
SAMPLE SIZE,
micrornola
Figure 2. Plot of A,€ vs. sample size of hydrochloric acid I. Reagent (1 M N a O H added in excess) warmer II. Reagent and unknowri at same temperature Ill. Reagent colder First point on each line represents result of appropriate blank erperiment
out for all determinations, and results were appropriately averaged. The relative standard deviation and error of the mean were + 2 and 3%, respectively. The experimental verification of Equation 10, on which the method is based, is illustrated in Figure 2. The further purpose of this figure is to show the effect of differences (of the order of 1 O to 2 ” C.) in initial temperature between reagmt and unknown solutions. I t illustrates the displacement in the plots (of A E us. sample size) caused by the reagent being warmer or colder than the unknown, as compared to the situation when the two solutions were isothermal. DISCUSSION
Figure 2 shows that the precision and accuracy of injection enthalpimetry are not impaired by small differences in temperature between reagent and sample solutions. This is accounted for by the fact that a m r m e r (or colder) reagent dissipates (or absorbs) a quantity of heat, Q‘, yielding Equation 11 in lieu of Equation 9.
When reagent and sample are isothermal Q’ = 0 and Equation 9 applies. Khenever Q’ # 0, the term Q’/c in Equation 11 yields a parallel displacement of the linear plot of AE us. sample size, with an Conintercept equal to k“Q‘/k‘c. sequently, a satisfactory calibration line (similar to the plots in Figure 2 ) can be obtained with ihe aid of two known samples of the substance to be determined. Cumbersome equalization of temperatures before mixing is unnecessary ; temperature differences up to +3’ were readily tolerable under the conditions prevailing in the present study. Katurally, however, as long as
= AHo
=
const.
(12)
as was assumed in deriving Equations 9, 10, and 11. Within the attainable precision and accuracy of 2 to 3y0, approximation 12 can generally be expected to hold when volumes and concentrations similar to those outlined in this paper are used. I n analyzing sample sizes of the order of 10 or 100 pmoles, present a t actual concentrations of 0.001 to O.OlJf, the feasibilit,y, precision, and accuracy of D I E compare favorably with conventional methods of volumetric analysis. DIE has signal advantages of rapidity, a complete determination requiring less than one minute. Unstandardized’ reagents can be used, provided they are added in sufficient excess to make the reaction a t least 99% complete. The evaluation of AE (or of the corresponding recorder pen deflection expressed in millimeters, if preferred) from automatically recorded injection enthalpograms is straightforward, as can be seen in Figure 1. The “overshoot” which is apparent in curves I and I1 (and to a lesser extent in curve IV) was caused by a n inconsequential transient overheating of the thermistor; the simple graphical extrapolation procedure illustrated in the figure m-as not affected by it. DIE is ideally suited for microchemical adaptations and for miniaturization; AE and A T depend solely on the actual concentration of the unknown sample and are independent of the volume taken for analyss. The reason for this remarkable feature of DIE is evident from Equation 9; both Q (the heat evolved or absorbed in the reaction) and c (the heat capacity) are proportional to the volume of the solution. Direct injection enthalpimetry is a method of virtually universal applicability. Any rapid process which involves a heat of reaction
1 A H o I > 1 kcal. per mole is amenable to use, whether exot,hermic or endothermic. The very numerous reactions which have been used in thermochemical titrations can all be adapted in principle to direct enthalpimetry (5, I O ) . These nclude a wide varietl- : acid-base, oxidation-reduction, precipitation, and complexation processes, in aqueous and nonaqueous solvents. DIE is readily adaptable to process stream control; a “reverse injection” technique appears par-
ticularly attractive, involving periodic diversion of samples into excess reagent and recording the corresponding temperature change in an appropriate adiabatic system. One specific application has been explored with this purpose in mind, because of its considerable public health interest. Based on a recently developed thermometric titration procedure ( 6 ) ,anionic detergents of the dodecyl benzene sulfonate type.e.g., ABS- have been successfully determined by DIE, using a suitable cationic surface active agent-e.g., a long-chain tetraalkyl ammonium ionas the excess reagent. LITERATURE CITED
(1) Greathouse, L. M., Abstracts, 132nd
Meeting, ACS, Sew York, 1967, p. 7B.
( 2 ) Greathouse, L. M., Jansen, RI. J., Haydel, C. M., ANAL.CHEM.28, 357
(1956). (3) Jordan, J., Chzmza 17, 101 (1963). (4) Jordan, J., Dumbaugh, W. H., Jr., ANAL. CHEM.3 1 , 210 (1959). ( 5 ) Jordan, J., Eaing, G. J., “Thermometric Titrations,” in “Handbook of Analytical Chemistry,” L. Meites, ed., Sect. 8, pp. 3-7, McGraa-Hill, Sew York. 1963. ( 6 ) Jordan, J., Pei, P. T., Javick, R. A,, ANAL.CHEM.3 5 , 1534 (1963). (7) McClure, J. H., Roder, T. M., Kinsev, R. H., Ibid., 27. 1599 (1955). (8) Marmstadt, H. I,.,Chambers, W. E., Ibzd., 3 2 , 225 (1960). (9) 3lalmstadt, H. I..,Winefordner, J. D., Anal. Chzm. Acta 20, 283 (1959). (10) Zenchelsky, S. T., ANAL.CHEM.3 2 , 289R (1960). RECEIVEDfor review April 20, 1964. Accepted July 1, 1964. Based in part on a doctoral thesis by, P. T-S. Pei. Sargent Award Symposium Honoring Robert Homer Cherry, Division of Analytical Chemistry, 147th Meeting, ACS, Philadelphia, Pa., April 1964. Work supported in part by U. S. Atomic Energy Commission Contract AT(30-1)-2133 with The Pennsylvania State University.
Correction Spectrophotometric Determination of Calcium in Milk Using 2,2’-( Eth a ned i y Iidened initr ilo )d iphe n o I [Glyoxal Bis(2-hyd roxya n it)] In this article by T. A. Nickerson et a2. [,\NAL CHEM.36, 1676 (1964)l the following sentence should be added under Procedure, page 1676, column 3. “In the case of milk, the proteins are removed by mixing equal volumes of milk and 20y0 TCA and filtering after 10 minutes to give a clear sample.” VOL. 36, NO. 1 1 , OCTOBER 1 9 6 4
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