Direct Enthalpimetry, A N e w Thermochemical A p p ro a c h t o Q u a nt it a t ive A na Iys is J. C. WASILEWSKI,l P. T-S. PEI, and JOSEPH JORDAN Department of Chemistry, The Pennsylvania State University, University Park, Pa;
b Under conditions of invariant heat c a p acit y, the change in tem per a tu re in an ideal adiabatic system represents a linear measure of the quantities reacted in a stoichliometric process. This simple principle i s the basis of direct injection entlialpimetry (DIE). Three hundred microliters of a relatively concentrated reagent, 6, was injected rapidly into a 25-ml. sample of a dilute unknown, A, and mixed within 0.01 second. For each specific unknown, B was judiciiously preselected and added in sufficient excess so that the reaction x A yB + zP was virtually complete within 10-2 second. The corresponding temperature increment (or decrement) was recorded as the unbalance potential of a thermistor bridge, yielding well-defined “injection enthalpolgrams.” Potentialities and limitations of DIE are assessed from data obtained in determinations involving a variety of exothermic and endo’thermic reactions. Advantages include broad applicability, rapidity, and adaptability to microanalysis and process control. An unusual feature is that unstydardized reagents may b e used.
+
I
years, an interesting trend has become apparent in contemporary analytical chemistry : the renaissance, in novel form, of classical methodological appro,sches whose basic principles have been known for many decades. Thus, precision null-point potentiometry (9) reliresents a modern application of the Kernst equation; and atomic absorption spectroscopy in its new and sophisticated forms (8) is based on theoretical foundations dating back to I3unsen’s day’s. The present paper describes a similar development in the field of thermoanalytical chemistry-the use of solidstate tenilierature sensors for quantitative determinations, based on the princilile that the change of t,emperature in an adiabatic system represents a measure of the reactants inlrolved in a stoic.liionirtrical1~wel.1-defined process. Ikcau*e heats of reaxtion are a very gcncwd ~ m i l ~ e r tofy chemical processes, h u r h “direct enthaIpimetry” is an analytical tool unmatrhed in its potential alililic~~bility.Sporadic examples of this aliliroac’h have been reported
s
( 1 , 2 , 7’). However, these were invariably restricted by the limitations of mercury thermometers, inherent in their lack of sensitivity, their high heat capacity, and their appreciable response lag. Significant experience has been accumulated since 1953 in the use of thermistors as temperature sensors, in the area of thermometric titration (5, IO).# Thermistors have unique advantages, including high sensitivity, negligible heat capacity, and instantaneous response. 13y using thermistor bridges in lieu of conventional thermometers, direct enthalpimetry has become feasible, as a rapid and convenient method for the analysis of submillimolar samples in very dilute solutions. The development described in this paper illustrates a situat,ion where modern instrumentation serves not merely as a convenience, but as a necessity for the workable implementation of an idea. THE PRINCIPLE
RECFXT
is correlated by Equation 2 with the number of moles of product, n p ,actually present when equilibrium is attained.
(2) where the enthalpy difference, AH3 is =
>Y
ni
ni
(4)
X
is the number of moles of the excess reagent added. The stipulated virtual completeness implies that : 2
np = - n i
(5)
X
the required excess of nA over nf4 depending, naturally, on the value of the equilibrium constant governing Reaction 1. Under the specified conditions z
-- n i ,AH
Q =
(6)
X
and for any given reaction
Q
=
kni
(7)
where
I n an ideal system, the integral heat effect associated with a reaction of the type
Q
where ni denotes, for example, the number of moles of an unknown initially present, while
np,AH
the heat of Reaction 1 (expressed in calories per mole of the product, P ) , and Q denotes the integral heat evolved (expressed in calories and assigned a positive value in the case of exothermic reactions, and a negative value when AH > 0 is endothermic). Ideality in this context implies that heats of dilution are negligible. If reagent B is added in appropriate excess, Reaction 1 may proceed to virtual completenessi.e.,
k
=
z
- -AH X
=
const.
(8)
whenever AH = const. Inherent in Equation 7 is a remarkably direct and simple method of quantitative analysis. EXPERIMENTAL IMPLEMENTATION
Under conditions of constant heat capacity, Q was measured as the corresponding change in temperature, A T , and recorded as the unbalance potential, AEj of a thermistor bridge:
AT
k n i - k’nt
= Q - =
-
c
c
A
-
A
(9)
A E = k“ni
(10) I n Equations 9 and 10, c is the effective total heat capacity of the system after addition of the reagent; k’ and k”
Present address, American Instrument Co., 8030 Georgia Ave., Silver Spring, Md. Initial Situation
Final Situation VOL. 36, NO. 11, OCTOBER 1964
2131
Figure 1 ,
Typical injection enthalpograms
I. 83.1 pmoles of HCI plus excess N a O H II. 101 pmoles of HJBOI plus excess N a O H Ill. 100 pmoles of Mg-’ plus excess EDTA IV. 104 pmoles of PbL2 plus excess EDTA IT. Injection time of 300-pl. 1M reagent into 25.0-ml. volume of unknown solution AE. Unbalance potentiol of thermistor bridge (Equation 10)
denote proportionality constants, which are assigned appropriate dimensions (degrees per mole for k‘, and volts per mole for k”) and can readily be determined esperimentally for a given reaction by calibration with a known amount of A . Heat capacity was maintained constant by carrying out the reaction in dilute aqueous solutions of constant volume. This was accomplished by injecting, rapidly 300 PI. of a concentrated d u t i o n (typically 1-11) of excess reagent into 25.0 ml. of a dilute ‘‘unknown sample solution” (typically 0.001 to 0.01.11). The experiments were performed with the aid of the adiabatic reaction cell and the temi)erature-nionitoring circuit of a conventional thermometric titrator (Titra-thermo-mat, American Instrument Co., Silver Spring: M d . ) Catalog S o . 4-8350). ‘The excess reagent was injected rapidly, either manually, using a 500-fil. syringe and a Chaney ;idaptor (Hamilton Co., 1’. 0. 130s 307, Xhittier, Calif.): or with an air-operated buret (.\mesican Instrument Co., Catalog KO. 4-2390). Reagent injection m s completed in 1 second or less. A E \vas recorded, within a time span of 0.5 second after mixing, as the pen deflection (which was strietlj- proportional to AE) of a suitable 1-mv. stripchart DC potentiometer (Model G 14, Yarian ;issociates, Palo Alto, Calif.; or LIodel 01 Co., 11-aterbury, Conn.). of general considerations affecting measurements in situations where sequential processes are involved ( 4 ) , the study was carefully restricted to reactions whose kinetics were sufficiently fast to be Tirtually complete within 0.01 second after mixing of the reagents. The time required for complete homogenization by mixing was
Table 1.
Equilibrium tonstant*
Unknown Reagento
XIg+2
TIME
ascertained to be also on the order of 0.01 second. Reagent grade chemicals and triply distilled water were used throughout. Accuracy was assessed with reference to “true values” (based on weighing out primary standard materials and lor determined by appropriate classical analytical procedures) which were accurate and precise to 0.1%. For lead and magnesium, respectively, the nitrate and chloride served as source materials. The EDTA reagent was prepared by adding’ 2 equivalents per liter of sodium hydroxide to an approximately 1.11 solution of disodium (ethylene-dinitriloj-tetradihydrogen acetate. experiments viere carried out a t room temperature (between 20” and 25” C.). RESULTS
To assess the potentialities and limitations of direct enthalpimetry as a new approach in quantitative analysis, the
Performance Characteristics of Direct Injection Enthalpimetry
Relevant
HCI H3BO3 Ph‘2
/
K, Kl
SaOH SaOH EDTA E1)TX
m
= 5 8 X Keb = 1 6 X
10” KMn= 1 . 3 X lo9
Ranges Investigated H m Ilnknown Concn of reactlon, sample size,< unknown, kcal /mole pmoles ’11 x 103 40 7 to 207 1 63 to 8 28 -13 5 -10 6 49 4 to 201 1 98 t o 8 04 104 t o 261 4 16 to 10 4 -12 8 +5,5 48.8 t,o 248 1 . 9 5 t o 9.92
Excess reagent injected as 300 p l . of unstandardized aqueous solution (approsinlately lM). K , = ionizat,ion constant of HCI: Kl = first ionization constant of HaBO3: KPb = [PbY]- ? / [ Y-41 [Ph + ? ] where Y-? denotes quadrinegative (ethylenedinitri1o)-tetraacetate anion: KM, = [LIgYI ;?/[Y-‘I [>Igt21. c In 25.0 r n l . of aqueous solution. ~
2132
ANALYTICAL CHEMISTRY
-
following selected problems were investigated : The determination of a strong arid with a strong base (hydrochloric with sodium hydroxide) as a model of performance under optimum conditionsviz., a highly exothermic neutralization process involying strong electrolytes. The direct, determination of boric acid with sodium hydroxide, as an example of a normally very difficult problem of quantitative analysis because of the extreme weakness of the acid. The determination of lead and magnesium with EDTAI,as interesting examples of exothermic and endothermic calorimetry involving chelation reactions.
-111 experiments were carried out in three to five replicates. Several concentrations (in a range betmen 0.001 and 0.1JI) of each unknown were determined. The data and conclusions presented below are based on the results of 100 experiments. Examples of typical AE recordings, called “injection enthalpograms” (IE). are illustrated in Figure 1. The similarity of the IE:’s obtained with strong and weak acids, shown in curves I and 11, is remarkable. The endothermic nature of the chelation of magnesium with EDT-1 (curve 111): which has been a matter of some controversy in the literature (S),is clearly evident, in contradistinction with the exothermic character of the exlwriment involving the determination of lead with EDT.1 (curve IY). *In over-all synopsis of quantitative data obtained by direct injection enthalpimetrg ‘is presented in Table I. Three to five relilicates were carried
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.31, 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.35, 1534 (1963). (7) McClure, J. H., Roder, T. M., Kinsev, R. H., Ibid., 27. 1599 (1955). (8) Marmstadt, H. I,.,Chambers, W. E., Ibzd., 32, 225 (1960). (9) 3lalmstadt, H. I..,Winefordner, J. D., Anal. Chzm. Acta 20, 283 (1959). (10) Zenchelsky, S. T., ANAL.CHEM.32, 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
2133
