range: 0 to 3000 keV nominally. The amounts of the chemicals were adjusted so that the expected counting rates of the samples would not exceed 45 dead time at the beginning of the first count, two minutes after the end of the activation. Seven spectra were collected for the unknowns spaced over a period of 25 hours to permit a good lever for the half-life estimates of the longer-lived activation products (Figures 5 and 6). Flux monitoring and other experimental detail followed closely the procedures used to collect the spectra for the standard library prepared several months earlier. The results of the analyses of the four samples are given in Table 11. DISCUSSION
The computer was able to identify positively each of the added elements and assay them with good accuracy. Some of the error indicated by the data may be accounted for by the difficulties encountered in weighing the small amounts of sample constituents. The large error for the As assay in Sample I is due to the fact that the computer used a relatively minor peak of ‘6As for the analysis. The computer reported that it did recognize a peak at 657 keV for this sample, but estimating a half-life of 38 hours could not make the assignment to arsenic. Using the 38-hour half-life, however, it calculated the resulting count rate at the end of the activation for this peak as 0.485 c/sec.
It was left to the experimenter to calculate a n arsenic assay of 0,485 c/sec/0.331 c/sec/mg = 1.465 mg, which is in much closer agreement with the actual arsenic content of Sample I. The choice as to how large a span of error in the half-life the program should tolerate for making a n assignment will have t o be improved from time to time as experience is gained with the use of the method. CONCLUSION
It could be shown by the present work that computerized instrumental activation analysis, as conceived several years ago, is indeed feasible, and that it is able to give both qualitative and quantitative acceptable results for multi-element determinations. The method described is free of the previous requirement of processing standards with the sample, leaves the experimenter a large amount of choice in the timing of the counts, andcan be readily carried out by non-technical personnel. ACKNOWLEDGMENT
The author Computation program and the operation
is indebted to Thomas G. Eichinger of the Dow Research Laboratory for writing the computer to Robert P. Madison for his assistance with of the reactor.
RECEIVED for review October 11, 1968. Accepted January 13, 1969.
Gas Enthalpimetry Pier Giorgio Zambonin‘ and Joseph Jordan Department of Chemistry, The Pennsylvania State Unioersity, 212 Whitmore Laboratory, University Park, Pa. 16802
Gas Enthalpimetry (GE) is an “equilibrium heat pulse” method applicable to reactions between gases and liquids. Gaseous samples were injected, under judiciously controlled experimental conditions, into thin walled adiabatic calorimeters-e.g., platinum lined Styrofoam. A temperature change was concomitantly monitored with the aid of automatic thermistor instrumentation which had the sensitivity of a thousandjunction thermocouple. Aquation and Bronsted acidbase reactions of the gases COz, SO,, NO,, and N204 were investigated systematically. Heats of reaction were determined by GE in a few minutes with a precision and accuracy of 1%, which is comparable to the capabilities of classical calorimetry with such systems. GE is ideally suited for quantitative gas analysis: CO, and SOs, were determined accurately in amounts between 0.5 and 1000 pmoles, in gas mixtures ranging from 0.1 to 100 ml in volume and containing from 1 to 50% of the “unknown.” Based on the comprehensive study of aqueous carbon dioxide, sulfur dioxide, and nitrogen dioxide systems, A H assignments and associated confidence intervals are assessed critically.
AN AUTHORITATIVE REVIEW on the status of gas analysis published 16 years ago ( 1 ) includes the interesting idea of utilizing the heat evolved in a hetereogeneous reaction as a means for monitoring concentrations in a gas phase. Specifically, the response of a hundred-junction thermopile was used as a measure of the oxygen content of a gas which was bubbled On leave from Istituto di Chimica Analitica, University of
Bari, Italy (1) H. Guerin, Bull. SOC.Chim. Fr., 19, 24 (1952).
through an aqueous solution of chromous chloride. An obvious development suggests itself, ciz to substitute a single thermistor sensor (which, if appropriately wired, has the sensitivity of a thousand-junction thermocouple) in lieu of the thermopile. Indeed, gaseous reagents have been successfully-albeit sporadically-employed in conventional thermometric enthalpy titrations (2, 3) as well as in the newer heat pulse method, “direct enthalpimetry” (4, 5). In this paper we report the first systematic assessment of a methodological approach, which relies on the measurement of temperature pulses engendered by the injection of gaseous samples into suitable reagent solutions. “Gas enthalpograms” were recorded automatically as the unbalance potential of a thermistor Wheatstone bridge. Results are presented and discussed which indicate that gas enthalpimetry is a generally applicable instrumental method for gas analysis on a macro-or-micro scale. Gas enthalpograms also provide rapid and convenient means for the determination of heats of reaction and the elucidation of relevant thermodynamics. The “model reactions’’ selected for this study included aquation and Bronsted acid-base equilibria of the type: COZ(g)
+ H~0(1)
=
CO?.aq
(1)
(2) B. J. Duffield, Thesis, MIT (1960). (3) D. N. Hume and B. J. Duffield, Abstracts, 147th National Meeting, American Chemical Society, Philadelphia, Pa., 1964, p 13B.
(4) J. C. Wasilewski, P. T-S Pei, and J. Jordan, ANAL.CHEM., 36, 2131 (1964). (5) J. Jordan, P. T-S Pei, and R. C. Buchta, Jr., Abstracts, 149th National Meeting, American Chemical Society, Detroit, Mich., 1965, p 30B. VOL. 41, NO. 3, MARCH 1969
437
8 rmostating Jacket
-\-
Nitrogen
B
15 Liter Flask
B-
Figure 2. Gaseous sample preparation unit and, consequently, Colihtion Heater Thermistor
Magnetic Stirrer
Figure 1. Gas injection heat pulse calorimeter A. Gas syringe; thermostated in work with NOz(N04) B. Adiabatic barrier: dewar wall or platinum-lined styrofoam cavity. Liquid levels: a and b used for thermochemical determinations; c used for analytical determinations
COS(9)
+ 20H-.aq
= C03*-.aq
+ HzO(l)
(2)
as well as their N 0 2 ( N 2 0 4and ) SOzanalogs. Theoretical Considerations. Signal Advantages of Gas Enthalpimetry. Thermochemical principles previously outlined ( 4 ) in conjunction with Direct Injection Enthalpimetry (DIE) are evidently valid for Reactions 1 and 2 which can be generalized in the form gG (8)
+ rR.aq = pP.aq
(3)
Experimental implementation involved judiciously controlled injection of a gaseous sample into a suitable aqueous reagent contained in an adiabatic cell. A corresponding “temperature pulse,” AT (“C), was measured in the solution. The integral heat Q (kcal) evolved or absorbed is given by the equation Q = CAT = -npAH
(4)
where capital letter subscripts identify the reactants inEquation 3. The symbols n and A H denote, respectively, the number of moles, and the heat of reaction expressed in kilocalories per mole of product. In general, C denotes heat capacity (expressed in kcal/degree) and
c = c, + c,
(5)
where the lower case subscripts a and s identify the adiabatic calorimeter and the reagent solution therein. Whenever Reaction 3 proceeds to virtual completion
np ‘v 438
0
P
-
g
The analytical and thermodynamic significance of AT is explicited in Equations 7a and 7b. In the present investigation conditions were such that C (Equation 5 ) was the same both prior and subsequent to injection of the gas. This, in fact, is the important advantage of injecting a gas whose heat capacity is negligible, rather than a liquid. Thus, elaborate precautions in adjusting temperatures of reagent and sample are unnecessary (except in rare special situations when equilibria such as NOz e N204 are involved in the gas phase). For this reason, the practical implementation of gas enthalpimetry is much simpler and less prone to extraneous errors than the previously described DIE methods in which a solution was injected ( 4 ) . Naturally, the applicability of the approximation in Equation 6 (on which Equations 7a and 7b are contingent) requires that the following conditions be met: a) the equilibrium constant of Reaction 3 must be sufficiently large; b) kinetics must be sufficiently rapid relative to the rate of gas injection. Requirements a and b are both favored by using a stoichiometric excess of reagent solution in the adiabatic cell. EXPERIMENTAL
Apparatus. Temperature pulses were recorded with the aid of the thermistor bridge and electrical calibration circuits previously described ( 4 , 6, 7). The “injection heat pulse calorimeter” used in this investigation is illustrated in Figure 1. Three types of adiabatic cells were used : Calorimeter I. A thin-walled 0.2-mm platinum crucible, 25 ml in volume, inserted into a Styrofoam block; Calorimeter 11. A thin-walled 0.2-mm borosilicate glass beaker, 5 ml in volume, in Styrofoam; Calorimeter 111. A 250-ml silvered thin-walled dewar flask, with a narrow neck ( 3 cm in diameter). The rationale for using thin walls was predicated by considerations of low heat capacity and rapid thermal equil( 6 ) P. Papoff and P. G . Zarnbonin, Ric. Sci. (Rome), 35 (I), 93 (1965).
no
ANALYTICAL CHEMISTRY
(7) J. Jordan, R. A. Henry, and J. C. Wasilewski, Microchem. J., 10,260 (1966).
Started
Finished
AT II 30 sec TIME-
Figure 3. Typical enthalpograms mmol of COz injected into 250 ml of 0.1M HCI (calorimeter 111, completely filled) 11-0.3 mmol of COZinjected into 125 ml at 0.10M KOH (calorimeter 111, half-filled)
1-1
TIME
--
Figure 4. Enthalpograms of SO2 injected into potassium hydroxide solutions in the presence of air. IS, 1F:start and finish of gas injection c anomaly due to oxidation of sulfite. I-O.OIM,
II-O.OZcM,
III-
0.5M KOH
ibration (8). The various designs were selected advisedly t o provide optimum conditions for the thermodynamic and analytical measurements outlined. Whenever necessary, Teflon needles were used to purge solutions with an inert gas (nitrogen). Gaseous samples consisted either of pure gases o r of mixtures. They were prepared for injection in the device shown in Figure 2. The desired gas (or gas mixture) was aspirated from a thermostated 15-1 flask into a suitable gas syringe (0.05- to 100-ml capacity supplied by Hamilton Co., Whittier, Calif., equipped with Chaney adapters), by inserting a steel needle through the silicone rubber septum shown in Figure 2. Subsequently, the syringe was detached from the steel needle, connected to the needle-inlet made of Teflon (Dupont) shown in Figure 1, and the gas introduced into the calorimeter. Alternatively, samples of small volume (1 ml or less) were injected directly into the calorimeter via the same stainless steel needle through which they were sampled. Procedures. Aqueous reagent solutions were used throughout. Prior to sample injection, care was taken to achieve thermal equilibration between the liquid phase in the calorimeter and the water vapor in the supernatant gas phase. Equilibrium was considered attained when the slope of the “temperature base line” remained constant for a reasonable time, while the solution was stirred at the same rate as in the actual experiment. By working with a new solution near room temperature, the initial equilibration time was o n the order of 5 minutes. When several samples were sequentially injected into a given solution (as in our recommended procedure for quantitative gas analysis, cide infra), no additional waiting time was required. Determination of Heats of Reaction. The heats of solution of carbon dioxide and sulfur dioxide were determined with the sequence of operations outlined below. An accurately known volume of pure gas (0.5 t o 1 mmol) was injected into calorimeter 111, which was completely filled (to level a in Figure 1) with a solution of strong acid in order to minimize formation of carbonate, bicarbonate, sulfite, and bisulfite. Injection was slow (50-100 sec) in order to allow for continuous equilibration. Temperature pulses of the type illustrated in Figure 3 (Curve I) were obtained. Under these experimental conditions, the volume of the gaseous supernate in the calorimetric cell was negligible, and nc in Equation 6 was effectively equal to the moles of gas injected. Similar techniques were also used to determine heats of reactions of the type: ~~
~~
(8) P. Papoff and P. G. Zambonin, Tuluntu, 14, 581 (1967).
-
In studies involving processes described by Equation 9, in which the product was a dissolved, aquated gas, thermostated solutions of sodium bicarbonate, sodium bisulfite, etc. were injected by the conventional injection enthalpimetry procedure ( 4 ) , into adiabatic cells filled with a solution of strong acid. The heats of neutralization of COS, SO2 were determined by sub-liquid level injection of a known amount of pure gas into calorimeter 111, half filled with a n aqueous solution of a strong base. This procedure yielded heat pulses, of the shape illustrated in Figure 3, Curve 11. Due to the rapidity of process 2 (in the presence of excess hydroxide), equilibration was fast and injection times as short as 2-3 sec proved satisfactory. The heats of the second dissociation step of carbonic and sulfurous acids were obtained by injecting thermostated solutions of sodium bicarbonate and sodium bisulfite into a solution of strong base. Heats of Reactions 8 and 10 were calculated with the aid of Equation 11 from enthalpograms obtained by injecting equilibrium mixtures of NOZ-NzO4 into solutions of hydrochloric acid and sodium hydroxide, respectively. Nz04
+ 20H-.aq
=
HzO(1)
+ NOB-.aq + NOs-.aq
(10)
In Equation 11, n denotes the total number of moles of NOs plus N204injected, the subscript i identifies Reaction 8 or 10, x is the mole fraction of NOz calculated from data given in Reference (9), and A H l l = $6.94 is the heat (IO) of the reaction : N204 (g) = 2N02 (9)
(12)
Analytical Determinations. Calorimeters I, 11, or 111 were of used depending on sample size. I n all instances only the calorimeter was filled with the appropriate solution (level c in Figure 1) and the supernatant gas space was (9) F. H. Verhoek and F. Daniels, J . Amer. Chem. Soc., 53, 1250 (1931). (IO) D. D. Wagrnan, W. H. Evans, S. Levine, and I. Jaffey, Narl. Bur. Srd. (US.)Circ. 500, 1952. VOL. 41, NO. 3, MARCH 1969
439
Table I. Thermochemistry of the Systems COZ-Hz0, SOz-H20,and N Z O 4 ( N O z t H a~t025 “C Heat of reaction,* kcal/mole AH1 = -5.5 i 0 . 1 AH2 = -27.0 i 0 . 2 AH13 = +2.25 =I= 0.03 AH14 +3.8 zt 0 . 1
Equilibriums
+ H 2 0 (I) C 0 2 . aq (0.0024.004M) + 2 OH- . aq (0.1M) COS2-. aq (0.0024M) + HzO (1) Cog . aq (0.01M) + H20 (I) H+ . aq (0.1M) + HC03- . aq HC03- . aq = H+ . aq (lO-13M) + COS2-. aq (0.01M) SO2 (9) + H20 (1) SOZ . aq (0.003-0.0065M) SO2 (g) + 2 OH- aq (0.02-0.1M) SOS2-. aq (0.0016M) + H 2 0 (I) SO2 . aq (0.01M) + H20 (1) = H+ . aq (2M) + HS03- . aq HS03- . aq H+ . aq (lO-13M) + SO3*- . aq (0.005M) NzO, (g) + H 2 0 (1) H+ . aq (0.35M) + NO3- . aq (0.002M) + HNOl . aq (0.002M) N z 0 4(9) + 2 OH- . aq (0.35M) HzO (1) + NO2- . aq (0.002M) + NO3- . aq (0.002M) HN02 . aq (10-ZM) = NO2- . aq + H+ . aq (0.35M) COz (8) COZ(g)
=
=
=
=
AHIS = -6.65 i 0 . 0 5 AH16 = -38.6 i 0 . 3
=
+
-3.42 i 0.03 -1.25 i 0 . 1 = AHg -12.9 i 0.1 = AHlo = -36.9 i 0 . 3 AH10 = +2.85 i . 0.03 Partial pressures of all gases listed (in equilibrium with water or aqueous solutions) were negligible, except in Reaction 1, where 0.07 < pco2 < 0.14 atmosphere. * Precision expressed as the standard deviation of the mean of 3-5 replicates. AH17
AH18
=
Table 11. Verification of Equations 22-24 Equation Heats (kcal/mole) calculated from No. Left side of equation Right side of equation 22 +5.1 i 0.2 +5.3 i 0.4 23 -4.7 i 0 . 2 -5.2 f 0 . 4 24 +2.85 i 0.03 1-2.8 i 0 . 4
maintained at atmospheric pressure through a minuscule opening cia the shorter needle made of Teflon (Dupont) shown in Figure 1. Samples consisted of the appropriate gas (carbon dioxide or sulfur dioxide) mixed with pure nitrogen or with air, and saturated-if desired and feasiblewith water vapor in equilibrium with the appropriate reagent solution. Suitable injection times were determined by trial and error. They proved to be on the order of 10-150 sec. Such gentle injection favored the formation of a multitude of small bubbles, optimizing conditions, by mutual diffusion, of attaining chemical equilibrium with the reagent, as well as saturation with water vapor of the milieu (nitrogen, air, etc.) in which the “analyte gas” was dispersed. It proved impractical to encumber the two smaller calorimeters, I1 and 111, with a n electric calibration heater. Instead, calibration was performed by injection of known samples of pure carbon dioxide into alkali hydroxide (Reaction 2). THERMOCHEMICAL RESULTS AND DISCUSSION In Table I are summarized the A H values obtained with the techniques outlined. Most gas enthalpograms were similar in shape to Curve I or I1 in Figure 3. The only exception was the neutralization of SO2 in a dilute solution of base that had not been previously deaerated. I n that case sulfite was slowly air-oxidized to sulfate, yielding the anomalies illustrated in portion c of Curves I and I1 in Figure 4. The anomalies were absect in deaerated solutions and in relatively concentrated alkali hydroxide (Figure 3, Curve 111), presumably because of a kinetic inhibition (11) of the process SOS2- 1 / 2 0 ~ = Sod2-. As mentioned previously, liquid reagents, (solutions of bicarbonate, sulfite, nitrite) were injected in selected experiments (Reactions 13, 14, 17-19). The corresponding enthalpograms were similar in shape to Curve I1 in Figure 3 except when nitrous acid was produced. Decomposition (12) of the latter
= = =
to NO and “ 0 3 , yielded an exothermic contribution, which, however, could be corrected by extrapolation. AH14 and AH18 in Table I were calculated by combining the assignment AHZo = 13.4 kcal/mole (13) for the reaction: H+.aq
+ OH-.aq
=
HzO(l)
(20 )
with our measured AH21values for the neutralization of bicarbonate and bisulfate ions: (HCOa-; HSOa-)
+ OH-
= (c03’-;
+ HzO
s03*-)
(21)
This indirect approach accounts for the relatively poorer precision of AHl4and AHls compared to AH,,, AHli,and AHl9 which were directly measured. It is evident from the chemical equations in Table I that the following relationships must necessarily hold:
+ AH,,) = AEj2 - (AH1 + 24HZo) (AHii + AHIS) = - ( A H I S+ 2AH20) = - (AH8 + 2AH20) (AH13
AH16
AH19
AH10
(22)
(23) (24)
Pertinent numerical comparisons are presented in Table 11. The internal consistency is very good and indicates that our experimental findings as listed in Table I are accurate. We conclude that gas enthalpimetry is generally suited for determining heats of reaction within 1%. This conclusion is further substantiated by Table 111 which lists heats of reaction determined in this study along with comparable data based on literature. When directly comparable calorimetric measurements were available, they agreed satisfactorily with this study, The performance of gas enthalpimetry is evidently similar to that of laborious classical calorimetric procedures. Gas enthalpimetry has the advantage of much simpler instrumentation and rapidity without loss in precision o r accuracy.
+
(11) L. C . Schroeter, “Sulfur Dioxide,” Pergamon Press, 1966, p 44. (12) A. N. Usubillaga, Thesis, University of Illinois, Urbana, 1962. 440
ANALYTICAL CHEMISTRY
ETHALPIMETRIC G.4S ANALYSIS In the presence of excess base-e.g., 0.5Maqueous KOHReactions 2 and 16 (see Table I) are ideally suited for the quantitative analysis of carbon dioxide and sulfur dioxide in
(13) J. Barthel, F. Becker, and N. G. Schmahl, Z. Physik. Chem. (Neue Folge), 29, 58 (1961).
I
I
I
$? 4 -
PRECISION
g;
3-
w*
>o
2-
-I> WW
I -
@
$2
En
I
I
I 3
E COz in air (1-60z v/v) analyzed in calorimeter 111 containing 100 ml of 0 . 5 M KOH plus 0.2M KzC03. 0 C 0 2 in air (1-60z v/v) analyzed in calorimeter I containing 10 ml of 0.5 KOH plus O.2M KzC03. A SO2 in nitrogen ( 4 6 0 % v/v) analyzed in calorimeter I1 containing 2 ml of 0.5M KOH
Table 111. Comparison of Reaction Heats Determined in This Study US. Data in the Literature Reaction AH (kcal/mole) No. This study Literature assignment 1 -5.5 - 6‘ 2 -27.0 -26.0b; - 2 6 . 9 13 +2,25 + 2 , 15d 14 +3.8 +3,55* 15 -6.65 -6.26e; -6.4 to -6.7J 16 -38.6 -39.50; -38.2 to - 4 0 . 5 h 17 -3.42 -3.86%; -3.91 18 -1.25 -2.3k 8 -12.9 -11.9* 10 -36.9 -35.4h 19 +2.85 +4.48l 0 Experimental value from (14) given to one significant figure only. * Calculated from heats of formation in (15). c Calculated by summation of AHl (Table I) with assignment by Roughton et at. (16) of (-21 i. 1) kcal/mol for the process COn (aq) 2 OH- (aq) = COS2-(as) H20(I). d Based on data obtained at several temperatures by a rapid flow method (17). E Experimental values based on Van’t Hoff isochore (18). J Based on calorimetric measurements in pure water: experimental data obtained (19, 20) after correcting (by suitable extrapolation procedures), for the contribution of partial formation of
+
+
HSOa-. 0
Based on calorimetry at high concentrations (0.74.8M) of
so2 (21). h
Concentration dependent calorimetric data (20): 10-ZM
