variable combinations specified by these maxima would not have a pronounced effect on the nieasurement sensitivity. Only a few of the systems investigated, howel-er, allow this latitude. The localized nature of the response niaxima in Figure 2 are generally typical and indicate the degree of regulation required to maintain maximum sensitivity and precision of measurement. For the majority of the systems studied, an increase in the signal intensity due to B change in flame parameters was accompanied by a parallel decrease in the flame background. Consequently, the signal intensity changes presented in Figures 1 and 2 are indicative of the
effects of the variables on the signal-tonoise ratio. LITERATURE CITED
(1) Amos, M. D., Thomas, P. E., Anal, Chznz. Acta 32, 139 (1965). (2) Amos, M. D., Willis, J. B., Spectrochim. Acta 22, 1325 (1966). (3) Broida, K. P., Shuler, K. E., J . Chern. Phys. 27, 933 (1959). (4) Buell, B. E., ANAL.CHEM.35, 372
(1963). ( 5 ) Dean, J. A., Carnes, W. J., Analyst 87, 743 (1962). (6) D'Silva, A. P., Kniseley, R. N., Fassel, V. A., AXAL. CHEM.36, 1287 (1964). (7) Fassel, 5:. A., Curry, R. H., Kniseley, R. N., Spectrochim. Acta 18, 1127 (1962).
otornetris cti
( 8 ) Gilbert, P. T., Jr., Xth Colloq. Spec. Intern., 171, Spartan Books, 1963.
(9) Kellev, PI. T.. Fisher. D. J.. Jones.' H. e., h . 4 L . CHEM. 31,'178 (1959). (10) Mandel, J., Stiehler, R. D., J . Res.
Natl. Bur. Std.. A 53. 155 119541. (11) Manning, D. d, A i - Abiorplion Newsletter 4, 267 (1965). (12) bIorrison, G. EI., Skogerboe, R. K in
"Trace Anal.: Physical Methods,;'
G. H. Morrison, ed., p. 6, Interscience,
New York, 1965.
(13) Slavin, W., Sprague, S., Manning, D. C., At. Absorption Xewsletter, No. 18, Perkin-Elmer Gorp., Norwalk,
Conn., February 1964.
RECEIVEDfor review July 21, 1966. Accepted September 12, 1966. Research supported by the Advanced Research Projects Agency.
.
rnmonia-
DENNIS G. PETERS and ABDOLREZA SALAJEGHEH Department o f Chemistry, Indiana University, Bloomington, Ind.
b Spectrophotometric measurements of the rate of disappearanceof thioacetamide have substantiated and extended previous information concerning the ammonia-thioacetamide reaction. The rate of this reaction exhibits a first-order dependence on the thioacetamide concentration and a second-order dependence on the ammonia concentration. Third-order rate constants for the ammoniathioacetamide reaction are 0.0055, 0.014, 0.024, 0.037,and 0.059 liter2 mole-2 minute-1 at 40°,60°, 70°,80") and 90" C., respectively, At a given temperature, an apparent increase in the third-order rate constant is observed for decreasing initial ammonia concentrations. This is due to a contribution by the hydroxide-catalyzed hydrolysis of thioacetamide to the overall rate of disappearance of In addition, sulfide thioacetamide. produced by the ammonia-thioacetamide reaction is oxidized by dissolved oxygen. If allowance is made for the latter two side reactions, the rate of disappearance of thioacetamide and the rate of formation of sulfide are equal.
quantitative studies of the kinetics of precipitation of zinc and nickel sulfides from ammoniaammonium ion buffer solutions by thioacetamide have been reported recently (8-4, 9). The rate of precipitation of each of these sulfides is controlled in part by a direct reaction between thioacetamide and the various metal ammine species and also by an amEVERAL
1824
e
ANALYTICAL CHEMISTRY
monia-thioacetamide reaction. This latter reaction is second order in animonia and first order in thioacetamide and produces sulfide ions which react rapidly with a metal cation to form the sulfide precipitate. Interpretation of precipitation reactions involving thioacetamide in aqueous ammonia solutions, and especially elucidation of the nature of the direct reaction between thioacetamide and metal ions, requires knowledge of the rate constant for the ammonia-thioacetamide reaction. The only published investigation of the ammonia-thioacetamide reaction is that of Peters and Swift ( 7 ) , whose results were based solely on measurements of the rate of formation of sulfide. Therefore, it was of interest to measure directly the rate of disappearance of thioacetamide by spectrophotometric means and to test the assumption made by Peters and Swift that the rate of formation of sulfide and the rate of disappearance of thioacetaniide are equal. In ammonia-ammonium ion buffer solutions, the role of the hydroxidecatalyzed hydrolysis of thioacetamide (1) as a source of sulfide is usually unimportant in comparison to the ammoniathioacetaniide reaction. However, as the ammonia concentration decreases and the reaction temperature increases, the contribution of the hydroxide-catalyzed hydrolysis to the rate of disappearance of thioacetamide and the rate of formation of sulfide can become significant. The effect of this hydrolysis on the apparent rate of the ammoniathioacetamide reaction is taken into account in the present study. For some experiments with reaction
times of 2 to 3 hours, Peters and Swift found a marked decrease in the rate of formation of sulfide. Moreover, the sulfide ion concentration itself was frequently less after 2 or 3 hours than after much shorter reaction times. These observations were attributed to oxidation of sulfide by dissolved oxygen. The work sunimarized below includes the results of specific experiments showing the effect of oxygen on the rates of formation of sulfide and disappearance of thioacetamide. Finally, as an aid to the verification of the reaction mechanism proposed earlier, measurements have been performed to determine the influence of the amnionium ion concentration and ionic strength on the rate of the ammoniathioacetamide reaction. EXPERIMENTAL
Reagents. Reagent grade thioacetamide was recrystallized from a two-to-one mixture of benzene and ethanol and was dried and stored over Drierite in a vacuum desiccator. The white solid did not change color over a period of a t least 6 months and gave clear solutions when dissolved in water. Stock solutions, usually 1.00F in thioacetamide, were prepared by weight, but were never kept longer than 1 day. Aqueous stock solutions of ammonia, animonium chloride, and sodium perchlorate were oreoared as described previously ( 7 ) . Amaratus and Procedure. The reac'tion vessel was similar to those used in previous studies ( 1 , 7 ) except that it was fitted with a sintered-glass gas-dispersion tube so that prepurified nitrogen could be bubbled through the a
*
reaction solution t o remove dissolved oxygen. However, the nitrogen was first passed through a gas-washing bottle containing an ammonia solution of the same concentration as the reaction solution. This was done to minimize changes in the ammonia concentration during the course of the reaction. For example, the loss of ammonia in a 15-minute period by volatilization from an originally 1F ammonia solution at 60' C. was reduced from approximately 15% t o about 2y0 with the use of the gas-washing bottle. For lower ammonia concentrations, the rate of loss of ammonia was considerably smaller. 4 reaction mixture was prepared from the various stock solutions (except thioacetamide solution) and distilled water, and heated in the reaction vessel to the desired temperature while nitrogen was bubbled through the solution for a t least 15 minutes to expel dissolved oxygen prior to the start of an experiment. Simultaneously, in a separate test tube, a portion of the thioacetamide solution was deaerated and brought to the same temperature. To begin the reaction, a volume of this thioacetamide solution was pipetted into the reaction vessel and the time was noted. Thereafter, nitrogen was bubbled continuously through the reaction solution t o exclude oxygen. The temperature of the gaswashing bottle and the test tubes containing the reaction mixture and the thioacetamide solution was maintained constant t o within ~ k 0 . 5 "C. by means of a thermostated water bath. Immediately after the addition of the thioacetamide solution, an aliquot of the reaction solution was titrated with standard hydrochloric acid to establish the initial concentration of ammonia. Samples of the reaction mixture were taken a t timed intervals and transferred into test tubes placed in an ice bath to quench the reaction. The analysis of a sample for sulfide ion was accomplished according t o the procedure described by Butler, Peters, and Swift (1, 10). The analysis of a sample for thioacetamide was carried out by dilution of the sample with distilled water followed by spectrophotometric determination of the thioacetamide concentration a t 262 mp (1, 8). Spectrophotometric data as well as absorption spectra were obtained with a Cary 14 recording spectrophotometer. RESULTS AND DISCUSSION
I n all experiments, with the exception of those mentioned in one section of this paper, the ionic strength of the reaction solutions was adjusted to 0.30 with sodium perchlorate solution. The ratio of the initial concentration of ammonia to that of ammonium chloride was usually five to one, variations only being made to determine the specific effect of ammonium ion concentration on the rate of the ammonia-thioacetamide reaction. In most kinetics experiments, the ammonia-thioacetamide reaction was followed until approxi-
Table 1. Third-Order Rate Constants for the Ammonia-Thioacetamide Reaction (Initial thioacetamide concentration, 0.0100 F. Initsialammonium ion concentration was 0.2 that of ammonia) Observed initial rate of disappearance of thioacetamide Third-order rate constant, IC', -d[CHsCSNHz] / d l , liter2 mole-2 minute-' mole liter-' minute-' (X106) Initial ["a], F Observed" Corrected* (a) Temperature = 60' C.; pH = 9.20 =k 0.05; pK, = 13.02; pOH = 3.82; [OH-] = 1.5 X 10-4M 0.69 0.200 0.017 0.015 0.81 0.218 0,017 0.015 2.0 0.360 0.017 0.016 3.6 0,500 0.014 0,014 7.4 0.750 0.013 0.013 12.2 1.00 0.012 0.012 (b) Temperature = 90' C.; pH = 8.62 f 0.05; pK, = 12.42; pOH = 3.80; [OH-] = 1.6 X 10-4M 2.2 0.167 0.078 0.044 5.0 0.270 0.069 0.057 7.5 0.066 0.057 0.337 14.9 0.061 0.057 0.496 27.1 0.060 0.058 0.672 a Calculated from the rate ex ression - ~ [ C H ~ C S N H Z ] =/ ~IC'[CHaCSKHz] ~ [NHsl2. Calculated by subtracting t i e initial rate of the h droxide-catalyzed hydrolysis of thioacetamide, -d[CHaCSNHz]/dt = ~ " [ C H ~ ~ S N[JH-], H Z ] from the observed initial rate of disappearance of thioacetamide; k" is 0.5 and 6 liter mole-' minute-', respectively, at 60' and 90' C.
mately 35 to 4oyOof the thioacetamide had reacted; however, in a, few cases the percentage of reaction reached 50%. The rate constant for each set of experimental data was obtained in the following way. A plot of the logarithm of either the thioacetamide concentration or the sulfide concentration as a function of time was essentially linear. The slope of the best straight line through the experimental points was determined by the method of averages (6). For the kind of data analyzed in the present study, this procedure yields results identical to the method of least squares. From the slope of the line through the kinetic data and from the value of the ammonia concentration a t the beginning of the reaction, the rate constant was calculated. The uncertainty in the value reported for each rate constant is in the neighborhood of =t3y0. Rate of Disappearance of Thioacetamide. The major purpose of the present investigation was to provide a firm foundation for understanding the kinetics and mechanisms of sulfide precipitations involving the ammonia-thioacetamide reaction. Therefore, i t was important to examine the validity of the assumption made by Peters and Swift (7) that the rate of formation of sulfide from the ammoniathioacetamide reaction is equal to the rate of disappearance of thioacetamide. These workers observed that plots of the logarithm of thioacetamide concentration US. time constructed on the basis of this assumption were linear and, therefore, proposed that the disappearance of thioacetamide followed the same kinetic equation as the formation of sul-
fide. The feasibility of studying the ammonia-thioacetamide reaction by means of spectrophotometry was suggested by previous work dealing with the acid-catalyzed hydrolysis of thioacetamide (1, 8). SPECTRA OF THIOACETAXIDE AND SULFIDESOLUTIONS.Absorption spectra for different concentrations of thioacetamide in water were identical to the spectrum published by Rosenthal and Taylor (8). The molar absorptivity of thioacetamide at 262 mp, the tvavelength of maximum absorption, was calculated to be 11700 liter mole-1 cm.+ which agrees well with literature values (1, 8). For thioacetamide conand 5 x centrations between 1 X 10-4F, Beer's law is obeyed to within approximately i1%. Sulfide ion has an absorption maximum a t 231 nip, In addition, sulfide absorbs significantly a t 262 mp, and concentrations above approximately 10-4M can interfere with the spectrophotometric determination of thioacetamide. However. in no experiment was the sulfide concentration sufficiently great relative to the thioacetamide concentration t o cause a significant error. Other experiments demonstrated that solutions of ammonia, ammonium chloride, and sodium perchlorate do not exhibit measurable absorption in the wavelength region between 230 and 300 mp. RATE CONST-4NTS AXD ORDER OF REACTION.The rate of disappearance of thioacetamide was followed spectrophotometrically in solutions with various initial concentrations of thioacetamide between lo-* and 10-2F and with ammonia concentrations in the VOL. 38, NO. 13, DECEMBER 1966
a
1825
range from 0.2 to 1.OF. Typical experimental data are presented in Table I, which lists apparent or observed thirdorder rate constants for the amnioniathioacetamide reaction at both 60" and 90" C. These rate constants were calculated on the basis of the measured rate of disappearance of thioacetamide and the kinetic equation:
- d [CH3CSNH,] dt
k'[CHsCSNHz] ["a]' proposed previously ( 7 ) . For any given ammonia concentration and temperature, identical third-crder rate constants were obtained for initial thioacetamide concentrations throughout the range between and 10-2F. I n addition, the rate of the ammonia-thioacetamide reaction was confirmed to be first order with respect to the thioacetamide concentration. However, the second-order dependence of the ammonia-thioacetamide reaction on the ammonia concentration is less obvious, since the observed thirdorder rate constants shown in Table I are not strictly constant but decrease as the concentration of ammonia is increased. This is especially true for the results a t 90' C. Such behavior might be explained by the presence of a term involving the ammonia concentration which appears in the denominator of the rigorous third-order kinetic equation derived below. The mechanism for the ammoniathioacetamide reaction suggested by Peters and Swift includes a rapid equilibrium reaction between thioacetamide and one molecule of ammonia
2"
CHs-C-SH I 2"
followed by the rate-determining attack on the intermediate by a second ammonia molecule KH2
I I
CHs-C-SH
+ NH3
kz --t
2" 2"
I
CHs-C=NH
+ NH4+ + HS-
The product acetamidine would undoubtedly hydrolyze to form acetate ion and to regenerate ammonia. Using the steady-state approximation, one can derive the following rate equation 1826
0
ANALYTICAL CHEMISTRY
- d [CHaCST\"2]
niade to correct the resulting pOH values, or the hydroxide ion concentrations, for salt effects, since uncertainties in the rate constants for the hydroxidecatalyzed hydrolysis of thioacetamide are of comparable, if not larger, magnitude. The true rate of the ammonia-thioIf k-1 >> kz[KH3] in the denominator acetamide reaction was obtained by subof the right-hand side of this equation, tracting the initial rate of the hydroxidethe rate of disappearance of thioacetcatalyzed hydrolysis from the total amide will appear to be first order with initial observed rate of disappearance of respect to thioacetamide and second thioacetamide. Corrected third-order order with respect to the ammonia conrate constants for the ammonia-thiocentration. On the other hand, the acetamide reaction were then calculated fact that the third-order rate constant from the true rate of the ammoniaincreases with decreasing concentration of ammonia could imply that kz[NH3] thioacetaniide reaction. Some representative results are listed in Table I. cannot be neglected in the above rate As indicated in Table I, the effect of the expression. However, before this conhydroxide-catalyzed hydrolysis on the clusion can be stated with certainty, it third-order rate constant is relatively is important to consider the role of the small a t high ammonia concentrations. hydroxide-catalyzed hydrolysis of thioAs the concentration of ammonia is deacetamide (1). creased, however, the significance of the EFFECTOF HYDROXIDE-CATALYZED hydroxide-catalyzed hydrolysis inHYDROLYSIS O F THIOdCETAlfIDE. Ancreases. In addition to its importance other reason why the third-order rate at low ammonia concentrations, the constant might increase as the concenhydroxide-catalyzed hydrolysis becomes tration of ammonia is decreased is that more prominent a t higher reaction temthe hydroxide-catalyzed hydrolysis of peratures. This is because the energy thioacetamide becomes important at low of activation for the hydrolysis reaction ammonia concentrations. It should be (20 kilocalories per mole) is larger than recalled that, while the ammonia conthat for the ammonia-thioacetamide centration was decreased in a series of reaction (12 kilocalories per mole). experiments, a constant ammonia-toTherefore, an elevation of temperature ammonium chloride concentration ratio causes a greater increase in the rate was maintained. Consequently, the pH constant for the former process. values of all solutions a t a particular The agreement among the corrected reaction temperature mere essentially third-order rate constants for different identical, so the rate of the ammoniaammonia concentrations a t 60" and thioacetaniide reaction decreased rela90OC. in Table I demonstrates that the tive to the nearly constant rate of the ammonia-thioacetamide reaction is first hydroxide-catalyzed hydrolysis of thioorder with respect to thioacetamide and acetamide. second-order with respect to ammonia. The hydroxide-catalyzed hydrolysis is Furthermore, this agreement supports first order with respect to both the the conclusion that the increase in the thioacetamide and hydroxide ion conobserved rate constants is due to the centrations. Butler, Peters, and Swift hydroxide-catalyzed hydrolysis of thio(1) deterniined the second-order rate acetamide rather than to the presence of constant for the disappearance of thioa term involving the ammonia concenacetamide to be approximately 6 to 7 tration in the denomiliator of the rate liters mole-1 minute-l a t 90" C. Csisiag equation. It should be emphasized the reasonable value of 20 kcal. per mole that these results do not preclude the for the energy of activation of the hyexistence of such a term in the rate drolysis reaction, one can predict secequation. The unusually low value for ond-order rate constants for other the corrected third-order rate constant temperatures. The second-order rate in 0.167P ammonia a t 90°C. points out constant for the disappearance of the imperfection of our correction prothioacetaniide is approximately 0.5 cedure vhen the rates of the hydroxideliter mole-l minute-l at 60" C. catalyzed hydrolysis and the ammoniaIn order to calculate the rate of the thioacetamide reaction are nearly identihydroxide-catalyzed hydrolysis of thiocal. acetamide, the hydroxide ion concentraIt is worth mentioning that ammonia tion must be known. The following is a major product of the hydroxideapproach to this problem was adopted. catalyzed hydrolysis of thioacetamide The pH of each reaction solution a t a (1). However, in comparison to the specified temperature was determined initial ammonia concentrations emwith a glass electrode designed for ployed in the present study, the quanhigh temperature measurements, and tity of ammonia produced by this hythe corresponding pOH was calculated drolysis is very small and cannot acby difference from the infinite dilution count for the variation of the third-order value of pK, for water a t the appropriate temperature (6). KO effort was rate constants in Table I. dt
-
VARIATIONOF THIRD-ORDER RATE COMTANTWITH TEMPERATURE. The effect of temperature on the third-order rate constant was determined from spectrophotometric measurements of the rate of disappearance of thioacetamide a t 40°, 60°, 70°, 80", and 90°C. in solutions initially 0.01F in thioacetamide and 0.72F in ammonia. The third-order rate constants, listed in order of increasing temperature and corrected when necessary for the hydroxide-catalyzed hydrolysis of thioacetamide, are as follows: 0.0055, 0.014, 0.024, 0.037, and 0.057 literz mole+ minute-l. The energy of activation was calculated to be 12 kcal. per mole, which is in agreement with the value previously reported ( 7 ) EFFECTOF A-mios~uivION. Experiments were carried out with the initial concentration of thioacetamide (0.01F) and the ionic strength both kept constant, while the ratio of the ammonia to the ammonium ion concentration was varied from one-to-one to twenty-toone. I n a typical series of experiments performed a t 90°C. and with an initial ammonia concentration of 0.75F, the observed third-order rate constant for the ammonia-thioacetamide reaction had values of 0.061, 0.061, 0.060, and 0.059 liter2 mole-z minutew1 for ammonium chloride concentrations of 0.037, 0.075, 0.15, and 0.30F, respectively. Although small corrections should be made for the effect of the hydroxidecatalyzed hydrolysis of thioacetamide, especially for the lowest concentrations of ammonium chloride, the results reveal no significant change in the thirdorder rate constant provided that even a low concentration of ammonium ion is present. However, the complete elimination of aniinonium chloride from a reaction mixture produces a substantial increase in the hydroxide ion concentration which, in turn, causes a relatively large contribution by the hydroxidecatalyzed hydrolysis of thioacetamide to the overall rate of disappearance of thioacetamide. EFFECT OF IONIC STRENGTH.Knowledge of the effect of ionic strength on the ammonia-thioacetamide reaction is of value in substantiating the reaction mechanism suggested by Peters and Swift (7'). Accordingly, the rate of the ammonia-thioacetamide reaction was measured for five different values of ionic strength under conditions of constant thioacetaniide concentration and ammonia-to-ammonium ion concentration ratio. In reaction mixtures containing approximately 0.6F ammonia, 0.12M ammonium ion, and 0.0018' thioacetamide a t 90' C., the corrected third-order rate constant was found to be 0.056, 0.057, 0.056, 0.061, and 0.067 liter2 mole-2 minute-1, respectively, for ionic strengths of 0.12, 0.30, 0.60, 1.12, and 2.12. The absence of any I
pronounced influence of ionic strength on the rate of the amnionia-thioacetamide reaction supports the proposed reaction mechanism involving neutral (uncharged) reactants. However, the small positive salt effect observed in these experiments is consistent with the fact that activity coefficients of uncharged solutes increase as ionic strength increases. Furthermore, in accord with the postulated mechanism, the ratedetermining attack by a second ammonia molecule on the CH8C(SH)(PI"&intermediate to form the final products, including NH4+ and HS-, could proceed through a dipolar activated complex. The rate of formation of such an activated complex would be enhanced by increases in ionic strength. On the basis of these results, one may conclude that precise adjustment or control of ionic strength is unnecessary when the ammonia-thioacetamide reaction is utilized for sulfide precipitations, because reasonable predictions of the rate of formation of sulfide can be made without exact knowledge of the ionic composition of the sample solution. Rate of Formation of Sulfide. From the viewpoint of analytical chemistry, it is the formation of sulfide rather than the disappearance of thioacetamide that is important for the precipitation and separation of metal cations. The rate of formation of sulfide from the ammonia-thioacetamide reaction was measured a t 60" and 90" C. for various initial thioacetamide and ammonia concentrations to provide data for comparison to the rate of disappearance of thioacetamide as well as to confirm the results of previous work ( 7 ) . Arerage values of 0.013 and 0.054 liter2 mole-* minutew1 obtained for the third-order rate constant are in good agreement with those of 0.012 and 0.055 liter2 mole-2 minute-1 a t 60" and 90" C., respectively, reported by Peters and Swift. 811 these rate constants pertain to the first 6O-nlinute reaction period. It is interesting that the third-order rate constant based on measurement of the formation of sulfide is less affected by the hydroxide-catalyzed hydrolysis of thioacetamide than that based on the rate of disappearance of thioacetamide itself. This is because only approximately one fifth of the thioacetamide undergoes direct hydrolysis to sulfide ions ( 1 ) . Thus, when the third-order rate constant for the ammonia-thioacetamide reaction is computed from the rate of formation of sulfide, there is little or no trend toward increasing rate constants a t low ammonia concentrations. However, another problem is encountered, namely the sensitivity of sulfide t o oxidation by dissolved oxygen. OXIDATION OF SULFIDEBY OXYGEK. Two observations by Peters and Swift suggested the need to investigate briefly
the oxidation of sulfide by oxygen. First, although the rate constant for the formation of sulfide from the ammoniathioacetamide reaction remained essentially constant during the first hour of the reaction, it exhibited a large and unexpected decrease after several hours. Second, in certain experiments for which the rate of sulfide formation was relatively small, the sulfide concentration was actually less after a long reaction time than after a short time. To ascertain the effect of oxygen on the rate of forniation of sulfide, the following experiments were performed. In one experiment, a solution initially containing 0.75F ammonia, 0.15F ammonium chloride, 0.15F sodium perchlorate, and 5 x 10-4Fsodium wlfide was heated at 90" C. in the reaction vessel while air was bubbled continuously through the solution. Samples of this solution were taken a t timed intervals and placed in an ice bath to quench the reaction. It was found that the absorbance of sulfide a t 231 mp decreased as a function of time. il sample taken after only 60 minutes showed no absorption a t 231 mp, and a portion of the solution gave no sulfide precipitate when added to an ammoniacal cadmium(I1) test solution. A similar experiment in which nitrogen !vas bubbled through the reaction solution revealed that sulfide still disappeared, but a t a rate several times slower than before. These experiments indicate that oxidation of Sulfide, probably t o elemental sulfur, can occur readily under conditions similar to those extant when the rate of sulfide formation from the ammonia-thioacetamide reaction is evaluated. It is likely that third-order rate constants based on measurements of sulfide formation are too small even for relatively short reaction times. Accordingly, care must be exercised whenever these rate constants are employed to predict the rate of precipitation of metal sulfides from ammonia solutions. Thioacetamide appears t o be less prone than sulfide ion to air oxidation. When essentially neutral solutions of thioacetamide were heated in the reaction tube a t 90" C. and nitrogen and then air were bubbled through the solutions for a t least 1 hour, no change was detected in the absorbance of thioacetamide a t 262 mp. Comparison of Rates of Disappearance of Thioacetamide and Formation of Sulfide. Inspection of the thirdorder rate constants evaluated in the present study and in the investigation by Peters and Swift suggests that the rate of disappearance of thioacetamide is consistently greater than the rate of formation of sulfide. A direct comparison of the rates of formation of sulfide and disappearance of thioacetamide in a single kinetics experiment VQL. 38, NO. 13, DECEMBER 1966
e
18
has confirmed this conclusion. The reaction solution contained approximately 0.75F ammonia, 0.15F ammonium chloride, 0.15F sodium perchlorate, and 0.01F thioacetamide. Samples of the reaction mixture u ere taken at timed intervals and were analy~ed for sulfide. After the complete removal of sulfide as hydrogen sulfide by acidification of the sample (IO), the thioacetamide concentration iyas determined spectrophotometrically at 262 mp. The amount of sulfide formed a t any time was always smaller than the quantity of thioacetamide which had disappeared, the difference increasing with the time of reaction. For example, the amount of sulfide present after 60 minutes was about eight-tenths of the amount of thioacetamide which had reacted. M7e believe that the difference in the rates of disappearance of thioacetamide and formation of sulfide is due t o the oxidation of sulfide by oxygen during
the course of the kinetics measurements and that, in fact, the two rates are identical. Definite proof that the rate of formation of sulfide is equal to the rate of disappearance of thioacetamide has been obtained in a study of the precipitation of lead(I1) sulfide by thioacetamide from ammoniacal EDTA solutions. The lead(I1)-EDTA complex does not undergo a direct reaction with thioacetamide; however, this complex does react rapidly with the suEide ions generated by the amnionia-thioacetamide reaction. The rate of precipilation of lead(I1) sulfide follows quantitatively the rate of disappearance of thioacetamide predicted from the data reported in the present investigation. Lnder the conditions of these experiments, sulfide escapes air oxidation because of its fast reaction with the lead (11)-EDTA complex. Full details of this precipitation study will be described in a subsequent paper.
ST. JOHN, W. J.
McCARTHY, and J.
T
are many factors which influence the measured signal and noise in analytical techniques based upon the measurement of luminescence (fluorescence, phosphorescence, and delayed fluorescence) of molecules in the condensed phase. So far no detailed treatHERE
1828
@
ANALYTICAL CHEMISTRY
E. H., Talanta
12,
357 (1965).
(3) Klein, D. H., Swift, E. H., Ibid., p. 349. (4) Ibid., p. 363.
(5) Levens, A. S., “Graphics in Engineering and Science,” p, 386, Wiley, New Pork, 1954. (6) Meites, L., “Handbook of Analytical Chemistry,” p. 1-34, McGraw-Hill, New York, 1963. (7) Peters, D. G., Swift, E. H., Talanta 1, 30 (1958). (8) Rosenthal, D., Taylor, T. I., J. Am. Chem. SOC.79, 2684 (1957). (9) Swift, E. H., Anson, F. C., in “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley, ed., Vol. 1.,I. ). 293. Interscience. New York. 1960. (10) Swift, E. PI., Butler, E. A,, ANAL. CHEW28, 146 (1956). RECEIVEDfor review -4ugust 8, 1966. Accepted September 22, 1966.
.
D.
WINEFQRDNER
Department of Chemisfry, University o f Florida, Gainesville, Ha.
b A general approach is used to derive equations which are concerned with the influence of experimental and spectral parameters on the photodetector signal, signal-to-noise ratio, minimum detectable sample concentration, and an analytically useful monochromator slit width in luminescence spectrometry. The general equations presented in this manuscript relate all important parameters involved in luminescence measurements. By the use of these equations, the influence of variation of any parameter on the shape of the analytical curve, the minimum detectable sample concentration, and the precision of measurement can be predicted. The use of these equations facilitates optimization of each parameter. Estimates of phosphorimetric minimum detectable Concentrations of several organic molecules obtained using the derived equations compared quite well with measured values using commercial equipment.
(1) Butler, E. A., Peters, D. G., Swift, E. H., AXAL.CHEM.30, 1379 (1958). (2) Klein, D. H., Peters, D. G., Swift,
oise Theory In ectrometry
plications of olecular Lurnine P. A.
LITERATURE ClTED
32607
ment of the experimental factors and the extent t o which these factors affect the measured detector signal, the noise, and the shape of analytical curves, has appeared in the literature. Therefore, in a practical analysis, the investigator is usually forced to rely on a trial and error approach to obtain the optimum experimental conditions. Trial and error optimization of parameters is generally time consuming and subject to considerable error. In this manuscript, a general approach to the theory is giyen, and equations are derived for the photodetector signal, signal - t o - noise ratio, and limiting detectable sample concentration as a function of sample characteristics and experiniental parameters. The derived equations are used to predict the influence of experimental parameters on the measured signal, the shape of the analytical curve, the signal - to - noise ratio, and the limiting detectable sample concentration. The approach used in the derivation is similar to that used by Winefordner and Vickers (%%’) in their theory concerning atomic emission flame spectrometry. DERIVATIONS OF SIGNAL AND SIGNAL-TO-NOISE EXPRESSIONS
Part I. The Signal. Several assumptions must be made which will facilitate discussion of the theory b u t
will not seriously limit its use. It will be assumed that the entrance and exit slit widths and heights are equal for each monochromator. bfost monochromators have equal entrance and exit slits or can be made t o have equal slits. No significant gain in resolution or in signal-to-noise ratio results if the entrance and exit slit widths and heights differ. Also, it will be assumed that the spectral band width of the excitation monochromator, s, is appreciably less than the half-intensity width of the excitation spectral band and that the spectral band width of the emission monochromator, s’, is appreciably less than the half-intensity width of the emission spectral band. The influence of spectral band width on absorbance and intensity values has been considered by Broderson (S) and others (4, 18). For convenience, it will also be assumed that the luminescence emission band shape is given by a Gaussian function of the wavelength (6). Finally it will be assumed that the intensity of absorption and emission are approximately constant over the spectral band widths, s and s’, respectively, and that the measured emission band is a result of only a single electronic transition. The most common experimental arrangement for measurement of luminescence (fluorescence, phosphorescence, or delayed fluorescence), consists Qf the
