time may cause extr:tction of other elements-e.g., Fe(II1). The cerium was determined spectrophotometrically with arsenazo (2). Stability of Extraci. Absorbances of the cerium complex and blank solutions remain constant, for at least 3 hours (Table 11). All the experiments were carried out at room temperature (about 25’ C.). Calibration Curve. The ceriumT T A system conforms to Beer’s law with concentrations oj up t o 10 pg. of cerium per ml. of organic phase. Assuming t h a t the extrxtion of cerium into the organic phase was complete, the apparent molar absorptivities were
9.3 X lo3 and 8.8 X lo3liter per molecm. a t 440 and 450 mp, respectively. I n this connection, it may be mentioned that the persulfate method (3) has a molar absorptivity of 5.6 X lo3 at 320 mp (authors’ experiment). Interference Study. Table I11 summarizes the results of the interference study. Most of the metals used were in the forms of sulfate and nitrate. Iron (111) gives a color with TTA, and more than 10 pg. of iron cannot be tolerated. Vanadium(V) interferes rather seriously: 1.1 mg. of vanadium gave an absorbance corresponding to about 10 pg. of cerium. Chloride should not be present (4). I n general, the present
method is more selective than the method (1) that involves the TTA extraction at p H 5.4. LITERATURE CITED
(1) Khopkar, S. M., De, A. K., ANAL. CHEM.32,478 (1960). (2) Onishi, H., Banks, C. V., Tnlanta 10,399 (1963). (3) Sandell, E. B., “Colorimetric Determination of Traces of Metals,” 3rd ed., p. 382, Interscience, New York, 1959. ( 4 ) Smith, G. W., Moore, F. L., ANAL. CHEM.29,448 (1957).
RECEIVEDfor review April 25, 1963. Accepted August 14, 1963. Contribution No. 1310. Work performed in the Ames Laboratory of the U. S. Atomic Energy Commission.
Rapid Determination of Binary Mixtures by Pseudo First-Order Differential Reaction Rates Conductometric Determination of Carbonyl Compounds LOUIS J. PAPA,l JOSEPH H. PATTERSON, HARRY
B. MARK, JR.,2
Deparfment o f Chemisky, University o f North Carolina, Chapel Hill,
b A general method is presented for the rapid determincition of binary mixtures based on di.Rerential pseudo first-order reaction ral.es. The method requires a knowledge of the total composition of the mixture and the measurement of the effective fractional life time; from this, the analysis of the mixture i s oiDtained using a predetermined calibrcition curve. Mixtures of carbonyl compounds were determined utilizing their differential reaction rates with hydroxylamine hydrochloride and/or semicarbazide hydrochloride. The reactions were followed by recordiig automatically the conductance as a function of time.
S
have developed kinetic met’nods of determining aldehydes and/or ketones. Blaedel and Petitjean (1) dotermined acetylacetone by reaction with hydroxylamine hydrochloride and by following the rate of increase of the hydrochloric acid concentration with high frequency conductance measurements. A calibration curve of rate of changs of concentration at a given time (in the early stages of the reaction) vs. concentration thus allows determinations to be made rapidly. Present address, 15. I. du Pont de Nemours and Co., Organic Chemical Division, Jackson Laboratories, Deepwater, N. J. * Present address, Department of Chemistry, University of Mit:higan, Ann Arbor, Mich. EVERAL IIWESTIGATORS
and C. N. REILLEY
N. C.
Malmstadt and Toren (2) determined individual aldehydes and ketones by following their reaction with hydrosylamine hydrochloride and/or semicarbazide hydrochloride. The reaction was followed potentiometrically with a special fast response pH measuring instrument. The time required for the p H of the reacting solution to pass between two preset values, At, was measured and from this a linear calibration curve was constructed relating At to the initial concentration of sample. Siggia and Hanna (6) were able to determine mixtures of these compounds by reaction with hydroxylamine hydrochloride. The reaction was followed by continuous titration of the hydrochloric acid as it was produced (which maintained the pH a t 3.5). They employed the second-order logarithmic extrapolation method to resolve the mixture. The method presented in this paper is based on the same reactions-ie., aldehydes and ketones with hydroxylamine hydrochloride and/or semicarbazide hydrochloride. The course of the reaction was followed automatically with a direct recording conductance meter (4). The mathematical treatment of the data is related to that of Roberts and Regan (6),but rearranged to render the method more adaptable to routine analysis. Several mixtures of aldehydes and ketones were determined with a relative error of 2.7% and the method wm feasible for mixtures whose rate
constant ratios were as low as 2.19 to 1. The method is rapid and simple and is not subject to interference by finite mixing times and by small amounts of acids or bases. It is also applicable to components which react in a parallel or stepwise manner with the reagent. EXPERIMENTAL
A water jacket cell (80-ml. capacity) is connected to a circulating constant temperature water bath which was regulated a t 25.1 i 0.1” C. A stock solution of hydroxylamine hydrochloride or semicarbazide hydrochloride is prepared in 70 t o 30 methanol-water (1 to 2 x 10-3M) and placed in the constant temperature bath for a t least 1 hour prior to analy&. Fifty milliliters of this reagent are placed in the cell (equipped with magnetic stirring motor and Teflon stirring bar) and the conductance electrodes are immersed in the solution. The recorder is started (chart speed 3 or 4 inches per minute) and when a steady baseline is reached (several seconds), sample is injected into the solution with a 2.0 ml. hypodermic syringe. The amount of sample employed can be varied as long as both [ A ] , and [ B ] ,>> R,. The injection is performed by rapidly immersing the needle below the solution level (to avoid bubbles) and rapidly injecting. The mixing time is fast (-3 seconds) compared to reaction rate. The opposite order of addition (reagent added to sample solution) is also employed. The reaction is allowed to run t o Procedure.
VOL. 35, NO. 12, NOVEMBER 1963
0
1889
I?+,
I
u
IO
sec.
L
0
,
I
02
04
06
I
08
A,/(A~+E,~
,, -t,-
T'41E
-
Figure 2. data
Analysis of butanone-2, pentanone-3 mixtures using hydroxylamine hydrochloride as reagent
Figure 1. Experimental rate curve for mixtures of p-hydroxybenzaldehyde and salicylaldehyde (semicarbazide hydrochloride as reagent)
completion and the time difference, t,, is measured (Figure 1). The longest time recorded for any of the compounds studied was 720 seconds. The fractional life time, t,, and a knowledge of A . B, are employed t o evaluate l / [ t e ( A o Bo)], which is then referred t o a calibration curve (Figure 2) to determine the mole fraction of A in the mixture. This calibraBo)] tion curve, a plot of 1/[te(Ao us. A,/& Bo),is constructed by employing the above procedure for pure A t o obtain l/(te.4,) qnd for pure B t o obtain l/(teBo)and then drawing a straight line between these two points. I n cases where either or both of these components are not available in pure form, mixtures of known composition may be employed t o construct this curve. The calibration curve for p hydroxybenzaldehyde, salicylaldehyde mixtures reported in this paper could not be constructed by determining the t, values for salicylaldehyde because it reacted too fast for measurement. Thus, the pure p-hydroxybenzaldehyde and known mixtures of the two species were used t o construct the curve. Complex kinetics may result in a nonlinear but reproducible calibration curve; such a situation would require determination of a series of mixtures, having mole fractions of A varying from zero t o one, in order t o construct the curve. The preferred method of addition is t o add the sample to the cell in 50.0 ml. total volume and inject about 1 ml. of the appropriate strength reagent. The amount of reagent added is not critical, provided that it is negligible compared t o A , and to Bo. This order of addition has the advantage that repetitive results can be obtained without changing the cell solution, thus saving time and quantity of sample. This order of addition is also desirable for
+
+
+
1890
o
ANALYTICAL CHEMISTRY
+
Typical calibration curve and experimental
determining carbonyl compounds which are not readily soluble. Principle. Roberts and Regan (6) presented a method for determining two components A and B simultaneously based on their reaction with a common reagent R . If the concentrations of A and of B are each much greater t h a n t h a t of R , the rate expression for irreversible second-order reactions is _ d _R=
dt
k ~ [ A l o [ Rf] k s [ B ] o [ R= ]
K*[$I
where K*
+
k ~ [ A ] o kB[B]o
(1)
(2)
and kA and k B are the second-order rate constants of il and B reacting with R. [ A ] , and [ B ] , are the initial concentrations of A and B. These authors then measured K*, k ~ k ,B , and ([.4],), and calculated [ A ] , and [B],. They reported that they could determine a mixture where kA/kB is less than 2 . This is certainly difficult t o accomplish by other kinetic methods. The method employed in this paper involved rearrangement of their equation with the result that a calibration curve can be constructed and the mixture resolved by determination of a time, t,, for a given fractional life, (l/e), and a knowledge of ([A], [BI o ) The integrated form of Equation 1 may be written
+
k
kB
x
(3)
Therefore, a plot of l / t ( [ 4 ] , f [Bl,) us. [ A ] , / ( [ A ] , [B],) (mole fraction A ) at given fraction reacted, RJR,, will yield a straight line. This straight
+
line plot serves as the calibration curve employed for the determinations presented below; Figure 2 represents a typical plot. It is now desirable to ascertain the optimum fractional life which should be chosen for measurement. Differentiating Equation 3 with respect to R l and then t o t yields d(dxa/dRr) - 1 - K*t dt pe-K*'
(4)
Thus, the minimum error in Z A , the mole fraction of [A],, occurs when K*t = 1. From the relationship, R J R , = exp(-K*t), it is seen that the minimum error occurs when R J R , = l/e. Measurements are then made at this fraction t o obtain the minimum error. Mixing times can sometimes obscure the point at which the reaction started, especially if this time covers an appreciable fraction of the reaction. This is most likely to occur, in the procedure presented, when the reagent is added to the sample. This can be circumvented by selecting an arbitrary time, tl, to serve as t = 0; tl should be selected as soon as possible after the mixing time. Figure 1 illustrates this procedure. It is seen that the mixing time interferes with accurate determination of R,. Thus,. a point tl (immediately beyond the mxing time) is selected as a reference and the value of R t , a t this time is determined as indicated in Figure 1. The time, t 2 , to reach Rt2!Rt, = l / e is then measured. The time, t, = ( t p - t l ) , is then used in constructing the calibration curve. Obviously, certain forms of rate lan-s-Le., other than that of individual first order dependences as given by Equation 1-may be subjected to a similar treatment. Simple exponential decay in [ R ]will obtain only in those caaes where [ R ]reacts 11-ith each species by pseudo first-order kinetics and hence can he factored entirely from the re-
maining terms in therats law expression. The remaining termb will then take on other forms depende it on the kinetic order of the reaction in respect to the indil idual iample speciei. RESULTS AND DISCUSSION
Witliin e\;perimental error, the calibration curves for all the mixtures determined were linear as predicted by Equation 3. Figure 2 s ' i o ~ the ~ s calibra-
Table 1. Determinaticsn of Carbonyls by Reaction with Hydroxylamine Hydrochloi-ide
%
Mixture A. butanone-2 13. pentanone-3
Pres-
% Found, A
kA/kB
11.6
10.9
3.7
11.6
10.1 22.5 22.5
ent, A
22.5 22.5 33.6 33.6 63.8 63.8 82.5 82.5 82.5
A. pentanone-3 13. diisobutyl ketone A . butanone-2
20.0 50.0 80.0
80.0 54.1
3-methyl butanone-2 A. pentanone-3 81.6 i ) . acetophenone 81.6
33.8 35.2 65.0 63.0 82.0 81.0 79.5 18.8 50.4 77.0 78.0 53.0
25.0
3.12
13.
62.5
62.5 62.5 62.5 42.6 42.6 21.8 21.8 A. pentanone-2 5. pentanone-3
20.0
50.0 80.0
78.2 76.8 63.8 64.0 62.0 60.8 41.0 40.0 21.8 21.8 19.5 49.2 78.5
25.3
2.19
Table II. Determination of Carbonyls by Reaction with Semicarbazide Hydrochloride
A. acetone
23A
A. cyclohexanone
40.2 B. cyclopentanone 77.5 A. p-hydroxybenzaldehyde
40. '3
B. salicylaldehyde 40. '3
20.13 20.13
22.0
48.2 75.2
2.8
29.7
41.2 -1 4.5 40.3 21.2 20.8
tion curve for the methyl ethyl ketone, diethyl ketone mixture (reaction with hydroxylamine), and is typical of all the curves obtained. Table I lists the results of determinations performed employing the hydroxylamine reaction uiid includes the relative rate con4,ants. Table I1 lists results of the reactions with sernicarbnzide and includes the relative rate constants of these individual components. The semicarbazide reaction was employed because several of the components reacted too rapidly with hydroxylamine a t the temperature employed. Thus, the reagents were changed rather than lowering the temperature. Nevertheless, the lower aliphatic aldehydes reacted too rapidly with both reagents; preliminary evidence indicates that mixtures of this type could be determined a t 0" to 5" C. Because the reaction of aldehydes and ketones with the hydroxylamine hydrochloride is an acid catalyzed reaction (S), nonlinear calibration curves might have been expected. As HC1 is produced, the individual reaction rates change [this rate dependence on p H passing through a maximum near pH 4.5 for acetone (S)]. However, Equation 4 requires only that the difference , conin rate constants, ( k s - k ~ ) be stant during the determination in order to obtain a linear calibration plot. It was also found that in the region from which the reported data was taken, the rates were almost constant; thus, it \vas decided that buffering or addition of excess HCI (4) was not necessary for these reactions. This method could be used even if the quantity ( k -~ka) is not constant as long as it is reproducible and the total carbonyl content is constant. In such cases, nonlinear calibration curves result. The method is a simple and rapid one for determining binary mixtures. This rapidity stems from the concentration of sample and the simplicity from the fact that the overall reaction is pseudo first-order. Because of the mathematical framework of the method, small rate constant ratios and small concentrations of A can be tolerated. The primary reason for this is that only a negligible fraction of the two components react; hence, A does not have to react t o completion before meaningful analytical data is accumulated as is the case in certain other kinetic methods of analysis (6). The ease of analysis is apparent from the procedure. The equipment consists of a cell which can be placed in any accessible area, a direct reading conductance meter, and a recorder. The determination is wually made by
simply injecting a t once a small quantity of the reagent into the cell which contains sample and automatically recording the change in conductance as a function of time. The exact quantity of reagent is unimportant as long as it is negligibly small compared to that of the t n o s,zml)le components. Repetitive results are obtained by injecting similar increments of reagent after the previous reaction is completed. Thus, the cell and sample need not be changed between repetitive determinations. This method is easily adaptable to automatic recording instruments of which the conductance meter employed in this paper is only the example. This adaptability to simple automation is supported by the fact that the mixing times do not interfere; thus, no special mixing apparatus is necessary. Because only a negligible quantity of A and B react, there is no appreciable accumulation of product and interference via side reactions will be at a minimum; thus, reactions which normally become complex in the latter stages will remain pseudo first-order throughout. Reactions such as stepwise addition (reduction of triple bonds) and parallel reaction of one compound (polyfunctional compounds) can be handled without limitation. Reversibility of reactions ii not a hindrance because the reactions are driven to completion by the high ratio of sample to reagent concentration. Another advantage of the conductometric method as applied to the determination of carbonyls is that interference by small amounts of acids and basic impurities can be eliminated by adding a somewhat larger amount of an appropriate buffer. Large amounts of conducting interferences will, of course, limit the sensitivity of the method. The method is not applicable to a series of samples which contain varying amounts of catalysts and in such cases one must resort to the logarithmic extrapolation method. LITERATURE CITED
(1) Blaedel, W. J., Petitjean, D. L., AXAL.CHEM.30, 1958 (1958). ( 2 ) Malmstadt, H. V., Toren, E. C.. Southeaatern and Southwestern Joint
SCS Regional Meeting, Analytical Division, S e w Orleans, 1961. (3) (%mder, A., 2. Physik. Chem. 129,
111927). (4) Reilhy, C. N.,
J. Chem. Educ. 39,
-4853 (1962). (5) Roberts, J. D., Regan, C., ANAL. CHEU.24, 360 (1952). (6) Siggia, S., Hanna, J. G., Ibid., 33, 896 (1961).
RECEIVED for review February 18, 1963. Accepted August 7, 1963. Research supported in part by National Institutes of Health Grant, RG-8349.
VOL. 35, NO. 12, NOVEMBER 1963
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