centrations, or pressures would be advantageous. The hydrogenation method is more adaptable to changes in these conditions than is the bromination procedure. LITERATURE CITED
(1) Clauson-Kaas, N., Limborg, Acta Chem. Scand. 1,884 (1947).
F.,
(2) Connor, T., Wright, G. P., Chem. SOC.6 8 , 256 (1946).
Analysis,” Vol. 3, p. 237, Interscience,
J. Am.
(3) Critchfield, F. E., ANAL. CHEM.31, 1406 (1959). (4) Hanna, J. G., Siggia, S., Ibid., 34, 547 (1962). (5) Kolthoff, I. M., Lee, T. S., Mairs, M. A,, J. Polymer Sci. 2, 199 (1947). (6) Lee, T. S., Kolthoff, I. M., Ann. N . Y . Acad. Sci. 53, 1093 (1951). (7) PolgBr, A., Jungnickel, J. L., “Organic
New York. 1956. (8) Saffer, A.,Johnson, B. L., I n d . Eng. Chem. 40, 538 (1948). (9) . . Sitzaia. S., Hanna, J. G., ANAL.CHEM. 33,@6’(1961).
RECEIVED for review September 12, 1962. Accepted December 17, 1962. Division of Analytic+ Chemistry, 142nd Meeting, ACS, Atlantic City, N. J., September 1962.
Analysis of Mixtures Using Differential Kinetics with Separation Processes SIDNEY SIGGIA, J. GORDON HANNA, and NICHOLAS M. SERENCHA O h Research Center, Olin Mathieson Chemical Corp., New Haven 4, Conn.
b Chemical kinetic considerations are applicable to separation processes for quantitatively analyzing components in unresolvable mixtures. Distillation, diffusion, and dialysis were used. Analysis by this approach i s simple and appears to be widely applicable to two-component systems. Three-component systems were successfully analyzed using dialysis.
C
ohiromwrs may be quantitatively determined in mixtures by application of chemical kinetic principles and equations to physical separation processes such as distillation, diffusion, and dialysis. I n these cases, separation of components need not be complete; in fact, the strength of this rate approach lies in making possible the analysis of systems where the components cannot be resolved by conventional separation methods. Chemical reaction kinetic equations have been accepted for many years. Their basis is the change in concentrations of the reactants with time Chemistry is the driving force causing the concentrat;ons to change. It was felt that thP kinetic expression used for chemical reactions might also apply if the cause of the change in concentration of components of a system were physical in nature. The common physical driving forces are temperature and pressure. Hence, if one takes a chemical system and imposes a temperature or pressure on it, so as to cause the amounts of the components present to change, one has a change in amount of material occurring as a function of time. Ilistillation and diffusion 11ere thus considered good candidate. for testinq the above thesis. Dial>sis was added, since it is a common separation technique where the rate considerations might be also used. The chemical mixtares to test this
approach were deliberately chosen so that none could be completely separated by the separation approach used. Hence, the change in concentration 21s. time is the element making analysis possible. The success of this rate approach means that one has the rate parameter which he can apply to systems not resolvable by conventional approaches. This has been shown to be true for resolving chemical s>stems using chemical reactions (2, 4, 5, 6). Differential rates of diffusion have been applied t o mixtures of gases based on an extension of the Maxwell diffusion equation ( I ) and on the application of Graham’s law to each component of a n effusing mixture (3). These methods do not involve the
direct application of the chemical kinetic principles as done here. What we call diffusion could also be looked upon as effusion, since a pressure differential is used on both sides of the orifice. However, t,he pressure differential is so small t h a t diffusion would appear to be the main governing principle. The true process we are observing is probably a combination of both. DISTILLATION
Apparatus. Thermostated oil bath. Vigreux distilling column, 470 mm. long. Distilling column, 470 mm. long, packed with 4-mm. glass beads. ,4 side arm connected the system t o
Table I. Analyses of Mixtures by Distillation
I.
l f i x t ~re i ii. Water
B. Acetic acid A. Formic acid R. Acetic acid 3. A. terl-Rut>-lalcohol
2.
B. Isobutyl alcohd 4. A. Isobutyl alcohol B. n-Butyl alcohol
5 . A. sec-Ruth-1 elcohol B. n-Butyl alcohol 6. A. Isoamyl alcohol
B. %-Amylalcohol 7. A. Butzraldehytle B. 2-Butanone Benzene R. Pyridine 9. A. Dioxane B. Toluene 10. A. p-Xylene B. o-Xylene 8. A.
Roiling points, C. 100
Weight yc A Found Present 18.1 9.5
18.0 10.1
8.4
9.4
14.9
15.6
0.9 1.9 16.5 66.8 90.0 12.3
1.0 1.9 16.5 66.6 88.2 13.0
17.7
17.6
12.2 16.7
10.4 18.8
22.0
22.9
11.4
10.7
17.9
20.0
118 101 118 82 107 107 118
89 118 132 138 75
so SO 115 101 111 138 144
VOL. 35, NO. 3, MARCH 1963
365
a condenser in reflux position. The side arm contained a take-off tube containing a stopcock which, when closed, allowed total reflux. Distilling flask, 250-ml. Procedure. About 100 ml. of t h e mixture, t h e total concentration of which in moles has been determined, is used as a sample. T h e temperature of t h e oil b a t h is adjusted t o 20' t o 25' C. above t h e boiling point of t h e higher boiling component of t h e mixture. The system is allowed t o come to equilibrium a t total reflux. The stopcock in the take-off tube is opened and the time is noted. Cuts are made at successive time intervals. Each cut is weighed and the total moles per cut are determined chemically or physically. The integrated first-order rate expression is : kt = 2.303 log
a--2
and a plot of log (a-z) against t yields a straight line. In this case, a is the total moles in the original sample and 5 is the moles distilled in time t . For two components distilling at different rates, two slopes are obtained. If t h e second slope is extrapolated to zero time, a t the point of intersection, y, z = al, the concentration of the faster distilling component, and log ( a
- Ul)
= y
The equation can be solved for 01. Results and Discussion. For practical purposes t h e application of the first-order rate expression describes t h e rate of distillation a t constant temperature. Plots of t h e d a t a for t h e separate distillations of benzene, toluene, and 2-propanol gave single straight lines. The results of the distillation analyses of mixtures are given in Table I. The method was first checked using mixtures of acetic acid and water. Although such a mixture can be analyzed easily by chemical means, it offered a system difficult t o separate by analytical distillation and one convenient to follow, As a result of the encouraging data obtained, other systems were analyzed. I n the case of mixtures of isomers, it was enough t o obtain the weight of each cut to know the total moles present. Cuts from the formic acid-acetic acid distillation were titrated with standard sodium hydroxide. For the benzene-pyridine and toluene-dioxane mixtures average molecular weights were used to calculate the moles in the sample and in the cuts. This practice, however, would introduce a significant error for mixtures of components with larger differences in molecular weight. The oil bath was held at a low enough temperature t o make the mechanical operations of taking and timing the cuts
366
ANALYTICAL CHEMISTRY
ume of gas is noted with the leveling bulb in position and then again at atmospheric pressure. Apparent volume is plotted against true volume. The diffusion capillary and tip are flushed nith the gas sample. The sample, approximately 50 ml., is drawn into the buret and the leveling bulb is positioned. The stopcock is turned SO that the buret connects to the diffusion capillary. The time and volume of gas are noted. The apparent volume of gas remaining in the buret is noted at successive time intervals and the true volume is obtained from the calibration curve.
[\\
\
\ . \
SLOPE
I -06, IC
20
30
t , MINUTES
Figure 1 . Distillation of mixture of isoamyl and n-amyl alcohols
practical and yet high enough to give enough points for the serond linear portions of the plots to be apparent before the distillation stopped. Distillation times for different mixtures ranged from 15 minutes to 1 hour Occasionally only a single straight line was obtained for the two-component sqstem. This indicated no resolution of the components and is analogous to the chemical reaction systems where the two components react a t rates which are too similar. I n the case of distillation, however, the situation can be remedied by adding a few plates to the column. For example, to separate the isobutyl-n-butyl alcohol and the n-butyl-sec-butyl alcohol mixtures it was necessary to pack the distilling column with glass beads. For these mixtures the use of the Vigreux column resulted in plots containing single straight lines. The Vigreux column mas used for all the other mixtures. Figure 1 is the plot obtained for the mixture of isoamyl and n-amyl alcohols.
As in the case of distillation, log is plotted against t . I n this instance, ( a - z ) represents the volume of gas remaining in the buret in time t. For two components diffusing a t different rates, two slopes are obtained. If the second slope is extrapolatpd to zero time, at the point of intersection y, z = al, the concentration of the faster difiusing gas, and (a-z)
log
(a
- al)
y
Solution of this equation for al gives the concentration by volume of the faster diffusing gas. Results and Discussion. Again, as in t h e case of distillation, t h e application of t h e first-order rate expression describes t h e rate of diffusion under the conditions described. Plots of the d a t a for single gases-nitrogen. oxygen, carbon monoxide, and 1butane-gave straight lines up t o t h e point where over 90% of the gas had escaped from the buret. Results for
Table II.
Analyses of Gas Mixtures b y Diffusion
'Mixture 8. Yitrogen B. Oxygen
DIFFUSION
Apparatus. A three-way stopcock at the t o p of a 50-ml. gas buret permitted connection of t h e buret to a sample gas source and t o a capillary diffusion tube, prepared b y sealing a fine asbestos fiber in a 4-mm. glass tubing. A leveling bulb was attached to the buret and mercury was used as the confining liquid. Procedure. T h e leveling bulb is maintained a t a constant height during t h e r u n . Its position is governed by t h e rate a t which t h e gas escapes through t h e particular capillary being used. This position is chosen such that the gas escapes a t a practically measurable rate. The level of the mercury in the bulb should be above the diffusion capillary a t the end of the operation. The buret is calibrated for volume of gas contained along its length while the leveling bulb is maintained at its prechosen height. Each apparent vol-
=
Volume 5; A Found Present 1.8 1.7 2.6 13.5 22.6 30.5
48.8
A. B. A. B. A. B. A.
B. A. B. A. B.
A. B. A.
B. A. B.
Hidrogen Sitrogen Hydrogen Oxygen Oxygen Carbon dioxide Hydrogen Helium Oxygen Brgon Hydrogen Argon Carbon monoxide Sitrogen Propene 1-Butene 1-Butene Sitrogen
79.5 4.2
2.4 10.9 23.4 29.3
50.1 i9.0 4.0
31.i
30.5
9.2
9.2
22.6
22.2
15.7
15.2
12.5
11.2
12.4
12.6
15.7
16.1
11.0
11.1
Table 111.
Analyses of Mixtures b y Dialysis
\Freight % A PresFound ent
Mixture 1. A. Potassium chloride 1 . 2 1 . 4 B. Potassium bromide 1 2 . 9 1 2 . 5 2.
8 1 . 3 81.2 A . Potassium chloride 9 . 1 10 7
B. Potassium iodide
3. A. Potassium bromide 3 1 . 3 29. -5
B. Potassium iodide
4. 50
25
75
mixture of
6.
7.
mixtures of two gases are given in Table 11. The slopes of the two portions of the curves in this case were much cloqer than in the cases of distillation and dialysis. However, the experimmtal points of the diffusion method were much more consistent, nearly all falling in a line. In general, for the inorganic gases, Graham's law of diffusion was followed, in t h a t the gas of lower molecular weight escaped a t a faster rate. HOKever, i t was possible t o analyze a mixture of carbon monoxide and nitrogen, n-hich have identical molecular weights, since carbon monoxide escaped faster. The organic gases escaped significantly faqter than the inorganic gases, although the molecular weights of the former were greater. Since the diffusion tube has a significant length, 1 to 2 mm., viscoqity of the gases. along with molecular weight. probably contributes t o their rate of escape. ;1plot of the data for the inixture of nitrogen and oxygen is shown in Figure 2. DIALYSIS
Procedure.
B. Sitric acid
-88 1
5 . A. Hydrochloric acid 17 0 16.9
1, MINU'ES
Figure 2. Diffusion of nitrogen and oxygen
A. Hydrochloric acid 24 6 2 3 . 3
-4tight k n o t is tied in
one end of 1l/s-inch-diameter cellophane dialyzer tubing. The sample, 0.02 t o 0.08 mole in 10 t o 1.5 ml. of deionized water. iq placed in the tubing along with a Teflon-coated magnetic stirring bar. A knot is then tied in the remaining olwn end of the cellophane tubing, allon inp 1 to 2 ml. of air to remain above the liquid. The tubing is placed horizontallv in a beaker containing 200 ml. of deionized n-ater and the time noted Although both ends of the tubing are immersed. Peepage through the exid* iTas not encountered. The tubing along n ith its contained solution of a is r ~ o l v e din the beaker b ~ means magnetic qtirring apparatus. I n thi. way, both the solution in the cellophane and the outqide liquid are agitated. At 5-minute intervals 2-ml. aliquots of the outside water solution are removed and the concentration of the dialyzed
8. 9. 10. 11.
12. 13.
B. Acetic acid -4. HJ drochloric acid B. Sulfuric acid A. Sodium formate B. Sodium acetate A. Sodium formate B. Sodium tartrate A. Sodium formate B. Sodium citrate A. n-Butylamine B. Isobutylamine A. n-But ylamine B. tert-But ylamine A. n-But ylamine B. see-Bu tylamine 8. Methylamine B. n-Butylamine
17.1 15.7 22.1 22 1
6.S
7.2
6.5
9.2
9.5
9.7
11.1
9.9
12.8 13.2
As in the above cases, log ( a - s ) is plotted against t, where a is the total concentration of the starting material in moles, and ;c is the moles dialyzed in time t . For two components dialyzing at different rates, two slopes are obtained. If the second slope is extrapolated to zero time, a t the point of intersection y, z = al, the concentration of the faster dialyzing component, and
- al) =
20 i , MINUTES
40
3C
Figure 3. Dialysis of mixture of potassium chloride and potassium bromide
1 4 . 3 13.7
material is determined by a n appropriate means.
log ( a
IO
y
The equation can be solved for the concentration of the faster dialyzing component. Results and Discussim. I n some cases better rnte plots were obtained b y first plotting t 1's. t, using t h e experimental d a t a . A smooth curve was drawn a n d points taken from this curye were used t o construct t h e final plot. This proccdure averages the errors in the experimental data and provides a large number of points to define clearly the straight-line portion of the final rate plot. The total moles of halide salts n a s determined hy titration with silver nitrate. The acids nere titrated n i t h standard base. The organic salts and amines were titrated with standard acid.
As in the above two cases, the firstorder rate expression can be used t o describe the rate of dialysis. Plots of the data for each of the materials listed in Table I11 gave straight lines. Results for mixtures of two components are given in Table 111. The method was used successfully for mixtures of halide salts, inorganic acids, hydrochloric and acetic acids, organic salts, and amines. A plot of the data for the mixtures of potassium chloride and potassium bromide is shown in Figure 3. Although the distillation procedure was limited to two-component systems by the mechanics of operation, and the diffusion method, by the similarity of slopes obtained, i t was possible to analyze three-component systcrns of halide salts and amines by dialysis (Table IV).
Table IV. Analyses of Three-Component Mixtures b y Dialysis
Weight yo Mixture Found Present 1. Potassium chloride 8.0 7.8 27.2 Potassium bromide 27.5 Potassium iodide 64.4 65.0 2. n-Butylamine 17.8 17.4 32.9 34.1 Isobut ylamine sec-Butj lamine 49.3 45.5
LITERATURE CITED
(I) Baxter, R. A., Beckham. L. J., J . Am. Chem. Sac., 5 5 , 3926 (1933). ( 2 ) Hanna, J. G., Siggia, S., A s . 4 ~ CHEY. . 34, 547 (1962). (3) Harris, F. E., Nash, L. K., Ibid., 22, 1502 (1850). (4) Lee, T. S., Kolthoff, I. 1 5 . j Ann. N . Y. Acad. Sei. 53, 1093 (1951). ( 5 ) Siggia, S.,Hanna, J. G., Asar,. CHEM. 33. 896 (1961). (6) Siggia, S., Hanna, J. G., Serencha, X. M., Ibid., 35, 362 (1963). >
,
RECEIVED for review September 12, 7962. Accepted December 17, 1962. VOL. 35, NO. 3, MARCH 1963
e
367
