A Physical Chemistry Laboratory Experiment R. NELSON SMITH and W. V. BOLLIGER Pomona College, Claremont, California
Tm work described in this paper was done in an effort to find a physical chemistry laboratory experiment which would illustrate the principles involved both in chemical kinetics and chemical equilibria and a t the same time utilize equipment that had not been previously used by the students. In this instance it was desired to employ a polarimeter. The traditional reaction to which this instrument is applied is the acidcatalyzed inversion of sucrose, for this reaction is rapid enough so that it goes to completion in reasonable laboratory time, shows a large change in rotation, and uses readily available chemicals. This inversion goes to completion, however, and neither the equilibrium constani nor the heat of reaction (if the experiment is performed at two temperatures) can be calculated frnm eouilihrium measurements. The fact that it is a -pseudo first-order reaction whose rate constants require little thought for calculation may, in some cases, make this experiment more elementary than desired. Most other reactions, such as the hydrolysis of methyl acetate, for which both rates and equilibria may be studied do not involve the use of new equipment. The hydrolysis of 1-menthyl formate was chosenfrom the many reactions considered for it gives a large change in rotation, is rapid, andgoes to an easily determined equilibrium position. As described in this paper, it is a second-order reaction carried out in solutions of tert-butyl alcohol and catalyzed by hydrochloric acid. Though neither the rate of hydrolysis of 1-menthyl formate nor its equilibrium constant has been determined before, the results in this paper do not represent an exhaustive study of this reaction. They include a study of the rates a t three acid concentrations a t two temperatures, and the equilibrium positions for the same conditions. dcid concentrations and temperatures were chosen which give rates convenient for student laboratory work. It was desired to observe a large change in rotation, so instead of studying the effectof changing the initial concentration of 1-menthyl formate, the largest concentration of ester in Beeping with solubility relations was used. Tertiary-butyl alcohol was used because it was found to be the most suitable solvent for appreciable quantities of reactants, products, and catalyst. The possible complications arising from formation of tert-butyl formate is negli~
~A
~~
gibly small because, in the presence of water, the hydrolysis of tert-butyl formate tends to be complete. The Matheson Co., Inc. (Paragon Fine Chemicals) has expressed its intention to list 1-menthyl formate in its forthcoming catalogue of organic chemicals. This compound has also been made in good yield at this school as a student preparation in organic laboratory by the method described below. The results obtained are discussed in relation ta studies made of other ester hydrolyses and directions for the student laboratory experiment are given. A simplified rate expression for second-order reactions going - to equilibrium is also given. GMenthvl Formate. Although other methods have been described ( I , 8) this procedure is simpler. Three hundred and forty grams of 1-menthol, 225 grams of formic acid (98-10070), and 150 ml. of toluene were put in a 2-liter round-bottomed flask and refluxed for two hours on a steam bath. This mixture was then distilled with a steam bath until the rate of distillation became slow. At this time the azeotrope of water and toluene came off a t 9&95OC. Direct heat was now applied to remove the azeotrope of water and formic acid which boils a t about 107'C. and the remaining toluene which boils a t about llO°C. The temperature then rose fairly rapidly to about 219°C. At this point, the residue was transferred to a 500-ml. distilling flask and distilled, and the distillate boiling between 219220°C. (730 mm. pressure) was retained. If dcsircd, fractional distillation under reduced pressure may be used. Yield was 8G87 per cent, D:: = 0.9329, ng = 1.4480, [a12 = -79.1. tert-Bdvl Alcohol. Eastman Kodak Co., white label #820, was used without further purification. HydrochloricAeid. Concentratedreagent-grade HC1 was mixed with distilled water to give solutions of approximately 1.5, 3, and 6 N. Polarimter. The instrument used was a Lippich half-prism type with sca'e graduatedlin 0.25' and a vernier for reading to the nearest. OiOlO. Waterjacketed polarimeter tubes, 2 decimeters long,' were used with water circulated so that tube contents were maintained at 25.00 * 0.02°C. or 35.00 * 0.05'C.
389
370
(+)
JOURNAL OF' CHEMICAL EDUCATION
The instrument was "zeroed" for each tube before comIn applying these equations to a polarimetric rate mencing a rate experiment. study, certain alterations can he made in equation 2 Preliminary Preparation. Three solutions of tert- to permit the direct use of polarimeter readings. To do butyl alcohol and aqueous HC1 were made by adding this one must express x and x, in terms of the correweighed amounts of the aqueous HC1 solutions to sponding polarimeter readings, a and a.. It was found weighed portions of tert-butyl alcohol. The ratio used experimentally that 1-menthol and Gmenthyl formate in was 1ml. of HCl solution to 9 ml. of tert-butyl alcohol. aqueous tert-butyl alcohol solutions did not obey the After mixing, weighed portions of these solutions lvere common expression used for calculation of specific titrated with standard NaOH solution. From these rotations, but t,hat, instead, [a]: Ivas given by the data the percentage by weight of tert-butyl alochol, expression water, and HC1 mere calculated for each solution. looff= Tya ["I'" - pl (5) Only slightly more than 5 ml. of Lmenthyl formate are wl miscible with 10 ml. of these solutions, and in the rati where P = per cent by weight of 1-menthol or 1-menthyl experiments it is not satisfactory to use more l-menthyl formate in the solution, a = observed rotation, 1 = formate than is represented by this volume ratio. length of tube in decimeters, W = total weight of Simple reaction flasks were made by sealing 3-cm. solution, w = weight of Gmenthol or 1-menthyl formate. lengths of 20-mm. Pyrex tubing to the inside bottoms For 1-menthyl formate in aqueous tert-hutyl alcohol of 125-ml. Erlenmeyer flasks. (9 ml. alcohol to 1 ml. water) over a range of 7.5 to Procedure. The rates and equilibria were deter- 37 per cent, [a],: = -70.0 0.1 and [a],: = -68.5 * mined as described under "Student Experiment." 0.1. For 1-menthol in the same solutions and over a Densities were determined by pycnometer and all runs range of 0.5 to 32 per cent, [a]:: = -42.9 0.1 and were made in duplicate. [a],D, = -42.4 * 0.2. When the solutions were 0.2 N in HCl, [a]:$ = -43.0 and [a],: = -42.6 for 2-menthol, CALCULATIONS and these were the values used in the calculations of The rate expression for the acid-catalyzed reaction t,hese runs. However, the effectof HC1 on the rotation 1 of 1-menthyl formate could not be determined because . 1-menthyl formate 1120 s 1-menthol + formic acid of hydrolysis; consequently the values given above for 1 aqueous alcohol solutions were used in calculations. No appreciable error is believed to be introduced in this manner. It was also shown experimentally that neither I-menthol nor 7-menthvl formate had anv effect on the specific rotation of thebther. where a = original concentration of ester, b = original Knowing the density, of the equilibrium solution concentration of mater, x = concentration of 7-menthol and assuming no change in density during the course and formic acid at time t , h a n d kz are the forward and of the reaction, one may express the moles-per-liter reverse velocity constants, and K is the equilibrium concentrations in terms of the weighed quantities and constant. Concentrations are expressed in mols per rotations, i, e,, liter. Harned and Pfanstiel (3) have integrated this equation to give a very for&dable-looking equation which can be and has been (4) used for the determination of kl. However, Equation 1 can be integrated (see Appendix) to the much simpler form
+
where A
=
2 ')).-
-
1 and zs = concentration of
I-menthol and formic acid a t equilibrium. By plotting -
log(
x
x
) versus t, lcl may be obtained from the k,
=
2.32, (slope) 2ab - (a b)z.
+
(3)
This method, over others, is recommended by Roseveare (5) for the determination of the most correct values of kl. The equilibrium constant is calculated by
where M is the mole weight and the subscripts F, M, and W refer to 1-menthyl formate, Gmenthol, and water, respectively. For a 2-decimeter tube a t 25'C., and using the ahsolnte values of rotations,
xe is calculated from Equation 9 using a,. Equation 2
is transformed by Equation 9 into t =
2.32.
k,[2ab
- (a + b)z,l
log
(A)
a
(a&b) x, - 1 and D = B \ & / - . a and b are calculated by Equations 6 and 7.
where A
=
(10)
- a.
B
- a" and
JULY. 1950 RESULTS
Observed changes in rotation varied from 14O to 16' depending on the temperature and acid concentration. Some typical plots of log
("-3 --
versus time are
shown in Figures 1 and 2. The velocity constants were calculated from these plots by Equation 3, and the equilibrium constants by Equation 4. These constants, together with equilibrium densities, are tabulated in Table 1. The dependence of these constants on the
A.
TABLE 1 Data for Hydrolysis a t 2S'C. 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Acid eoneentration, moles per litw
equdzbnum solution
0.0959 0.0960 Av. 0.0960 0.1942 0.1942 Av. 0.1942 0.3720 0.3665 Av. 0.3692
0.854 0.854 0.854 0.857 0.857 0.857 0.860 0.860 0.860
Time in minutes
Densit~,
d,, Of.
Rate constant, kr
4.18 X 4.22 X 4.20 X 8.65 x 8.75 X 8.70 X 1.81 X 1.77 X 1.79 X
Equilibrium constant,
K
0.828 0.810 0.819 0.757 0.778 0.768
lo-' lo-'
lo-'
lo-L lo-' lo-'
0 = 0.3692 N HCI. 0
10:' lo-'
0 845 0.845 0.845 0.847 0.847 0 847 0.851 0.850 0.851
9.95 X. 9.55 X 9.75 x 2.01 X 2.02 x 2.01 x 3.94 X 3.97 x 3.96 X
lo-' 10-
lo-' lo-%
lo-3
0.719 0.694 0.706 0.635 0.584 0.609
stoichipmetric acid concentration is shown in Figure 3. It will he noticed that the initial velocity of this reaction, under the conditions studied, is slower than the velocity of the major portion of the reaction. The straigbt-line plots of Figures 1 and 2 indicate that, except in the initial stage, the reaction is clearly second order. For the range of acid concentration studied, the velocity constants are given by the analytical expressions kns= 5.06 X
kas = 1.08 X
lo-" C
- 1 X lo-'
(11)
- 3.8 X
(12)
10-
3
0.0960 N HCI.
one can determine the energy of activation as a function of acid concentration. This varies from 21,600 calories per mol in 0.05 N HCl to 14,600 calories per mol in 0.4 N HCI. By substitution of the equilibrium constant values shown in Table 1 in t,he integrated form of the van't Hoff equation
B. ~-Data for Hydrolysis a t 35-C. 0.0949 0.0949 AT. 0.0949 0.1910 0.1913 Av. 0.1912 0.3675 0.3675 Av. 0.3675
= 0.1942N HCI, and 0
where C = HCI concentration in moles per liter. The equilibrium constants are sensitive to slight errors in the equilibrium polarimeter measurements and may show considerable variation under identical experimental conditions. This is evidently true of other methods also, for Griffith and Lewis show such variations as 4.55 * 0.25 for methyl acetate equilibrium constants and Harned and Pfanstiel such variations as 3.74 + 0.27 for ethyl acetate. By substitution of results obtained from Equations 11and 12 in the integrated form of the Arrhenius equation
one can determine the heat of reaction as a function of acid concentration. The heat of reaction is 1400 calories per mole over the range of acid concentration studied.
100 200 300 400 5M) 600 700 800 900 1WO 1100 Time in minutes rimrs 2.
+ :()
Data at 35'C. nottad as Lo. ran". D.termin.tion of Velocity constant.
0 = 0.3675 N
mm.
for th.
HCI, 0 = 0.1912 N HCI, and 0 = 0.0949 N HCI.
JOURNAL OF CHEMICAL EDUCATION
arid concentration, the velocity constant has a linear dependence on the stoichiometrie acid concentration. For ethyl acetate (7) the equilibrium constant is independent of the acid concentration until t,he ratio of water concentration to HC1 concentration becomes small. When the ratio is G.24, the apparent equilibrium constant is 6.35; when 5.75 the constant is 7.17; and when it is 4.61 it is 8.83. The normal value, with a large excess of water (water-acid ratio of about 380), is about 4.4. The water-acid ratio used with 1-menthyl formate varies from about 9 in the more concentrated to about 35 in the more dilute solutions. This decrease in equilibrium constant with increasing HC1 concentration at low water-acid ratios has been ascribed by Jones and Lapworth (7) to a decrease in the activity of the water by HC1, the decrease being greater the greater the relative amount of HCI present. No data were obtained for 1-menthyl formate to check the observations made by ot,hcer (3,s)that, for a given concentration of catalyzing HC1, the velocity constants increase with the initial concentration of the ester. This may be explained in terms of the generally accepted mechanism for acid-catalyzed ester hydrolysis (O),
HCI Conrentrntion in mola/liter
Fig"-3
-
Upper curves allow dependence of equilibrium constant, K, on aoid con-
centration. Lower aurves show dependenae of rate canstant8, k ~ on , aoid concentration. 0 = 2S°C. and 0 = 3S'C.
DISCUSSION
The rate-determining step is considered to be the decomposition of the ester-water-proton complex. If this is true, then it is evident that as the concentration of ester is increased relative to that of mater, the equilibrium shifts to give a higher concentration of the complex and the reaction proceeds more rapidly than mould be expected from collison freqnrncy alone.
The results for the acid-catalyzed hydrolysis of 1mcnthyl formate are pretty much in keeping with those for other esters. There are, however, certain points worthy of comment. Except for the data of Friedman and Elmore (4) for methyl acetate, there seem to be no published data which indicate that the initial rate is slower than that for the remainder of the reaction. STUDENT EXPERIMENT [These directions assume that the student will be These authors do not discuss this point or mention that their data show this, but since they too were studying provided with a tert-hntyl alcohol-water-HC1 solution hydrolysis under second-order conditions, it may be that whose weight composition is known, and react,ion flasks this phenomenon is associated r i t h low water+ster of the type described (see Experimental). The acid concentration most appropriate for a given laboratory ratios. I t seems a little surprising that the velocity constants schedule may be ascertained from Table 1 or Figures are a linear function of the stoichiometric concentration 1 and 2. This reaction could probably be run under of HCl rather than the activity of the HCI. The data first,-order conditions by greatly reducing the ester of Schreiner (6) and of Harned and Pfanstiel (3) for concentration. If this is done, however, i t will he a t ethyl acetate show that the values of ratios of the the expense of precision of measurement for the total velocity constants to acid concentrations decrease with change in rotation will also be greatly reduced.] Turn on the sodium vapor lamp. Circulate 25'C. increasing acid concentration, pass through a minimum and rise sharply a t acid concentrations above one water and 35'C. water through the jackets of two clean, normal. However, their data also show that these dry polarimeter tubes. Be sure that windows are on values are essentially constant over the range of acid M y and will not leak. Accurately weigh a clean, dry concentration of about 0.03 to 0.1 M in one ease and reaction flask, with rubber stopper. Carefully pipet 5 0.05 to 0.5 in another case. Over a limited range of ml. 1-menthyl formate into the center section of there-
JULY. 1950
373
action flask, stopper, and reweigh. Pipet 10 ml. of the tert-butyl alcohol-water-HCl solution into the outer section of the reaction flask, stopper, and reweigh. Clamp the reaction flask, being careful not to mix rractants, in the 25°C. constant-temperature bath. Similarly prepare another flask for the 35°C. bath. While the samples are coming to temperature equilibrium, observe and record the "zero point" polarimeter readings for each empty polarimeter tube, reading to the nearest 0.01". Whenever possible, polarimeter readings should be checked by making several independent observations with the !he adjustment. Remove the flask from the 25'C. bath, wipe the outside, shake the contents vigorously, and record the time of mixing. Immediately transfer the contents to a polarimeter tube and fill the tube until the liquid level is just below the constricted portion of the neck of the tube: Be wre that all air bubbles are removed from the light path and insert a rubber stopper in the constricted portion of the neck. Take a polarimeter reading as soon as convenient and then every 10 or 15 minutes, recording the time of each measurement. The time intervals may he extended to periods of one-half hour to an hour as the reaction slows donn. After the 25'C. reaction isunder way, start the 35% reaction in the same way described for 25°C. Make a careful determination of the equilibrium polarimeter readings. Equilibrium is indicated when there is no further change in polarimeter reading over s period of two or three hours, or by alloxing the reaction to stand overnight. Insert a calibrated thermometer (with a small bulb) into the solutions in order to ascertain the true temperatures of the solutions. Determine the density of each equilibrium solution for the temperature at which the rate was determined, by pycnometer or Westphal balance. From the original weights of reactants used, the composition of the tert-butyl alcohol-mater-HCl solution, equilihrium polarimeter, and density measurements, calculate (in moles per liter) the original concentrat'Ion of Z-menthyl formate and water and the equilihrium concentrations of 1-menthol, formic acid, ester, and water. For this purpose, Equations 6,7, and 8 or 9 may be used. For Gmenthylf~rmate[or]~~ = -70.0and[a1,4 = -88.5; for l-menthol, [or]: = -43.0 and [ N ] ~=~ ?-42.6. For all equations and calculations involving optical rotntions, it will be simpler to use the absolutc values rather than the trne negative values of rotation. This is permissible since all calculations involve only the ratios of rotation differences. Calculate the equilibrium constants for each temperature. Using the van't Hoff equation, calculate the heat of reaction. For each temnerature. d o t lon ,
A
- ) f D2 versus time - a*/ \a
2nd draw the hest straight line through the experimental noints. D is a constant for a eiven reaction mixture (see equation 10) and a and or, are the optical rotations respectively, For this log at tirne t and plot, if the "zero point" ~ola&eter correction is applied to the constant D,it is unnecessary to correct the observed values of or. From the slopes of these plots,
-
calculate the rate constants for each temperature. Using these rate constants, calculate the energy of activation for this reaction at the acid concentration used. Calculate the acid concentrations used. It will be noted that the acid concentrations are not identical at the two temperatures because of the change in density; this makes no appreciahle error in the activation energy. ACKNOWLEDGMENT
The authors are indebted to Professor Corwin Hansch for t,he good method of preparing Z-menthyl formate which is described in this paper. APPENDIX
In(egratio7b of Equation 1 to simplified form. Use Equation 4 to transform Equation 1 into
2
=
k,(a - a ) ( b kt(&- x)(b - x ) - -
- rc).cz
h2
(i)
I'kpand the right-hand side of Equat,ion (i), collect twms and simplify to d.c = h ( a
dl
+ b)z. - k, ah]z4 - &,(a + ~ ) x . ~+x k ~ a h '(ii) xs2
let k,nh
=
+ b) x, = n.
m; lcl(n
+
dz . .= (n - m)z2 - n x ~ z mz,9 dl %= ~~
(iii)
On elimination of m and n and after simplifying, this int,egral hecomes
C is evuluated by boundary condition of x t = 0.
If A
= (a*)xe
=
0 when
-1, then Equation (v) hecomes
LITERATURE CITED (1) TCH~.OAEFF, L., Bw., 31, 364 (1898). , A m . chi%. phys., [7];20,423 (1900). (2) R k a ~ A,, J.'Am. C l ~ m Sac., . 44, (3) HRNED, H. S., AND R. PFANSTIEL, 2193-2205 (1922). H., D., AND O. V. E r . v o ~ ~ibid., , 63, 864-867 (4) P ~ ~ e n v m ,,"A11 \La",.
(5) ROSEVE~RB, \lr.E., ibid., 53, 1651-1661 (1931). (6) SCHRCINER, E., Z. amTg. allyem. Chen~.,116,102 (1921). rm row^^. w. .r.. A. ~ ~ ' W O R T AJ. . Chem. SOL . 99.. 14271432 (1911). (8) GRIFFITH,R. O., AND W. C. M. LEWIS,ibid., 109, 67-83 (IYIOI. f, organic (g) ILEMICK, A, E,, tIElectrOnic Chemistry," 2nd ed., John Wiley and Sons, New York, 1949, p. 414. '
