THEDIPOLE MOMENTS OF ALKANETHIOLS
Nov., 1958
1427
THE DIPOLE MOMENTS OF AIXANETHIOLS BY S I M ~MATHIAS O AND EURICO DE CARVALHO FILHO Departamento de Quimica, Faculdade de Filosojia, Cihcias e Letras, Universidade de 8% Paulo, Sb Paulo, Brazil Received March $1, 1968
A number of alkanethiols were carefully purified and the boiling oints, refractive indices and dielectric constants were determined. The dipole moments of these compounds in benzene soKtion and in the pure liquid state at 25" were calculated. I n the last case, the equations of Debye, Onsager and Yasumi and Komooka were employed and the results compared with corresponding values in solution. The best agreement was presented by Onsager's equation. Alkanethio1s.-1-Propanethiol and l-methyl-l-propaneAccurate experimental determinations of the diwere prepared according to the method described by electric constants of pure liquids are still relatively thiol Backer and Dijkstra6 by the condensation of the cprrescarce. It is the purpose of the present paper to sponding bromides with thiourea and subsequent saponificasupply such experimental data for a number of . tion of the reaction product with a 5N sodium hydroxide alkanethiols and to interpret the results obtained solution. Ethanethiol, 1-pro anethiol, 2-propanethiol, l-butaneby applying some of the most important equations and 1-pentanettiol were purified according to the derived from current theories of dielectric polariza- thiol method described by Ellis and Reid6 by dissplving the thml tion. in a 20% sodium hydroxlde solution, extracting with a small
Experimental 1. Preparation and Purification of Substances.-The substances for the present investigation were purified by appropriate chemical or physical methods, with subsequent distillation in a fractionating column. The general procedure in the fractional distillation already has been described in a previous paper.' Semi-helices of glass were used as packing material. The substances were distilled either under atmospheric or reduced pressure and,. when desirable, under an atmosphere of dried, oxygen-free nitrogen. The purity of the substances was controlled by specific analytical tests whenever the presence of a certain impurity was suspected. The analysis of the refrartive indices of the various fractions was a valuable aid in the selection of the method of purification. It was decided to adopt as a "criterion of purity" the ebulliometric method described by Swietoslawski,a based on the difference between the boiling and condensation temperatures, as described below. This difference is reported here as A t and called the "degree of purity." With the exception of cyclohexane, 1-propanethiol and 1-methyl-I-propanethiol,all substances used in this work were commercial products supplied by Eastman Kodak Company. Cyclohexane .-The commercial product (from Schering Kahlbaum, Germany) was dried over phosphorus pentoxide for a few days and then submitted to a fractional distillation. 1.4236, b.p. 78.0' a t The middle fraction had the values TPD 701.5 mm. and the degree of purity At = 0.00 f 0.02'. The refractive indices reported by Timmermans8 are 72% 1.42366, 1.42358 and 1.42354. The boiling point, a t 701.5 mm., calculated from the tables of Stul14is 78.0". Benzene .-The product (thiophene-free) was dried over phosphorus pentoxide and submitted to several successive fractional distillations. The fractions used for the measurements had the values: n% 1.4979, b.p. 77.0' a t 696.6 mm. and the degreeof purity At = 0.00'. The refractive index agrees with the value reported by same pressure, Timmermans and the boiling point, a t calculated from the tables of Stull, is 77.1 Chlorobenzene.-After drying over phosphorus pentoxide for a few days, the substance was submitted to a fractional distillation. The middle fraction had the'refractive index This fraction n% 1.5218 and degree of urity At = 0.05 was redistilled through t i e column, after drying it again with phosphorus pentoxide, and the middle fsaction obtained showed the values: n26D 1.5218, b.p.129.0' at 704.7 mm. and degree of purity A t = 0.00". The refractive in~ and 1.52190, dices reported by Timmermans are n 2 51.52208 and the boiling point calculated from the tables of Stull is 129.4' at the same pressure.
tp.
.
(1) S. Mathias. J . A m . Chem. SOC.,72, 1897 (1950). (2) W. Swietoslawski, "Ebulliometric Measurements," Reinhold Publ. Carp., New York, N. Y.,1945. (3) J. Timmermans, "Physico-Chemical Constants of Pure Organia Compounds," Elsevier Publishing Co., h e . , New York, N. Y., 1950. (4) D. R. Stull, Ind. Enp. Chem., 89, 517 (1947).
amount of benzene, and steam distilling the alkaline solution until clear. After cooling, the solution was acidified slightly with 15% sulfuric acid, and the thiol distilled out. The product was dried over anhydrous calcium sulfate or calcium chloride and submitted to successive fractional distillations under an atmosphere of nitrogen. 2-Methyl-1-propanethiol, I-methyl-1-propanethiol and 2methyl-2-propanethiol were purified as described in a previous paper .I 1-Hexanethiol and I-heptanethiol were purified by successive fractional distillations under reduced pressure in an atmosphere of nitrogen. 2. Determination of the Boiling Point and the Degree of Purity.-The ebulliometers used in these measurements were built in our laboratory and based on the model recommended by Swietoslawski7 for the determination of the degree of purity of small amounts of liquids. With an apparatus of this type, it is possible to determine, at the same time, the boiling and the condensation temperatures with an error smaller than 0.001'. In the present case, however, these measurements were undertaken as a routine method for a criterion of purity. The thermometelds were of the Anschiitz type with a scale divided in 0.2 They were standardized carefully by comparison with a certified thermometer. With the help of a lent, it W&S possible to read to 0.04" and, in the case of differential readings,. using the same thermometer, to within OQ2". This recision was sufficient to cover the degrees of purity I to IIfof the scale proposed by Swietoslawski.* The control of overheating was done by anal zing the variation of temperature with the velocity of redlx. For every li uid there exists a range where the velocity of reflux varies &ile the temperature remains constant. Above or below that range, the temperature varies. The boiling and condensation temperatures should, therefore, correspond to equal velocities of reflux and should remain within the range where the temperature is constant with varying reflux velocity. Atmospheric pressures were measured by means of a barometer (Negretti & Zambra, London) certified by the National Physical Laboratory, Teddington, England. The pressure was checked by determining the boiling oint of pure water with a certified thermometer in the difPerential ebulliometer Pressures smaller than the atmospheric were measured with mercury manometers. All temperatures and pressures reported in this work were properly corrected. The estimatcd error in the boiling points is f 0 . 0 4 " ; in the degree of purity +0.02O; and in the pressure f0.2 mm 3. Determination of the Refractive Indices.-The refractive indices a t 25.00 f 0.05" for the sodium-D line were determined by means of a Pulfrich refractometer. The
.
.
~
.
(5) €3. J. Backer and N. D. Dijkstra, Roc. trau. chim., 61,290 (1932): H.J. Backer, M d . , 64, 215 (1935).
(0) L. M. Ellis, Jr., and E. E. Reid, J . A m . Chem. SOC.,64, 1674 (1932). (7) See ref. 2,Fig. 11, p. 19. (8) See ref. 2. p. 80.
SIMAOM A T H I ~AND S EURICO DE CARVALHO FILHO
1428
instrument was recalibrated by the method described in a previous w0rk.l I n the case of ethanethiol, 1-pentanethiol, 1-hexanethiol and 1-heptanethiol the measurements were extended to cover a number of wave lengths. 4. Determination of the Dielectric Constants.-An apparatus of high stability, based on the heterodyne beat method, was designed and built in our laboratory. Only the: general features of the outfit will be given here. A more detailed description of the apparatus will be published in the near future. A crystal oscillator, with a frequency of 999 kc. sec.-l* was connected to a variable oscillator of the Franklin type, the LC circuit of which contained the precision measuring capacitorg and the dielectric cell connected in parallel. The difference in frequency of both oscillators, coming from the mixer, was amplified through an audiofrequency amplifier and applied to the Y-axis of an oscillograph. A signal of 100 c. sec.-1, su plied by an audiofre uency oscillator, was applied to the z-axis of the oscillograp%and a Lissajous figure was used as null-point. In order to attain a high stability, the outfit was installed in a constant temperature room and a set of carefully controlled batteries used as d.c. source for the amplifier and oscilla.tors. The temperature of the room was kept around 25" to within 0.5', a circumstance which proved very favorable for the final adjustment of the temperature of the thermostat which contained the dielectric cell. All measurements were made a t 25.00 i 0.03'. The dielectric cell consisted of two concentric metal cylinders rigidly fixed by means of six small spacers of Pyrex glass. The cylinders, which had soldered platinum wires for the connections, were first nickel plated and then chrome plated. This treatment proved to be very satisfactory for the thiols studied in this work. The outer cylinder was made to shield the inner one, which was connected to the high potential. The condenser thus obtained was fitted into two concentric Pyrex glass tubes, afterwards closed a t both ends, to which were soldered capillary tubes with ground stoppers. Some of the good features of the cell were the small amount of liquid required (about 8 ml.), the small capacity of the external connections, and the possibility of a rapid attainment of a homogeneous temperature in the internal part of the cell. The measurement of the capacity of the cell with dry air had an error lower than 0.05%. This error is naturally smaller when the cell is filled with a liquid. The dielectric cell was calibrated according to the method described by Vos.10 Cyclohexane, benzene and chlorobenzene were selected as standard liquids. For the dielectric constant of these liquids at 25' the valueall 2.015, 2.274 and 5.621, remectively, were taken for the calculation of the replaceable capacity of the cell when filled with dry air. This capacity was independent of the dielectric constant in the range considered, as shown by the corresponding values obtained for the three standard liquids 80.02, 80.09 and 80.08 ppF., in the above order. The average value 80.06 ppF. was taken for the replaceable capacity of the cell. The dielectric constant E for a liquid was calculated by means of the expression E = -
c 2
- c1 + eo C
where C1 and Cz are the readings in the precision capacitor when the cell is filled with dry air and with liquid, respectively, C is the replaceable capacity of the cell, and EO the dielectric constant of dry air at 25" and 1 atmosphere. The value of EO was taken12 as 1.0005. The estimated error in the dielectric constant determinations is lower than 2 or 3 units in the third decimal place. (9) Type 722 N General Radio Company. (10) F. C. de Vos, Rec. Irau. chim., 69, 1157 (1950). (11) A. A. Maryott and E. R. Smith, "Table of Dielectric Constants of Pure Liquids," National Bureau of Standards Circular 514, Washington, 1951. (12) A. A. Maryott and F. Buckley, "Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State," National Bureau of Standards Circular 537, Washington, D. C., 1953. The value indicated in this table (e - 1 ) l O S = 536.5 d= 0.3, refers to air (dry, Cor free) at 20" and 1 atmosphere. The corrections for 25' and YO0 mm., taking into account the carbon dioxide preaent in the air, bre smaller than one unit in the fifth decimal place.
1701. 62
Results and Discussion The alkanethiols studied in the present work were obtained in a satisfactory degree of purity. According to the criterion introduced by Swietoslawski,2all substances under consideration showed a purity of degree I11 or higher, as indicated by the results joined in Table I. TABLE I SOME PHYSICAL PROPERTIES OF ALKANETHIOLS Substance Ethanethiol I-Propanethiol 2-Propanethiol 1-Butanethiol 2-Methyl-] -propanethiol 1-Methyl-1-propanethiol 2-Methyl-2-propanethiol 1-Pentanethiol 1-Hexanethiol 1-Heptanethiol
B.p. At, OC. Mm. OC. 32.9 704.1 0.02 6 5 . 3 701.5 .OO .OO 4 9 . 8 696.2 .OO 95.7 703.0
dz4
( ~ S C O ) ~€16
0.83147O 1.99615 .8359Sb 2.01936 .80895b 1.98145 .8367gb 2.03433
6.667 5.720 5.952 5.073
4 0 . 2 132.2
.02
.82880b
35.5
130.0
.05
.82456b 2.01733
5.466
61.6 122.9 149.7 174.5
699.4 697.5 698.6 696.2
.OO .02
.79426* , 83750a .83826O . 83891a
5.341 4.672 4.344 4.109
.OO .02
2.02290 4.961
1.98921 2.04546 2.04727 2.06248
L. M. Ellis, Jr., and E. E. Reid, J . Am. Chem. Soc., 54, S. Mathias, ibid., 72, 1897 (1950). 1674 (1932).
Refractive indices a t 25" for a number of wave lengths have been reported in a previous work' for the propanethiols and butanethiols. As such data for the other alkanethiols were not found in the literature, and as they are required for the determination of the refractive index extrapolated to infinite wave length in the visible region, the measurements were made and the results listed in Table 11. In the case of the sodium-D line, these results agree very closely with the values selected by Rossini, et al. l 3 TABLE I1 REFRACTIVEINDICES AT 25' OF SOME ALKANETHIOLS Wave length,
A.
Ethanethiol
1-Pentanethiol
1-Hexanethiol
1-Heptanethiol
6678 5893 5876 546 I 5016 4713 4471 4358
1.42418 1.42754 1.42759 1.43001 1.43342 1.43632 1.43915 1.44067
1.44078 1.44391 1.44395
1.44403 1.44711 1.44716
.....
.....
1.44649 1.44953 1.44959
1.44928 1.45194 1.45457
1,45342 1.45500 1.45765
1.45478 1.45734 1,45988
.....
.....
,....
.....
Table I contains also the density values used in the calculations, the square of the refractive indices extrapolated to infinite wave length, and the dielectric constants measured. l 4 As is well known, the classical Debye equation where
10is
the dipole moment, M the molecular
(13) F. D. Rossini, K. S. Pitzer, R. L. Arnett, R. M. Braun and G. C. Pimentel, "Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds," Carnegie Press, Car. negie Institute of Technology, Pittsburgh, Pennsylvania, 1953. (14) Measurements of dielectric constants of liquid alkanethiols found in the literature are: for ethanethiol at 1 5 O , 6.912 (Y.L. Wang, 2. phyeik. Chem., B46, 323 (1940)); for 1-butanethiol at 25O, 4.952, and for 1-pentanethiol at 25O. 4.547 (W. 8. Walls and C. P. Smyth, J . Chem. Phys., 1, 337 (1933)). The last two values are about 2.5% lower than the values listed in Table I.
'
THEDIPOLEMOMENTS OF ALKANETHIOLS
Nov., 1958
weight, d the density, E , the dielectric constant, n, the refractive index for an infinite wave length, k the Boltzmann constant, T the absolute temperature, and N the Avogadro number, is not applicable to polar molecules in the pure liquid state. There are, however, a few polar compounds where the dipole moment calculated by equation 1 from the dielectric constant of the pure liquid seems to agree with the value obtained from dilute solutions in non-polar solvents. This is actually the case in some aliphatic amines studied by ShiraiJ15who concludes that the reason why Debye’s formula is valid in these pure liquids is the absence of a dipolar interaction. The three compounds studied by Shirai are diethylamine, isopropylamine and triethylamine. It was thought, therefore, of interest to examine Debye’s equation in the case of the alkanethiols studied in the present work. The most important equation, however, which has been applied to polar liquids, is Onsager’s16 equation fl02
3
9kT M (E __
47rN d
- n ’ e ) ( 2 ~+ nzm) e(n2m
+ 2)’
(2)
The dipole moments of polar molecules in the liquid state calculated by this equation agree, in a general manner, with the values obtained in the gaseous state and in dilut,e solutions in non-polar solvents. There are, however, a few instances where this equation fails. This is the case for highly associated liquids. It recently was found that in the case of polar molecules where the dipole moment is changed by mechanicalinteractions, the dipole moment calculated by Onsager’s equation varies considerably with the temperature,” whereas in a number of polar compounds, as reported by Bottcher, this variation is practically negligible. The validity of the recently proposed Yasumi and Komooka equationlg has not yet been tested.
As a contributjon to this end, it seemed pertinent to apply this equation to the alkanethiols considered in this work. The dipole moments of the alkanethiols calculated by equations l, 2 and 3 are presented in Table 111. These results show that the dipole moments calculated by Debye’s equation increase with the extension of the carbon chain in the normal thiols. In the case of Onsager’s and Yasumi-Komooka’s equations the dipole moments in the normal compounds are practically independent of the length of the carbon chain. For the three equations, the isomers of propanethiol and butanethiol show a slight variation in relation to the normal compounds, in the same order as previously reported for the polarization of these compounds.20 (15) M. Shirai, Bul2. Chem. SOC.Japan, 29, 518 (1956). (16) L. Onsager, J . A m . Chem. SOC.,68, 1486 (1936). (17) J. A. A. Ketelaar and N. van Meurs, Rec. trau. chim., 16, 437 (1957). (18) C. J. F. BWtoher, Phvsica, 6, 59 (1939); “Theory of Electric Polarisetion,” Elsevier Publishing Co.,Amsterdam, 1952, p. 325. (19) M. Yasumi and H. Komooka, Bull. Chem. SOC.Japan, 29, 407 (1956). (20) 8. Mathiaa, THIEJOURNAL, S?, 344 (1953).
1429
TABLE I11 DIPOLE MOMENTS (IN D )OF ALKANETHIOLS IN THE LIQUID STATE AT 25’ Substanae
Debye
Onsager
YasumiKomooka
Ethanethiol 1-Propanethiol 2-Propanethiol I-Butanethiol 2-Methyl-1-propanethiol 1-Methyl-1-propanethiol 2-Methyl-2-propanethiol 1-Pentanethiol 1-Hexanethiol 1-Heptanethiol
1.22 1.26 1.32 1.30 1.30 1.36 1.38 1.33 1.36 1.38
1.57 1.55 1.64 1.54 1.53 1.65 1.67 1.54 1.55 1.55
1.66 1.65 1.74 1.64 1.63 1.75 1.78 1.66 1.68 1.69
Table I V summarizes the results of the measurements in benzene solution for ethanethiol at 25’. The three columns show, respectively, the weight fraction of the solute wz,the dielectric constant of the solution eI2, and the specific volume of the solution vI2. TABLE IV DIELECTRIC CONSTANT AND SPECIFIC VOLUMEOF BENZENE SOLUTIONS OF ETHANETHIOL AT 25” W2
€19
ma
0.000000 .008999 .019904 ,031860 .045856
(2.277) 2.310 2.348 2.391 2.441
(1.1446) 1.1452 1.1459 1.1466 1,1474
The corresponding data for the propanethiols and butanethiols already have been published.20 The molar polarization at infinite dilution PZwas calculated by the method of Halverstadt and Kumler.21 The electronic polarization PE was taken as equal to the molar refractivity for infinite wave length R m , and the atomic polarization PA was calculated by the expression PA = 0.027P~,based on the value determined by KuboZ2for the ethanethiol in the gaseous state. It should be remarked, however, that the value reported by Kubo for the atomic polarization of ethanethiol is wrong, and should be 0.5 cc. instead of 2.5 cc. His value is based apparently on the molar refractivity reported erroneously in the tables of Land~lt-Bornstein.~~ Table V shows the values of the polarizations and dipole moments of the alkanethiols in benzene solution at 25”. The dipole moments of some alkanethiols in benzene solution have been determined previously by a few authors. In order to compare their results with those listed in Table V, a recalculation, based on the original data published by these authors, was undertaken according to the method of Halverstadt and Kumler, by taking into account only the more dilute solutions which did satisfy the condition of linearity in the graphs of e12 vs. wa and v12 vs. w2. Thus, from the data of Hunter and (21) I. F. Halverstadt and W. D. Kumler, J . A m . Chem. Soc., 64s 2988 (1942). (22) M. Kubo, Sci. Papers Inst. Phys. Chem. Reeearch ( T o k y o ) , 29, 122 (1936). (23) Landolt-Bornstein, “Physikalisch-~hemische Tabellen,” Vol. 11, Julius Springer, Berlin, 1923, p. 974. The reported density should be 0.83907 instead of 0.8931.
NORMAN BAUERAND Jos6 A. REINOSA
1430
TABLE V MOLARPOLARIZATIONS (IN CC.) AND D I P O L E MOMENTS (IN D ) OF ALKANETHIOLS IN BENZENE SOLUT~ON Substance
PI
Ethanethiol l-Propanethiol ZPropanethiol l-Butanethiol 2-Methyl-l-propanethiol 1-Methyl-l-propanethiol 2-Methyl-Zpropanethiol
64.06 70.58 72.70 76.47
PE
PA
PO
p
18.63 0.50 44.93 1.48 23.10 .62 46.86 1.51 23.20 .63 48.87 1.55 27.63 .75 48.09 1.53
75.97 27.66
.75 47.56
1.53
78.69 27.69
.75 50.25 1.57
80.05 27.90
.75 51.40 1.59
P a r t i n g t ~ none ~ ~ calculates the value 1.48 D for ethanethiol, 1.44 D for l-propanethiol, and 1.39 D for l-butanethiol. From the data of Walls and S m ~ t hthe , ~ value ~ 1.51D is obtained for l-butanethiol. It is seen that the value determined from Hunter and Partington’s data for ethanethiol agrees with the one listed in Table V, while the (24) E. C. E. Hunter and J. R. Partington, J . Chem. Soc., 2062 (1931); 2812 (1932). (25) W. 9.Walls and C. P. Smyth, J . Chsm. Phys., 1, 337 (1933).
Vol. 62
values for l-propanethiol and l-butanethiol are somewhat lower. For this last compound the value obtained from the data of Walls and Smyth agrees with the one listed in Table V. In comparing the dipole moments of the alkanethiols determined in the liquid state (Table 111) with the results obtained in benzene solution (Table V), it is seen that, from the three equations used in the liquid state, it is Onsager’s equation which agrees the best with the values in benzene solution. Furthermore, it is the value 1.57 D determined by means of this equation for ethanethiol in the liquid state which agrees, better than in benzene solution, with the only value available in the gaseous state, 1.56 D determined by Kubo.22 In the case of the isomers of l-propanethiol and l-butanethiol, the dipole moments in benzene solution show deviations in the same order, though much less pronounced, as in the liquid state. Acknowledgment.-The authors gratefully acknowledge the financial assistance given to this Laboratory by the Rockefeller Foundation (New York) and the Conselho Nacional de Pesquisas (Rio de Janeiro).
THE VAN SLYICE REACTION BETWEEN NITROUS ACID AND PHENYLALANINE BY NORMAN BAUERAND Jos6 A. REINOSA Chemistry Department, Utah State University, Logan, Utah Received M a y 18, 1968
Rates of nitrogen evolution from the reaction of phenylalanine with nitrous acid in the pH range 2.4-2.8 were measured, using both gas volumetric and mass spectrometric techniques and making corrections for nitrous acid decomposition. None of the possible first-, second- or third-order rate expressions involving the three amino acid species and other principal ions or molecules can account for the observed dependence of rate on reactant concentrations. An analysis of the secondary salt effect for systems containing zwitterions shows that the activity coefficients for amino acid dissociation must be known before the kinetics of this Van Slyke reaction can be worked out in detail. However, the corrections for the secondary salt effect are not great enough to ex lain the variation in rate constants observed for the aim le rate law expressions. The pH dependence of secondary salt e g c t s is different, under certain conditions, depending on wfether the amino acjd catipn of the zwitterion is the reactant; this should prove useful in distinguishing alternative reaction mechanisms involvmg Zwitterions.
Although there is some information on the special behavior of amino acids in the Van Slyke reaction,2,athe rate laws are not established and no data are available for the case of phenylalanine. We find that this amino acid is particularly suitable for study because (1) the nitrogen it produces is not seriously diluted with other gases from .side reactions, in contrast to glycine2; and (2) because its reaction rate is so much greater than for simple amines that the crucial low pH range (2 to 3) may be investigated without incurring excessive corrections for nitrous acid decomp~sition.~We report here a preliminary study of the reaction, including a discussion of the particular role which the secondary salt effect plays in this case where zwitterions as well as cations and anions may be involved in the rate law. ( 1 ) Supported by Western Regional Project W-31, Utah State Agricultural Experiment Station. (2) A. T. Austin, J . C h m . Soc., 149 (1950). (3) J. C. Earl, Reaearch (London),8, 120 (1950). (4) G. J. Ewing and N. Bauer, THIBJOURNAL, 62, 1449 (1958).
Experimental The two techniques used here for measuring the gas evolution rates and correcting these for nitric oxide production have already been described.4~6 The stock reactant solutions were mixed so as to maintain a constant ionic strength (1.0) and a desired pH by adding the necessary amounts of sodium chloride and phosphate. The reaction temperature was maintained a t 30.0’.
Results and Calculations Table I presents the results of five gas volumetric runs in the pH range 2.40-2.80. The Values Tblank and ‘?‘net, where T = Tnet -k Tblank, represent the initial rates of gas evolution from the nitrous acid blank and from the Van Slyke reaction itself, respectively. The gas volume us. time curves,b whose tangents at time zero gave the Tvalues, showed a considerably greater curvature than in the corresponding reaction between methylamine and nitrous acid.4 The slope decreased by a factor of about two over a period of three hours for (5) J. A. Reinosa, Thesis, Utah State Agricultural College, 1957.
