THE HEAT CAPACITIES AND FREE ENERGIES OF FORMATION OF THE METHYLAMINES
Approved:
Approved:
Dean of the graduate School.
THE HEAT CAPACITIES AND FREE ENERGIES OF FORMATION OF THE METHYLAMINES
THESIS
Presented to the Faculty of the Graduate School of The University of Texas in Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
By
Frank Weldon Jessen, B.A., B.S.Ch.E., M.S.Ch.E. 400 East 43rd. St. Austin, Texas June, l933
Preface
Recent developments in refrigeration practice have been largely responsible for the great number of substances that has been proposed as suitable refrigerants. Monomethylamine has been suggested as a material which would perhaps serve as a refrigerating agent. The present investigation was prompted by the importance of establishing reliable thermal data for this compound.
The Author wishes to express his thanks to Dr.W.A.Felsing under whose direction the investigation progressed. He also wishes to express his gratitude to Mr.W.L.Benson, who helped in the preparation of the apparatae. He also expresses his appreciation to Mr. F.V.L. Patten for his cooperation with the micro gas analyses.
Table of Contents
I. General Introduction.
II. The Historical Development of Methods of Measuring Heat Capacities of Gases.
III. The Experimental Determination of the Heat Capacities and Free Energies of the Gaseous Methylamines,
IV. Discussion of Results and the Accuracy Attained.
Summary.
General Introduction The Heat Capacities and Free Energies of Formation of the Methylamines
The purpose of this investigation was the experiment a,l determination of the heat capacities and the free energies of formation of the mono- and di-methylamines as gases. The literature records no values for these quantities and since a knowledge of them is extremely important in their proposed use as 1 refrigerants, their determination was made the object of this investigation. To show adequately the necessary theoretical aspects underlying the determination and use of these thermodynamic Quantities, a somewhat historical development of these relations will be attempted.
Theoretical considerations of the atomic concept of matter were perhaps first elaborated by John Dalton in 1803. Though his concept of atoms was not new, his postulates made plausible the then known laws of chemical combination. These were (a) that the atoms of different elements were of different weight and (b) tha,t the atoms of the same element were of the same weight.
Avogadro’s hypothesis, advanced about 1805, furnished the basis for the combination of the atomic concept of matter with the kinetic theory of gases as developed by Boyle, Gay- Lussac, Berzelius, and. other; in addition, this hypothesis facilitated the determination of atomic weights and the establishment of definite combining weights of the elements, as was done by Cannizzaro.
2 The discovery by Dulong and Petit that elements in the solid state have approximately the same atomic heat capacity aided markedly in the determination of atomic weights from combining weights. This law was, incidentally, the first definite statement regarding the heat capacities of solid substances.
The development of the kinetic theory of gases gave an insight into the distribution of energy which is added to a gas. By the application of the First Law of Thermodynamics to the necessary consequences of the kinetic theory, it became evident that if the average kinetic energies of the molecules of two gases are equal the gases must be at the same temperature. Thus the temperature is a measure of the mean kinetic energy of the molecules of the gas. Since the addition of heat energy brings about an increase in temperature, the correlation of the structure of the gas and the amount of heat necessary to bring about a rise in tempera,ture must be presented in greater detail.
The specific heat is usually defined as the amount of heat necessary to "bring about a unit change in temperature per unit weight of substance. Since the time of Mayer it has been known that the heat energy added to a given amount of gas distributes itself into two portions. The first portion changes the internal energy content and hence the temperature, while the second portion is consumed in performing work against the surroundings. By maintaining the gas at a constant volume, the specific heat obtained is called the specific heat at constant volume, designated c v . Similarly, if the gas is allowed to expand against a constant external pressure when heated, the specific heat value obtained is called the specific heat at constant pressure, designated c . P Molecular heat capacities, 0- and CL, are obtained by multiv p plying the respective values of c v and c by the molecula,r P weight of the gas. Thus, from consideration of the kinetic theory previously mentioned
Cv = (4s-) (i) k / V
in which U denoted the total intrinsic energy of the gas and T the absolute temperature. Since no work is done on the surroundings (no change in volume), the heat absorbed is equal to the increase in the internal energy.
The molecular heat capacity at constant pressure may be evaluated by application of the law of conservation of energy. The heat content, H, of a system is defined by
H = U + pv (2)
where H is the heat content of the system, U is the total energy of the system, and pv is the pressure«volume product. Since the volume changes when a gas is heated at constant pressure, the heat absorbed differs from the increase in internal energy by the amount of work done upon or by the surroundings. Differentiating H = U + pv with respect to T, keeping p constant,
4 Op ( ”
Since U is independent of the pressure and the volume
M «< (s)
Assuming the ideal gas law, pv =RT, and differentiating with respect to T at constant pressure, there results
p f R (s')
This relation combined with the one above yields the important result that
c p - C v = R (7)
for one mole of ideal ga.s.
Another important relation between these two heat capacities is the ratio Cp/C v , commonly designated by V . This ratio may be determined by methods not involving calorimetric 4: measurements; two of these are the familiar Kundt and the X / 5 Clement-Desormes methods. If the value of Vis known, both
0 and C may be calculated by a combination with Equation (7). P v Also, if either or C v is known, the other may be calculated for an ideal gas by Equation (7) or by the ratio
Cp/C v = Y (8)
The classical kinetic theory of ga.ses leads to the relation
1/2 mu 2 = 3/2 kt (9)
where 1/2 mu s is the average kinetic energy per molecule and k is a constant of proportionality. Per mole of gas, the average kinetic energy is
(1/2 mu 8 ) = 3/2 RT (10) mole
The addition of heat energy to a monatomic gas at constant volume should increase only this kinetic energy of translation. Accordingly, mona,tomic gases should possess a value of C v = 3/2 R, which Drediction was brilliantly verified by the work of Kundt 6 and Warburg for mercury vapor and which has since been substantiated with other monatomic gases, such as helium, zinc vapor, and even electron gas.
In addition to the energy of translation, diatomic molecules acquire rotational energy, which fact is not true for monatomic molecules. The considerations of quantum mechanics have been applied to this rotational motion of molecules; the usual expressi for its evaluation is
TT = n(n + l)h 2 ( I;L ' u r — ' '
where I is the moment of inertia, h is Planck’s constant, and n takes the values 0,1, 2,3, for the various Quantum states. Most of the diatomic gases at room temperature have a rotational energy of RT per mole; since the increase per degree rise in temperature is, therefore, R calories, it follows that the total heat capacity at constant volume of a diatomic gas becomes
C v (dietomic gas) = 3/2 R + R = 5/2 R (12)
No statement is made regarding the heat capacities of polyatomic gases, since the various degrees of freedom, or ways in which the added heat energy distributes itself, is not known with definiteness. The problem has been attacked by numerous investigators who have attempted to correlate quantitately the heat capacities of tri- and polyatomic molecules with their structure. An extended discussion of the problem and references 7 are presented by Partington and Shilling. When real gases not conforming to the ideal gas laws are considered, it is found that the heat capacities are not constant at all temperatures but are dependent upon the temperature. Various functional relations have been proposed, but the functional form usually employed to present empirical values takes the form
C = A + BT + CT 2 (13) P
It is not amiss to present a few of the applications of an accurate knowledge of heat capacities in order to present the importance of these quantities in modern chemical problems. The quantitative estimation of free energies, entropy decreases, fugacities, etc. requires an exact knowledge of heat capacities, as will be shown in the following paragraphs.
If the increase in heat content accompanying any given change in state is known at one temperature, is it possible to calculate this quantity at any other temperature? This may be answered in the affirmative by presenting the relation, known as Kirchoff’s law:
d(iH) n = AC.dT (14) Jr
where AC is the difference between the heat capacities of the resultants and the reactants of the change in state. Thus, if the value of AO assumes the usual form
AC = a + bT + oT® (15)
Equation (14) becomes
d(AH) = (a + bT + cT s )dT Jr
AH t =AH q +aT + "b/2 T 2 + c/3 T 3 (16)
and
where is the increase in heat content at the temperature T and AH 0 is the constant of integration evaluated hy means of the value of AH at one temperature.
Increases in free energy content accompanying a given change in state are determined under isothermal conditions. However, it is often of importance to evaluate the free energy
increase attending this same change in state at a different temperature. The general second law free-energy equation
d - (17)
shows clearly how this may be done. In this equation -AF is the decrease in free energy content accompanying the change in state and the other symbols have their usual significance. If the temperature range is such that the value of AH is not constant, by making use of Equation (16), the relation becomes
d /-AF\ AH O +aT + t> 2 T® + C/3 T 3 , . 4 = —2 dT (18) It/ t s
Integrating, these results
-AF = -AH o /T +ain T + b/2 T + c/3T 2 + I
AF = AH 0 - aT In T - b/2 T® - c/6 T 3 - IT (19)
or
The integration constant, I, may be evaluated when one value of the free energy increase at a given temperature is known.
The symbol H was defined by Equation (2); whenever a system changes from an initial state to a second or final state, the change in heat content is given by the relation
Hs - H x = AH (20)
and Equation (2) may be rewritten as
AH =AU+ P AV ■ (21)
when the pressure is kept const©,nt. The ouantity -AH may he looked upon as represnnting the useful energy which becomes available when the change of state ta,kes place at constant temperature and pressure.
I 'See Felsing and Thomas, J,lnd.Eng.Chern. 21, 1269 (1929) Felsing and Wohlford, J.Am. Chern,Soo, 54, 1442-5 (1932) Ashby, Thesis, Univ, of Texas, (1931) ~ Hsia, Zeit<Tech.Physik, 12, 550 (1931) Planck’ and Vohl, Forbs,Ceb.lngenierw A. 2, 11 (1931)
and Petit, Ann.Chim,Phys. 10, 395 (1819)
3* J.R.Mayer,Ann,der Physik 42, 233 (1842)
4 'Kundt, Pogg.Ann. 187, 497 (1866); 135, 337, 527 (1868)
s'Clement-Desormes, Jour.de Phys. 89, 321, 428 (1819)
S’Kundt and Warburg, Ann.Physik (2), 157, 353 (1876)
and Shilling, The Specific Heats of Gases , Benn, London, 1924, pg. 22
Calories/degree Monatomic Diatomic c v 3/2 R 5/2 R °p 5/2 R 7/2 R
The following table presents a comparison of the heat capacities of ideal mono- and diatomic gases at 25° C.
The Historical Development of Methods of Measuring Heat Capacities of Gases
The methods for measuring heat capacity quantities are those concerned with C D , C v , and / (the ratio Cp/C v ). The methods for each quantity will be taken up, as nearly as is possible, in a separate section.
k . Methods for
The principle involved in all determinations of the heat capacity at constant pressure is naturally the same: the measurement of the heat required to raise the temperature of a given amount of gas through a definite temperature interval. The various methods proposed and used differ in many details of manipulation and construction of apparatae. However, two fundamental differences are immediately apparent. (a)The gas may be heated through a given temperature to and then passed into a calorimeter, where it shares its heat content with that of the calorimeter, leaving at the temperature Ts. This is known as the Method of Mixtures. (b)The gas may pass at a constant rate past a heater, the temperatures before and after the heater being measured differentially. This is known as the Constant Flow Method.
The Method of Mixtures was first proposed by Delaroche 8 and Berard. They passed a gas at constant pressure through a
heater, where it attained the temperature into a calorimeter at a lower temperature, where it imparted part of its heat to the calorimeter. Its temperature dropped to Ts, while that of the calorimeter was raised At degrees. The heat capacity could be calculated immediately from the indicated measurements by the relation
C p = M-At-W.E. (22) m(Ts -T]7
where m grams of gas of molecular weight M have caused a temperature rise of At degrees a calorimeter whose water equivalent is W.E. This equation neglects, of course, the corrections which must be applied for heat loss by radiation, conduction, and convection.
Improvements in this original method of Delaroche and 9 ' 10 11 Berard were made by Haycroft, by Bauermann, by Regnault, by 12 13 14 Wiedemann, by Dittenberger, and by Escher. Holborn and 15 Henning used the method for high temperature heat capacities 16 of air. McCollum modified the method by passing a cooled gas into a calorimeter equipped with heater to affect the cooling effect. In this modification the determination of the water equivalent of the calorimeter and temperature changes are eliminated. Corrections for heat loss must be made, however, as usual.
17 The Constant Flow Method was proposed by Callendar a. and is based upon the precise method of measuring small temperature differences produced when a constant flow of gas is maintained past or through an electrical heater the energy input of which is accurately known. If, with a given amount of electrical energy E«i, the difference in temperature of the gas as it leaves the calorimeter, Ts, and as it enters, Ty, is Ts - Tn, or AT, C n is given by the relation
n _ A— (23} G p - mAt
in which E«i is the electrical energy supplied; e, the heat loss to the surroundings; m, the mass of gas flowing per second; and M, the molecular weight of the gas. The quantity e is the heat loss of the calorimeter to the surrounding bath depending on the temperature difference between the two. It can be shown that this va,lue, when AT is small, is proportional 18 to AT, and the expression obtained for 0$ is
r _ (E-i. - e)M _ E-iM £ K 7 (24) °P~ ~“Eft Sit f 1 4 '
The value of K can be eliminated by a series of experiments varying m and E*i to keep a relatively constant At. 19
The method has been developed by Swann, who was the
first to use it for determining the specific heat of adr and 20 21 entensively by Scheel and Heuse. Nernst employed the method for the determination of the specific heat of ammonia.
B.Methods for Measuring 0 • *s'6" " " "’V
In 1864 Akin proposed a method for determining C v directlv; however, the method had so many faults that it has 23 been discarded. Bunsen, in 1867, determined the specific heat at constant volume by an explosion method. By this method a known volume of explosive mixture of gases is mixed in a bomb with a known volume of inert gas. When the mixture is exploded, the temperature of the gases becomes rather high. If the quantity of heat actually given to the inert gas and the temperature after the explosion are known, then the mean specific heat from the original temperature to the explosion temperature may be calculated. The temperature of explosion may be calculated from the maximum pressure observed after the explosion by use of the following relationship:
Ta/Tj *= Pa/Pj'e) (25)
where e is the ratio of the number of molecules before to that after explosion. Also, the total heat involved in the explosion is given by
AH. , , = [mC . . + NO ~ . ] AT (26) total v(r) v(i)J
where AT is the temperature rise; m, the number of molecules of products; n, the number of molecules of inert gas; C v ( r ), the heat capacity at constant volume of the reaction products; and 0 v (i), the heat capacity of the inert gases. This heat is evidently the known heat supplied by the reaction at Tj; hence
miH Ti = + nC v(l) ] AT (27)
or
AEL =Pc, . + OCC ~.~l AT (28) T v(r) v(i)J
where is the ratio n/m. If the value of is known, then the only unknown is C v ( r ). Argon is often used as the inert gas.
24 25 26 27 Vieille, Mallard and LeCha.telier, Petavel, Bone, . 1 ’,28 29 Pier, and Bjerrum have all contributed improvements and modifications of the method. The main changes proposed were those of measuring more accurately the explosion pressure, providing for better methods of ignition, and in making the corrections for 30 heat losses. Wohl, in particular, working with a bomb with enamelled walls reduced the heat losses to 0.4 per cent in determining the maximum temperature of the explosion. The explosion. method has one particular advantage, recently advanced and employed, namely that the heats of dissociation of various sub-
stances from the explosion of mixtures may be determined.
Probably the best direct method for determining 0 is that 31 « v due to Joly. His method involved the use of the steam calorimeter in which the heat capacity of the substance under investigation is determined in terms of the latent heat of steam, by measuring the amount of water condensed on its surface. The apparatus consisted of two bulbs or globes with small inverted cones of platimum as receivers for the water condensed. These were sus« pended from balance arms and suspended in a steam chamber. The lead wires from the bulbs to the receivers were surrounded by platimum resistance wire and these were heated by means of an electric current in order to prevent condensation on the wire. The masses of each bulb were adjusted so that the same quantity of steam condensed on both bulbs. Then one bulb was filled with the gas studied at known conditions of temperature and pressure, and the two bulbs were again placed in the steam chamber and equilibrium was established. Steam was admitted and the weights required for compensation of the excess of water condensed on the bulb containing the gas. The specific heat at constant volume was obtained by the relation;
C v m(T2 -T t ) = W.iH v (29)
where is specific heat at constant volume; m, the mass of the gas in the bulb; Ts, the temperature of the steam chamber; the original temperature of the gas; W, the weight of water con- densed; and AH V , the latent heat of evaporation of water at the temperature Ts. Errors in radiation and conduction may be assumed to be eliminated, although slight corrections are necessary for the thermal expansion of the globes and for the bouyancy effect.
33 33 Trautz and Grosskinsky and Trautz and Hebbel have developed a “differential” method of determining C . The method depends on the fact that a small amount of the gas in the interior of a large volume of gas is hea.ted in a very short period of time, generally about 0.2 seconds. This heating produces an adiabatic compression in the remainder of the gas, which thus the calorimeter and eliminates corrections for the calorimeter, heat equivalents, etc. Although the method appears to be dependent on numerous factors (such as the thermal conductivity, compressibility, and radiation losses), the results seem to be accurate to within about 1 oer cent. Trautz 34 and Kaufmann have further developed the method, although some criticism is still being directed against the method. It may prove still to be a popular method.
C.Methods for Determining Cp/C v
A knowledge of would allow a calculation of assuming the gas to "be ideal, as is shown in ecuation(7). A knowledge of the ratio Cp/C v , known as , would, in connection with Equation (7), allow a calculation of the values of both C a.nd of C v . Accordingly, it is of distinct value to ascertain accurately this ratio
35 One of the methods proposed is that of Kundt, based upon the velocity of sound. No calorimetric measurements need be made; however, the method does depend upon a knowledge of the equation of state of the gas investigated and upon the accurate determination of the wave length set up in the apparatus by some source of oscillation.
The velocity of an irrotational wave transmitted by a fluid is expressed by the relation
p - J k/d (e (30)
where kis the modulus of elasticity and d the density. The modulus of volume elasticity, k, is defined, of course, by the ratio of hydrostatic tension P to the dilation dv/v;
k = P/(dv) (31) V
In the case of a wave passing through a gas, the rarefactions amd condensations take place so rapidly that there is no possibility of tempera.ture equalization between the layers thus formed. Hence the expansions and contractions are adiabatic and not isothermal.
Accordingly, if dv denotes the change in volume due to an increase dp in pressure, the modulus of volume elasticity becomes
k = -J2 = -v dp (32) -dv/v
The velocity of propagation of the wave becomes
_ L vTdn (S 3 / \| D dv
By differentiating the general adiabatic expression for an ideal gas,
pv = constant (34)
there obtains the relation
+ pv^ Z = 0 dv
or
42 = - Y d.V y v'
dv ’ v (35)
Substituting this value of dp/dv in the velocity Equation (33), there results
which simplifies to
m _ ,rv / = f (36)
Thus, if two different gases are placed consecutively into a Kundt tube, there may be written, if the pressure is kept co n s t an t, —
VZ b , _ A ,= Vr and
From these relations it follows at once that
J/L = . (37) "Tx /l
where and Ms are the molecular weights of the two gases and lj_ and Is are the experimentally determined wave lengths. It is obvious that the and A< x are proportional to the wave lengths a,nd Is and that the densities, under like
conditions of temperature and pressure, are proportional to the molecular weights. If one of the gases is a standard gas, the the gas under investigation may be calculated by means of the observed quantities and Equation (37) Thus if the standard gas is air, Equation (37) becomes
y _ y Mala* V = 1.403 29.02 lx®
Experimentally, Kundt used two tubes directly connected with a sounding rod. zThus the same vibration was assured in both tubes, one of which was filled with the gas studied and. the other with air. The velocity of sound was measured by determining the wave lengths in the two tubes. These were estimated by Must figures". A fine powder such as lycopodium powder, cork dust, or finely ground silica was placed in the tubes. When the sounding rod was put into vibration, the powder would heap up at the point of one half the wave length, since the tubes were always adjusted to resonance by a movable rod from the other end. This method gave the best dust figures. The distance between the dust.figures was obtained by measurement 6 on a scale below the tubes. Kundt and Warburg determined for mercury vapor at about 300-350°0 and found it to be 1.666, 36 showing mercury vapor to be monatomic.Wftllner made some ex- periments using the method developed by Kundt with good results.
37 Martini used a vertical tube with a liquid seal instead of 38 the Kundt dust figure method. Low also used this method, 39 40 using water as the liquid. Ramsey and Niemeyer used the 41 Kundt method when working with Argon. Behn and Geiger improved the Kundt method by sealing the tube in which the gas is placed. The tube was suspended in the center and balanced. 42 The tube itself was used as a source of sound. Schßler made an improvement on the method of Behn and Geiger in that he sealed a side tube in a central position to the gas tube. Irregularities caused by unsymmetrical ends were avoided in this manner. Part-43 ington and Shilling, working with the Kundt method have shown that small quantities of moisture (.58 relative humidity) do not 44 affect the wave lengths. Grfineisen and Merkel employed a 45 method due to Thiesen to determine the velocity of sound in air and in hydrogen. The method consists of a high frequency resonator which is attached to a tube at one end of which is a very thin membrane of German silver. The tube is put in resonance and the point of maximum resonance is judged from listening through a rubber tube coming from a point near the diaphram.
46 Blackett and Rideal, working on the velocity of sound method, introduced the idea of using a platimum tube, the walls of which served as heating units. Thus for work at higher temperatures, a uniform temperature of the gas inside was obtained. 47 Kees on and Itterbeek also made some minor improvements on the Kundt method of determining Cp/C v .
An even earlier method of determining C n /C v was the > 48 adiabatic expansion method developed by Clement and Desormes. The method makes use of a large bulb or reservoir containing the gas at a pressure slightly larger than atmospheric# The container may be opened quickly by means of a large bore stopcock and as quickly closed. While the gas in the reservoir is expanding, it cools slightly; and on again reaching the bath (or room temperature) the pressure increases to a value larger than atmospheric less than the original pressure. If Vis the volume of the reservoir;Pi, the initial gas pressure (greater than atmospheric); P s , the final pressure (greater than atmospheric, but less than Pi); and p is the atmospheric pressure, then
P x =P 4 and P s = P+ p s
where and p s are small compared to P. The escaping gas does work amounting to
W = P X V - PeV =pP + Pj) -(P + p s )] V = (Pj * Ps)V
As the temperature again rises due to leakage in of heat, bringing the temperature from (T -t) to T x while the pressure changes from P to (p+p 8 ). Hence the heat input, at constant volume, is
given by
4H = Heat input = N’C v {t -(T-t)J= N*C v ’t (38)
To evaluate H, substitue its value
N = PV/RT ZIH = PV/RT’C v *t (39)
The value of t, the drop in temperature due to expansion, may be evaluated by considering the process of heating the gas from (T-t) to T for the following conditions:
P,V, + p s , V,T, PV = R = P + Pe’V
PV = T-t P + E
from which
whence
pg =-i_ P + pe
But since p s is small compared to P,
t/T! = p s /P (40)
Hence Equation (37) becomes
A H = PV/RT • PeT/p • C v
H — p®V/R • Cy
or
This ”heat input” is equal to the work of expansion; hence
W= A H (Pi “Pe)V “ pg»V>Ctr R R —»-£?, _ „ P x -Pe
But since
C P -C v C v
whence, there results
Cp/Cy = Pj/ ( -pg) (41)
This equation indicates, hence, that from the observed values of and p s , the ratio Cp/Cy may be evaluated.
49 A decided improvement was made by Lummer and Pringsheim. They employed a larger container of about 90 liters fitted with a stopcock for quickly releasing the pressure and with a delicate platimum resistance thermometer for measuring the temperature change. The ideal gas law may be rewritten to read
pv = (Cp -C V )T (42)
and
p dv + vdp = C D dt - C v dt (43) Jr
The work done by a change, in an adiabatic change as this, on the surroundings (i.e. p dv) must be equal to the loss in energy (i.e. -Cydt). Hence, it follows that
p dv = - C v dT
and, hence.
vdp = C n dT (44)
Substituting for v its value RT/p, there results
RT/p *dp = C n dt p R dp = dT gww». ..aasAw aa —PgCTWTT-iw p T -C P v dlnp= d In T C P ln = ln Ss- LY J Pl T 1
= (45) 11 Pl
or
Thus, Lummer and Pringsheim measured the temperature and pressure decrease on expansion and from these were able to calculate the ratio
50 51 52 Moody, Shields, and Adcock and Wells have contributed minor improvements in technique and form of apparatus. 53 Brinkworth’s attempt to use a smaller reservoir was not successful.
55 In 1853 Assmann devised a method for determining based on adiabatic compression and expansions. The method employed a U tube containing mercury. The gas was put into the tube, the ends closed, and the liquid made to oscillate. From the time of vibrations, the ratio of the specific heats was deduced. The method has not found favor among investigators; and, although it 56 has been tried numberous other it does not seem to yield satisfactory results.
57 Leduc has recently published a critical review of the methods and results of determination of specific heats of 58 gases. Rinke 1 has employed a rather ingenious device for determining | • A glass tube 55 cm. long and 1.6 cm. in diameter is passed through a rubber stopper into a 5-6 liter flask. A steel ball is dropped into the tube and oscillates in the tube with a period of about one second. The period of vibration is measured with a stop watch (.1 second) and C p /C v determined from the derived formula
C n 47T mV —£ =k = (46) C v qSpT 5 p= b + mg/q
where m is the mass of ball; V, the volume of bottle in cc; q, cross section of tube in square cm.; p, pressure in cm. of Hg.; T, period; g, gravitational constant; and b, barometric pressure. 59 It has been developed by Brodersen. By photographic measurements of the steel sphere the period of oscillation is obtained very accurately and the method is then supposed to attain the same degree of precision as the Kundt Must figure” method. However, the process is shown not to be quite adiabatic, but compensation for this fact is obtained with proper corrections. Recently 60 61 Andrews and Andrews and Southard have calculated the heat 62 capacity from Raman spectra measurements. Henning and Justi 15 recalculated the data of Holborn and Henning using an equation of the form _ .
where the & values are derived from the Raman spectra.
Calculation of the specific heats from band spectrum analysis using the Planck-Einstein function has also recently become of importance since it affords a means of determining values that are not so easily obtained by other direct methods. However, since these calculations are quite involved and since
the measurements required are foreign to the methods employed in the following investigation, no attempt will be made to include this method of arriving at the specific heats.
g - ■ - ' '" " """ • 11 11 ■ " — — ... Delaroche and Berard, Ann, de Ohim, 81, 98(1812); 83,106(1812)
9.Haycroft, Trans.Roy.Soo.Edin, 107 195 (1826) Ann. Chim. Phys. 26, 298, (1824) 10.Bauermann, Ann,Physik 41, 474 (1837) 11.Regnault, Mem, de VAcad. 26, 1 (1862) 12.Wi ed emann ~ Phy si k. 157, 1 (1876) 13 .Dittenberger.Forbsch der Phys. (III) 53,339 (1897) 14.Escher,Ann.Physik 42, 761 (1913) 15.Holborn and Henning,Ann. Physik 23, 809 (1907) 16.McCollum,Jour.Am.Chern,Soo. 49, 28 (1927)
17.Callender, Proc. Roy.Soc.A. 67, 266 (1900) 18. Partington and Shilling, Specific Heats of Ca,ses,Benn.London, 1924, pg. 47. 19.Swann, Proc,Roy.Soc. (A) 82, 147 (1909)
20.Scheel an d Heuse ?Ann.Physik, 37, 79 (1912); 40, 473 (1913 21.Nernst, Zeit,Electrochem. 16, 96 (1910) 22. Akin, Phil .feg. 27, 341 '(1864) 23. Buns en,Ann.Physik, 131, 161,(1867)
24.Vieille, Oompt.rend. 95, 1280(1883); 96, 116 (1883); 115, 1368 (1893) 25. Mallard, and LeChatelier, Ann.des.Mines, 4, 379(1883) Bull.Soc.Ohim.(ll) 39, 2, 98, 268 (1883) 26.Petavel, Phil.Trans.A 205, 363 (1905) 27.80ne, Phil.Trans.A 215T575 (1915) 28. Pier, Zeit.Elektrochem. 15, 537 (1909); 16, 897 (1910) 29.B.1errum,Z.Physikal Chern. 79, 513 (1912); _B7, 641 (1914) 30.W0h1, Zeit.Elektrochem. 30, 36(1924)
31.J01y, Proc.Roy.Soc. A. 45, gg(1888)TThil.Trans.A, 188,73 71891) Proc.Roy.Soc.A. 4g,440(1890); 55, 380 (18947
32.trautz and Gros ski ns ky, Ann.Physik. 67, 462 (1922) 33.Trautz and Hebbel, Ann.PWrTk, 74? 285 (1924) 34.Trautz and Kaufmann "Ann. Physik [53 5, 581-605 (1930)
35.Kundt, Poßg.Ann. 137, 457(1866); 135, 527" (1868)
6. Ibid.
36.Wfillner, Wied,Ann. 4, 321 (1878)
3^.Martini, Nuov, Cim.(ii) 137'11, (1882); (viir4, lU3.(lBft3T 38.L0w, Ann.Physik. 52, 641 (1894) 39. Ramsey, Jour♦cEem.Soc. 67, 684,(1895) 40 .Niemeyer, Diss.Halle, 41.Behn and Geiger, Verh.d.deut.phys.Ges. ,9. 657 (1907) 42.Sch81er, Ann.PhyslET 45,' 91371914) 43.Partington and Shilling, Phil. Mag. 45, 416 (1923) 44.Gr5neisen and Merkel, Ann.Physlk 66, 344 (1921) 45.Thiesen, Ann.Physik. 24, 401 (1907); 25, 506 (1908) 46.Blackett and ft ideal,” Ifature 125. 816-7“ ( 1930)
47♦Keeson and itterbeek, Proc ♦Ac ad ♦Sei ♦Amsterdam, (1930) 48♦ Clement and Desormes, 3our« de PhyFT 89 , 321, 428 (1819)
49.Lummer and Pringsheim. Wied,Ann, 64,552 (1595)
Bloody, pHys.Zeit. 13, 363 (1912) — — 51.Shields7 525 (1917) 52.Adcock anT Wells, Phil. Mag. 45, 541 (1923) 53.Brinkworth, Proc 510 (1925) 55 ♦As smann, Ann.Physik, 85, 1 (1852) 56.Mftller, Ann.Wy'sik, 16, 94 (1883) 56.Hartmann .Ann.Physik"l6, 252 (1905) 57•Leduc,Chem.^ey. 6~ 1-16 (1929) 58.Rinke1? PhysikTgT 30, 805 (1929)
F9.Brodersen, Z.Physik 62, 180-7 (1956) " 60. Andrews, J.Chem.Ed. 8, 1133-43 (1931) 61. Andrews and - Southard, Phys. Rev. 35 670-11 (1930) 62. Henning and Justi, Z. , 191-4 (1930) 15. Ibid.
The Experimental Determination of the Heat Capacities and Free Energies of the Gaseous Methylamines
The object of this investigation, as stated in the Introduction, was the experimental determination of the heat capacities and free energies of formation of the gaseous methylamines. The determination of the heat capacities will be described first, arid the determination of the free energies, from equilibrium measurements, will be described later. As stated, no data for these quantities are recorded; a single value for the heat capacity 1 of liquid methylamine at 20®C is given by Planck and Vohl.
The Heat Capacities
The Methods-The method used in this investigation was the 20 continuous flow method of Scheel and Heuse, appropriately modified* Some modifications were introduced by following some 54 55» of the recent work of Thayer and Stegman and of Thayer and Haas. The apparatus is shown in Figure 1*
The Procedure,—The procedure and manipulation employed may best be described by reference to the figure. The gas was circulated in the closed system by means of the reciprocating elevators (E) which actuated the mercury valves (V), The direction of flow of the gas stream is clearly shown by the arrows. All measurements were made without stopping the constant flow of gas. This was accomplished in the following manner: the by-pass (L) was closed by raising the mercury level, and the gas was forced to flow through the calibrated bulb (C); when the level of the mercury reached a point (X), the normal flow of gas through(C) was blocked and the gas was diverted into the space being emptied by the bulb (S). Bulb (S) containing mercury was raised by means of a hydraulic lift. This method provides a very accurate means of controlling the gas flow through the calorimeter, practically identical to the normal flow. After the definite volume of gas contained in (C) has been passed through the calorimeter, the by-pass (L) was again opened and the gas allowed to circulate through the system until the mercury level in (S) was at its normal position. The time required for the gas to flow through (C) was taken with a stopwatch, points X and X* being controlled with small electric contact points. A constant pressure was observed on the manometer (D) indicating that a uniform flow of gas was maintained through the system when taking a measurement. There was never more than 2-5 mm. variation in pressure and this variation was equalized since the pressure dropped a little at the beginning of each determination and increased slightly at the end. There was always a slight increase in pressure occasioned by the short time elapsed in lowering the level of the mercury in the by-pass (L):about one-half hour was required
to re-establish normal condition of flow. The capillary tubing and stopcocks (R) were place in the system in order to regulate the rate of flow of gas. This could also be done by merely changing the gear ratio of the reduction gear driving the elevators of the circulating system.
The Calorimeter.—The calorimeter followed the design of Scheel and Reuse. Figure 2(a) illustrates the calorimeter and Figure 2(b) gives the details of construction of the heating unit. This heating unit was made of 300 cm. of double silk covered manganin wire wound on a small glass tube. It was shellacked to insure complete insulation. The outside brass tubing (T) was machined to fit the glass tube (F) of the calorimeter, over which it was placed and fixed by means of De Khotinsky cement. Inside the brass tube was fitted a copper tube (E) with a copper gauze soldered on one end. The space between the walls of the copper tubing and the heater wire was packed with copper shreds (B). This insured adequate contact for the gas passing through the unit. The resistance of the heater unit was measured potentiometrically, using a 10 ohm standard resistance, calibrated by the U.S.Bureau of Standards, as reference and it was found to be 109.30 ohms.
The Thermoelements*—All temperature measurements were made with a 15 junction copper-nickel thermoelement constructed 56’ according to the specifications of La Mer and Robertson. Although 57* Tsutsui questions the dependability of the copper-nickel multi-
junction thermocouple, no discrepancy was found with the couple used. The thermoelement was 86 cm* in length, the ends being staggered so as to avoid undue bulking* Each terminal was encased in a very thin walled (0.15 mm. 15 cm. length seamless silver tube and further Insulated with napthalene. The thermoelement was used differentially, i.e. the "cold” junction was placed in the lower end of the calorimeter at (G), Figure 2(a), while the w hot” junction was placed well within the heater unit at (I). In this manner the difference in temperature between the incoming gas and the gas leaving the heater unit was obtained directly. This procedure was justifiable since the calibration showed a uniform temperature gradient.
A copper-constantan 10-junction thermocouple was also constructed in the above manner and calibrated.
The Calibration of the Thermocouples* — The two thermocouples were calibrated (1) at the freezing point of mercury, (2) at the freezing point of water, (3) at 25°C - .01 °C (temperature maintained in a thermostat to within •01°C as determined by a Bureau of Standards calibrated thermometer), and (4) at the transition point of Na s SO4«IOH s O (32.383°C). All electrical measurements were made using a Leeds and Northrup type K potentiometer in conjunction with a Standard Cell and a H.S. galvanometer* Table I gives the data of the dalibration and Curve I shown the calibration curve for each thermoelement*
In order to test the apparatus the heat capacity of carbon dioxide-moisture-free air was determined, a number of the determination being tabulated in Table 11. The following equation also 54 used by Thayer and Stegman was used to calculate the specific heat.
c D = -utxl (46)
where C p is the specific heat in watt sec./bm; E is the energy input; M is the mass of gass flowing per second; 4 T is the rise in temperature of the gas stream; ♦ K is the heat loss constant of the calorimeter* The current input into the heater was measured with a calibrated milliammeter.
The value of the heat loss constant K was found by considering that 0$ and K were constant at any one temperature and that E/m .A t and E/M 4 T were variable. Thus by varying the mass of gas flowing per second, adjusting the heat input to keep the temperature rise in the gas stream constant, and obtaining several such values, K was determined; K for air was found to be 0.492x10" 4 .
Sample Calculation; Temperature = 24.9 Volume of calibrated bulb C = 528.7715 cc. t = 55.6 sec. Potentiometer reading = .001617 volts Density of methylamine at O°C =1.4128 gn/L.(from unpublished data of (1 + A ) values of methylamine). M = x 1.J128 x x = e 01232 gin / gec . 1000 55.6 760 gm/sec. m — 01.617 = a 8405
Substitution of the above experimental values in Equation (24) results in the expressions.
C p = 3.05005 1 - ; 00 0 1518 -J (a) % ' 3 - 4333 [ x - C p = 3.0102 £1 - . ;M g lS5B -3 <»>
The solution of these equation yields an average value of K -4 equal .492x10 •
Specific Heat of Methylamine .--Methylamine gas was generated by the action of 40 percent KOH on C.P.mono-methylamine hydrochloride. The gas was dried over KOH pellets, redistilled twice at low temperatures (from an ice-salt mixture to a COg-ether mush), and subsequently passed into the closed system.
The specific heat was determined in the manner described above at O°C, 25°C, and 50°C. Table 111 gives a summary of the results obtained with methylamine gas. K was found to have the same value as that obtained for air.
The value of Cp, the molar heat capacity of methylamine gas, thus obtained may be expressed as a function of the temperature.
c n = 9.53 + O.IIOBT - 1.212x10 -4 T® Jr
The Heat Capacity of Dimethylamine.—Dimethylamine was produced from C.P. dimethylamine hydrochloride by the action of KOH on the solid salt. The heat capacity measurements were carried out in the same manner as for monomethylamine. The data are presented below.
These data were used to calculated the molal heat capacity relation.
C p (CH 3 ) s NH ( )= 5.595 -0.1148 T + 0.000,275T e
which may be expected to hold well over a fairly large temperature interval.
The direct determination of the heat capacity of trimethyamine was not attempted during this investigation.
The Ratio Cp/Cy for the Methylamines
The Method, —The method of this investigation for the determination of the value of Y , the ratio Ct)/C v , is the 4 60* method of Kundt, as modified by Saha, Some improvements in connection with the production of sound were developed during this investigation. The method may be described briefly as follows. A glass tube 92 cm. long and (3.5-4 cm) in diameter was fitted as shown in Figure 3. At one end of the tube a telephone receiver, connected to a high frequency vacuum tube os-61’ cillator, served as a source of sound. This receiver was placed inside a special machined brass fitting. Special graphitic packing was employed to secure a tight joint between the tube and the coupling enclosing the telephone receiver (R), The other end of the tube was also fitted with machined brass points and couplings. A rod (L) of glass to which a cork disc (C) was attached served to vary the length of the vibrating column of gas. A tight joint was made in the latter case in the same manner cited above. The whole tube and special ends were placed in a trough-like thermostat.
The oscillator was made to vibrate at a definite frequency and the nodal lengths of the vibration were determined by moving the adjustable rod, the various lengths being read direct from a meter stick placed alongside the tube. Values for the half wave lengths were first obtained for air (COg and moisture free), and then the values for the particular gases under investigation were determined. By means of Equation (37),
f = 0.04834 M l s Ao
the ratio C /C v was immediately calculable; in this formula the nodal lengths are substitued, since the nodal lengths are 1/2 the wave lengths.
The apparatus was filled with dry, carbon dioxide free air, the sound frequency set, and the nodal lengths determined# The air was then removed and the apparatus filled with the particular amine; the nodal length was then measured for this gas. The appropriate air calibration is Ifsted,hence, with the particular amine; these are given in the following tables#
Grand Average 1/2 A = 11.49 cm.
Grand Average 1/2 A = 10.28 cm. Fro From the value of l 0 = 2(11.4^cm and 1 » 2(10.28) cm, the value of Cp/Cv was calculated to Joe
, I Y for CH 3 NH S = 1.2020
Grand Average 1/2 A = 11.17 cm
Grand Average 1/2/\ = B.llcm.
Grand Average 1/2 A =7.19 cm.
From the data of this table, the values of } for dimethylamine and trimethylamine gas were calculated; these values are
y for (CH3) s NH = 1.149 Y for (CH 3 ) 3 N = 1.184
As an incidental determination 9 the value of Y for ethylamine, CgHgNHe, was determined in the same apparatus. The value for 1/2 A for air was that determined for the determination of y for the di- and trimethylamines, as given in Table VI.
Grand Average 1/2 A = B*o7 cm
From these data, the value of / for monoethylamine was calculated to be
Y for C e H S NH s = 1*135
The value for all the amines investigated are tabulated in the
the accompanying tabled
The Free Energies of Formation of the Amines
The free energy decrease attending a given change in state may be determined in several ways* These are, respectively:
l.By the determination of the equilibrium constant, K, in a ’’reversible*’ reaction and the calculation of the free energy decrease by means of the relation
- A F = RT In K
2.8 y the measurement of the reversible electromotive force, E, of a voltaic cell, the change of state of which is the desired change in state* In such a case
-Z) F = ENF
3*By the determination of the heat capacities down to very low temperatures and the use of these data with other thermal data to calculate -Z)F by means of the third law of thermodynamics.
+ t /OS,
4* By the proper combination of suitable reactions for which the change in free energy is known,
The first of these methods which was used to determine a free energy decrease of a certain reaction, which combined with other free energy equations, as indicated by the fourth method, led to the desired free energy decrease attending the formation of the mono- and dimethyl amines. The equilibrium constant for the thermal dissociation of these amines led to the free energy decrease attending these dissociations.
The Thermal Dissociation of Mono-Met hyl amine.-- Some evidence for the dissociation of monomethylamine at higher temperatures to form hydrogen cyanide was noticed, since a distinct odor was observed when heating glass tubing which had been in 62’ contact with the gas. Muller cites a variety of products formed when methylamine is passed through a tube at temperatures varying between 1240°C and 1320°C. Among the gaseous products given by him were NH 3 , 1.5-1. HCN, N s , C, H s and CH<, There was no C s H4,C e Hg,CgH$. The time of passage 63 of the gas was 24-»76 minutes. H.G.Denham found that the reduction of HCN with hydrogen gas to form methylamine, according to the reaction + —followed the course of a unimolecular reaction in dilute solution. The results indicate clearly that the reaction
HCN + 2H S
is reversible* However, no equilibrium data exist; neither are the results obtained indicative of the primary reaction products.
In order to obtain the equilibrium constant for the dissociation of methylamine, the gas was heated in a Pyrex tube of 600 cc capacity at a constant rate in an electrically controlled furnace. The pressure was measured at various intervals by means of an absolute monometer read by means of a cathetometer. The temperature was determined by means of a calibrated Ptrhodium thermocouple, the voltage being measured on a Leeds and Northrup Type K potentiometer.
Only a very small volume (1 or 2 drops) of a light brown colored liquid was obtained. The liquid was readily soluble in water. When acidified with S0 8 and subsequently titrated with 64 silver nitrate solution according to the method of Vorlander, it was found to contain a small quantity of dicyanogen.
Samples of the gas were obtained after each run by allowing the gases to expand into an evacuated gas pipette of approximately 200 cc capacity. The tip of the pipette was immersed in a solution of slightly acidified silver nitrate and the stopcock of the gas sampling pipette opened. A white precipitate indicating the presence of cyanide was obtained. The residual gas was passed into a smaller pipette. The precipitate obtained was dissolved with KCN solution to confirm the presence of HCN; the AgCN was subsequently determined quantitatively. The filtrate from the original precipitate was treated with the modi-65 fied Hessler reagent of Francois. No ammonia was found. The residual gas was analyzed by combustion methods, first, in a Burrell Gas apparatus and later in a special micro gas analysis 66 apparatus described by Mr .J. S. Swearingen of this laboratory.
The gases thus analyzed contained approximately 88% He, 10-12% CH4, no nor nor C s Hr# o
The fraction dissociated was calculated from the pressure measurements at the different temperatures by means of the relation
p obs * = 1+ 2x ( 47)
where x is the fraction of the amine dissociated on the assumption that the reaction of dissociation is solely that of the reaction
OH 3 NHeZ±HCM ♦ 2H S
and that the actual presence of other products, present in only small quantities, is indicative of secondary reactions# The term P ca x C signifies that pressure which would be exerted within the reaction vessel if the amine had not dissociated; it was calculated by means of Charles 1 law.
From the calculated fractions dissociated, the values of the dissociation constant at equilibrium could be calculated by the relation
K = (U • (p t )S < 4B >
where x is the fraction dissociated and the observed total pressure# This relation is merely the equilibrium constant of the reaction
K = ■ P HCN* P H S (49 ) p ch 3 nh s
expressed in terms of the fraction dissociated and the total observed pressure, The data of the investigation are presented tabularly below.
original pressure was 144♦83mm# at 307>5°K; in the other measurements the original pressure was 155.26 mm. at 306.6°K).
From these values of K, the free energy decrease attending the reaction at each temperature was claculated by the usual relation
-/IF = RT In K T (°K) K -/)F 614 6.240x10”® -14,624 cals -5 686 1.078x10 -12,017 cals 765 1,796x10"® - 9,611 cals 800 4,338x10"® - 8,649 cals
The Free Energy of Formation of CH ? NH g »<--The heat of combustion of gaseous methylamine was taken to be 259,000 cals/mole.
67 This value is a weighted mean of three values; Muller cites a 68 value of 261,400 cals./mole; Lemoult gives a value of 258,100 69 cals/mole; and Swietoslawski and Popov cites a value of 256,100 cals/mole for the combustion of liquid methylamine, which combined with the latent heat of vaproization of -6200 1 cals., as determined by the relation of Felsing and Thomas for 25°C., makes a value of 262,300 cals.
i +4 1/2 Og, % — 2COg/ % 4 SHgO,«. 518,000 cals« The heat of combustion of graphitic carbon to form
gaseous carbon dioxide is 494,240 cals/mole, a value due to 70 Roth and Naeser.
C (graphite) + ° s (g) " COs (g) * 94,240 cals ‘
The heat of formation of liquid water of 68310 cals, is 71 due to Rossini.
H s , , + 1/2 O e , . = H s o,,. + 68310 cals. (g) (g) (1)
The heat of combustion of gaseous hydrogen cyanide is 72 taken as 159,700 cals., as determined by Berthelot
+ sc(g)$ c (g) = ® + 2ss®(g) + s®(g) + 319,400 cals. From these data, the heat of formation of CHgNHg at
25°C may be calculated as follows:
®298 s £CH$NHe(g)+ 4 1/2 *= 518,000cals, 2(J H) + (0) = 2(-94,240) + 5(-68310) + (0) + 518,000cals. ZIH 2QB CH 3 NH s(g) = -6015 cals. = -6000 cals. (50)
Likewise the heat of formation of hydrogen cyanide is calculated by the following procedure.
E (g)~ + s (g)* 5 (g)*319,400 cals. 2(21//) + (0) = -68310 4 2(-94240) + (0) + 319,400 cals zIHg 9B HC:: g — +31,305 cals. • 31,300 cals. (51)
In both the combustion of and HCN, it was assumed that the combined nitrogen burned to elementary nitrogen during com- 73 bustion. This is according to the findings of Lochte and Wilde, who could detect only the most minute quantities of combined nitrogen among the products of the combustion bomb.
The heat of dissociation of CH 3 NH S at 25°C may be calculated immediately from the above data:
H 29 8: CH 3 NH e(g)^HCN(g) + 2H S(g) + (-6000) = (31,300) + (0) + -AH = +37 . 300 cals ’ < 5B)
This heat of dissociation has been calculated for 298°K; the equilibrium data, however, are known only at higher tempera tures (i.e. 614°K and up). Hence the heat of the dissociation must be calculated for these higher temperature; use is made of heat capacity data and Kirchhoff 1 s law
H) = Z 1 c*dT ,
which has been discussed before.
CH 3 NH B | )+ 2H E ( g )- 37,300 cals, at 298°K d(zJH) = = f(C pHCN + 2C pHs ) -C p CH 3 NH s 3 dT = 12.28 -0.1109 T + 0.000,123,42T® dT (53)
To arrive at the above value of 4 c, the following heat capacity data were employed;
C n H s = 6.50 + o*ooo9 T P C p HCN = B*Bl - o*ool9 T + 0.000,002,22 T s C p CH 3 NH2 = 9.53 + O.IIOBT - 0.000,121,20 T s
The heat capacity relation for hydrogen is that suggested by 74 Lewis and Randall; the equation for HCN is that of water vapor; it is assumed that HCN would behave like the triatomic water molecule; and the relation for monomethylamine is that of this investigation.
Integrating Equation (53) above, there results
AH- = Z>H O + 12.28 T - 0.05545T® + 0.000,041,14T 3 (54)
where AH o is the constant of integration. The value of AH o can be determined by substituting for A its value of +37,300 cals, at 298°K, and solving. The relation becomes
= 37,478 + 12.28 T - 0.05545T® + 0.000,041,14T 3 (55)
which may be used to calculate the heat change accompaning the dissociation at any temperature of the range over which the heat capacity data are applicable. In order to be able to evaluate the free energy decrease attending the dissociation at any temperature, use is made of
the general second law free-energy equation
d(-Z>F/T) = Z3H/T® dt (56)
Substituting the value of A H of Equation in this relation, there obtains
- 37,478 4 12.28 T - 0.05545T® + 0.000,041,14T 3 T V —— * (57)
which, on integrating, yields the relation
-^P T = -37,478 + 12.28 T In T - 0.05545T® + 0.000,020,57T 3 + IT (58)
where I is the constant of integration*
To evaluate I, use is made of the values of calculated from the equilibrium constant data for 614°, 765°, and 800°C. The values give the following values of I:
I - -14.62, using -z!Fgj4 = -14.74, using -zJF?6S = -14.87, using -Z)F 800
The mean of these values is -14.74. The general free energy relation, hence, becomes
-^F T = -37,478 + 12.28 T In T - 0.05545T® + 0.000,020,57T 3 -14.74 T. (59)
The following tabular view shows the comparison of the calculated and observed values of the free energy decrease; the calculated value at 298°K is included for the sake of completeness.
Table XI Comparison of Calculated and Observed- Free Energy Values
Thus, the following free energy equation at 25°0 may be written
F 29 8: CH 3 NH^ g) = 2Hs (g)“ 25 ’ 403 cals * 74
Lewis and Randall state A Fggg for to be 28910 cals., combining this with the above free energy equation, there results
FoaaS CH NH E/ . = HCN, .+ 2H S , . - 25,403 cals. 3 K (g) (g) (.4 P) = (28910) + (0) - 25,403 cals. af 298 ~ +3507 cals., (61)
or, in equation form
P 298: c (g pa P h ) * K S( g ) + 2 VS CHSNHg -3507ca15. (62) 62»
The Thermal Dissociation of Dimethyl amine • — Muller studied the decomposition of dimethylamine at 1200°G and obtained the following products: HON, NH3, N s , 0, H s , CH<, C S H 4 , C e H s , and C 6 H 6 , 75 Recently Taylor has shown the decomposition of dimethylamine
to be a homogeneous unimolecular reaction between 480°C-510°C* Various products were obtained depending on the experimental conditions* The thermal dissociation of dimethylamine gas was followed in exactly the same manner as that of monomethylamine, except that a quartz reaction vessel was used instead of a Pyrex one* The dissociation follows the relation
(CH 3 ) s ♦ GH 4 * H s
as was evidenced by the analyses of the gases at equilibrium. A slight amount of secondary products was produced, as in the case of monomethylamine, but in the main the products agreed with those indicated by the equation. Again the relation
Fobs* - 1 + 2x p calc
gives the fraction,x, dissociated, and the equilibrium constant
K = P HCM> p CHr P H g (63 ) P (CH 3 ) e NH
may be expressed in terms of the fraction dissociated by
K _ (x.P t )(x.P t )(x.P t ) = t , (64) (1-x)
The following tabular view presents the data obtained in this investigation.
(The original pressure was 171.82 mm at 298°K for the values marked with an asterik; for the other two the original pressure was 183.90 mm at 298.5®K.).
From the values of K, the decrease in free energy decreases attending this decomposition at the various temperatures may be calculated. These are given below in the Table XIII •
The Free Energy of Formation of DimethylamineThe calculations for the free energy of formation of dimethylamine followed those of monomethylamine exactly and will not be repeated* The data used, in addition to those already described for mono ethylamine are given below*
l.Heat of Combustion of Dimethylamine (g) = 422,000ca15. at 298°K«
2.Heat of formation of Methane (g) = 18,070 cals, at 298°K 3.C CH 4 (g) = 3.00 + 0.0228 T - 0.000,004,80T s 4 * c (CH*) e NH $ 5.595 -0.1148 T + 0.000,275T®
The value for the heat of combustion of dimethylamine gas is that given by I*C.T*; the heat of formation of methane is 76 that due to Rossini; the heat capacity relation for gaseous CH< 77 is due to Randall and Gerard; and the heat capacity data for dimethylamine is that of this investigation*
The following important relations were obtained:
Hpqo * (CHrz) sNH/_\ = HCN + CHa, . + Hs. . 0 (g) (g) ( g ) “(g) T AE = 22,511 + 12.715 T + 0.0683 T® - 0.000,092,53T® (65)
P 29B S < CH S = HCN (g) + CH 4(g) + H s(g) -AF t ZF t _ 22,511- 12.715 T In T - 0.0683T® + 0.000,046,26T 3 + 94.00 T (66)
Using this last equation the values of the free energy decrease attending the thermal decomposition of the dimethylamine at the various experimental temperatures and at 298°K were calculated. These are given in the following table.
The following free energy equation at 25°0 may now be written:
P 29B s (CH 3 ) s NH (g) = HCN (g) + CH 4(g) + H e(g) - 24,092 cals. (67)
Using the free energy content of HCN (g) as before and using the free energy content of CH* (g) at 298°K to be that 78 given Parks and Huffman as -12,200 cals., the equation may now be written
f 29Bj (CH ; ) E NH (g) = HCN (g) + CH< (g) + H S(g) - 24,092 cals. (^ p 29B> = (28910) + (-12,200) + (0) - 24,092 A F g9B (CH 3 ) s NH (g) = -7,382 cals., (68)
or, in equation form.
F 2C(graph) + 1/2 v + 3 1/2 He , = (CH ) e NH + 7,382 cals. 298: * (g) (g) 3 (69)
irrbid
20. Ibid
54. Thayer and Stegman, J,Phys,Chem, 35, 1504 (1931) 55. Thayer and Haas, J.Phys.Chem. 36, T 127 (1932)
20. Ib id ~ “ 56»Robertson and La Mer, J. Phys* Chern. 35, 1953(1931) 57*.Tsutsui, Tokyo Scientific Papers, Institute of Physical Chemical Research, 11, 93 ——
58’.Grueisen and Merkel, Aim.Physik (4), 72, 193 (1923) 59’.Hebb, Trans.Roy.Soc.Canada 13, (3), IUT, (1919) 54. Ibid
51. Ibid 54. Ibid
——“——— 60’. Saha, Indian Jour,Phys. 6, 445 (1931) 61 .Grace Mdfather, *lll6sTs, Univ,of Texas (1929)
'('2), ’45," 439 (1886) 65.H.G.Denham, Z.physlk.Chern 641-94 (1910)
64.Vorander, Ber. 44, 2455 (1911) 65. Francois, Compt.rend. 44, 567-9 (1907) * * J»Pharm.Chim.(67), 25, 517-22 (1907) 66.Swearingen, Thesis (Ph.D.)\ Univ, of Texas (1933)
68 .TO, 403 (1907) 69.Swietoslawskl and Popov, J.Chern.Phys. 22, 395 (1925) 70. Roth and Naeser,Z.Elektrochem, 3l 461 71•Rossini, B•S•J♦Research 3, 34 (1931) 72.BerthelotAnn.OEImTphys.(5), 23, 243,252 (1881)
74♦ Lewis and Randall, Thermodynamics,McGraw Hill Book do. N.Y.,1924 pg. 800
74. Ibid, p. 590 ~ lbid 75. Taylor, J.Phys.Chem. 36,1960 (1932)
76♦Rossini.B.S.J.Research 6,49 (1931) 77. Randall Eng. Chern ♦ 20, 1335 (1928)
Figure 1
Figure 2
Figure 2b
Table III The Specific Heat of Air
Figure 3.
Cu-Ni Cu-Const Hot. Junction Cold June. Microvolts/°C Volts Volts Cu-Ni Cu-Const. 0.012880 0.005135 Ice Freezing pt. of Hg. -38.88°Gt.05° 331.6 132.1 0 0 Ice Ice — — — 0.008148 0.003220 25°ci .01 Ice 326 128.9 0.011090 0.004270 Transition pt. Na s S0 4 .10H s 0 32.383°C Ice Average 342.6 334.06 131.2 130.73
Table I Calibration of Thermoelements
Data foi ■ three experimental values for calculation oi (1) P = 741.04 (2) p = 741.04 (3) p = 740.63 T = 24.9°C T = 25.1®C T = 24.9°C T = 4.8405°C T = 4.8175°C T = 4.8405°C E = 0.18192 E = .18192 E = .18192 M = .01232 M = .01093 M = .01248 M S = .0001518 M s = .0001195 M s = .0001558
C n at 25°C Method Investigator 20 6.965 Continuous flow Scheel and Heuse 58» 6.936 Velocity of sound Grilneisen and Merkel 59’ 6.952 Velocity of sound Hebb
The value of Cp thus obtained agrees with some of the more recent determinations given by the following investigators.
C at 25°C Method Investigator 1 1 Bi 6.947 Adiabatic expansion Shields 54 6.945 Continuous flow Thayer and Stegmann 6.970 Continuous flow Author ♦s
T o°c As 5.3550 5*4862 5.5788 M 0.01280 0.01249 0.01271 E 0.15780 K C P watt sec/ gm cal/mol 0.492x10" 4 1.6110 1.5770 1.5462 av. 11.97 11.72 11.48 11.72 5.4876 0.01232 1.7485 12.98 5.3255 0.01093 0.17500 0.492xl0“4 1.7700 13.14 5.6402 0.01248 1.6992 av. 12.62 12.91
Table III The Heat Capacity of Monomethylamine Gas
T 4_t M E K C p watt sec/gm cal/mol 5.4720 0.01049 1.8528 13.76 50°C 4.8815 0.00936 0.19264 1.8450 13.69 5.3785 0.01248 1.8760 av 13.92 .13.79
T ’ T M E K Op re: i ( W C) Watt-sec '/gm. Cal./mol. 10 4.3430 0.01440 0.11920 4.71X10" 5 1.4685 15.802 12 4.3350 0.01413 0.11920 4.71x10" 5 1.4850 15.975 25 4.5620 0.01634 0.14175 n 1.5670 16.870 25 4.5784 0.01705 0.14175 w 1.5225 16.380 40 4.8355 0.01241 0.14175 n 1.6750 18.030 50 4.9986 0.01324 0.15780 n 1.7450 18.770 50 4.9942 0.01378 0.15780 n 1.7230 18.550
Table IV The Heat Capacity of Dimethylamine Gas
A.Calibration with Air (dry and C0 s free). T = 26 e C T = 24.5°C T = 26.3°C p = 747.60mm p = 747.57mm p = 746.21mm = 11.60 cm = 11.65 cm /J = 11.50cm = 11.70 = 11.25 = 11.45 = 11.65 = 11.35 = 11.30 = 11.60 = 11.50 = 11.35 = 11.50 = 11.60 = 11.25 = 11.70 = 11.50 Av. 11.62 Av. 11.48 A-v '. 11.37
Table V The Determination of Y for Monomethylamine
B♦Experimental Data for CH ? BH g I = 25°C T = 26°0 T = 26°C p = 744.78mm p = 744.78mm p = 744.38mm 4A= 10.25 cm = 10.35 cm /A= 10.20 cm 10 <30 10.20 10.10 10.50 10.30 10.20 10.40 10.20 10.10 10.55 10.20 10.20 10.42 10.30 10.20 Av. 10.41 Av. 10.27 Av.10.17
A.Calibration with Air (dry and C0 e free) T = 26°C T = 24.5°C T = 26.5°C p = 747.60 mm p = 747.57mm p = 746.21mm = 11.40 cm /A = 11.2 cm A = 11.3 cm 11.25 11.8 11.1 11.15 11.0 11.4 11.30 11.2 11.1 11.20 10.95 11.0 11.25 11.05 11.1 Av.11.31 Av.11.03 Av.11.16
Table VI The Determination of Y for Dimethylamine and Trimethylamine Gases.
B.Experimental Data for T = 27°C T = 26.5°C T = 27°C p = 748,55mm p = 748.55mm p = 748o05mm %/{ = 8,04 cm = 8.25 cm = 8.04 cm 8.3 8.6 8.0 8.1 8.1 7.9 8.0 8.2 7.7 8.1 8.2 8.1 8.0 8.0 8.0 7.9 8.4 8.2 8.0 8.2 7.9 8.2 Av. 8.04 Av.8.25 Av. 8.04
C.Experimentai Data for (CH ? ) ? H C = 26°C T= 26°C T = 25°C p = 744.10 mm p = 744.10 mm p = 744.00 mm = 7.30 cm XA = 7.1 cm O = 7.46 cm 7.3 7.1 6.83 7.3 7.1 7.43 7.1 7.2 7.46 7.1 7.05 7.46 7.15 7.05 7.43 7.30 7.1 6.83 7.1 6.83 AV. 7.22 av.7.10 Av ’. 7.24
T = 25°C T = 25°C T = 25°C p = 752.3mm p = 756.36 mm p = 751.52 mm O = 7.85 cm A = 8.2 cm £A = 7.9 cm 8.05 8.1 7.8 8.15 8.2 8.0 8.15 8.3 8.1 8.00 8.3 8.0 7.90 8.1 7.9 8.00 8.3 8.2 AV.8.01 Av. 8.2 8.1 Av. 8.00
Table VII The Determination of for Monoethylamine
Amine \ / Temperature (°C) 26° (CH 3 ) e NH 27° 1*149 (ch 3 ) 3 n 26® 1*184 c s h 5 nh s 25® 1*135
Title VIII.
C4H4 Sa CH 4 Total 88< 10# 98.0< 0 83.-5 ' 99.4# 0 85< 12# 0
Table IX Analysis of Residual Gases of Decomposition of CH3NHe
Temperature % Dissoc. Pressures (mm) K °K lOOx Obs. Calc. (calculated by Eq.48 614 2.082 319.67 306.90 6.240x10" 6 686 2.550 374.00 364.70 1.078x10"$ 765 5.450 429.75 387.50 -3 1.796x10 So 0 16.040 471.71 357.20% —3 4.338x10
Table X The Thermal Dissociation of Monomethylamine
Temperature »4f=RT In K - dp(calc. by 0bs.(in cals) Eq. (59) (cals) 298° ------ -25,403 614 -14,697 -14,624 686 f -12,017 765 - 9,611 - 9,611 800 - 8,545 - 8,649
Temperature pressures(mm) K (lOOx) Obs. Calc. (calculated by Eq.(64) 744 6.30 525.92 458.36 -4 1.1275x10 794 11.30 592.16 457.79# 6.583x10" 4
Table XII The Thermal Dissociation of Dimethylamine Gas
Temperature % Diss. Pressures(mm) K (lOOx) 66s. Calc. (calc, by Eq.(64)) 811 17.70 777.96 499.64 3.610x10" 5 826 17,90' 741.96 476.24« 3.814xl0" 3 841 19.85 805.75 484.89* 5.620x10" 3
T°K K -4F =RT In K 744 »4 1.1275x10 -13,440 cals. 794 -11,525 " 811 -3 3.610x10 - 9,060 " 826 3.814X10 -3 - 9,140 " 841 5.620x10 ° - 8,658 "
Table XIII The Free Energy Decrease Attending the Thermal Dissociation of Dimethylamine
Dissociation of Dimethyl amine Temperature "k 7 =HT In K - F( calc • by (Ots.) in cals. in cals 298 009 ® /Cy i | W <7 744 -13,440 -10,611
Table XIV The Free Energy Decrease Attending the Thermal
Temperature -4P = RT In K -ZF (calc, by fe K (Obs.) in cals* Eq. (64) in cals. 794 -11,525 -9,796 811 - 9,060 -9,401 826 - 9,140 -9,031 841 - 8,658 -8,721
Discussion of Results and the Accuracy Attained
This experimental investigation has yielded the following results:
** JTV I.C CH 3 NH e(g) = 9.530 + O.IIOBT - 1.212x10 T®
2.C (CH )«NH ,= 5.595 -0.1148 T + 2.750x10” 4 T® P 3 Tg)
3.C p /C = Y for CH 3 NH S = 1.202 at 26°C for (CH 3 ) b NH = 1.149 at 27°C for (CH,),N = 1.184 at 26°C o o for C S H S NH S = 1.135 at 25°C
4. e9B CH 3 NH B( } = +3507 cals.
5. <£lF Q (CH,) S NH. = -7,382 cals. 298 3 (g)
The values attained in the determinations of heat capacity of the gaseous mono- and dimethylamine are considered accurate to within 0.5 per cent. In making this estimate, the accuracy of the temperature measurements and the exactness of determining the heat energy imparted to the gas stream while in the heater unit was thoroughly considered. The temperature rise was measured differentially by means of a thermocouple capable of measuring a temperature rise of 0.00303°C*, since 4t, the temperature rise was usually about 5°C., the accuracy attainable was approximately 0.07 per cent. The electrical energy supplied was determined by means of instruments calibrated against U.S.Bureau of Standards instruments and were reliable to at least 0.1 per cent • Time intervals were measured with a high-grade stopwatch
The heat capacity relations may safely be used over the temperature interval )°C to 150°C.
The values of the ratios of C n to C obtained in this p v investigation are well within the usually specified limits for the method employed. The greatest difficulty encountered in the use of this method was the exact detection of maximum sound intensity. These points, however, were determined with a greater accuracy than is possible with "dust figures".
The values of the free energy content of the mono- and dimethylamines are considered to be the least reliable of the data obtained. As a matter of fact, it is difficult to estimate the accuracy attained. This is true for several reasons. First, although the dissociations proceed primarily according to the indicated relations, there are some secondary reactions taking place. Some condensible material of clear to light brown color was formed in both of the dissociation experiments. The calculation of the equilibrium constants did not take this material into account. Hence, an error is introduced, though it is believed to be small. Second, the heat capacity data for monoand dimethylamine were extended over a rather large temperature range, not experimentally covered in their determination. This extension of range may introduce an error in the values of the free energy content thus found. Third, the heat capacity relation for gaseous HCN was assumed to be identical with that of water vapor, another tri-atomic molecule. This was done because no heat capacity data for gaseous HCN exist. This assumption has been made by other investigators; but this does
not guarantee its correctness. This would affect, naturally, the correctness of the final result. Fourth,the heats of combustion of the amines and of hydrogen cyanide may be in error • Recorded data for these quantities are very few and are perhaps considerably in error; and Fifth, the free energy content of _ 78 hydrogen cyanide, due to Lewis and Randall, is based upon rather meagre experimental data.
The paucity of accurate thermochemical data is rather discouraging, and it is hoped that the heat capacity data of this investigation will prove to be real additions to that small body of accurate thermochemical and heat capacity data now available.
78. Lewis and Randall, ThermodynamicV/ (1928) pg.
Summary
l.The specific heats of gaseous mono- and dimethylamine have been determined, and the heat capacities expressed as a function of the temperature.
2.The ratio of the specific heats has been determined by the velocity of sound method for the mon-, di-, and trimethylamine and also for monoethylamine.
3.The thermal dissociation of monomethylamine at 614°- 800°K has been shown to proceed according to the reaction,
+ 2H S
4.The free energy of formation of monomethylamine has been calculated to be
= * 3507 cals«
s.The thermal dissociation of di-methylamine at 794-841°K shown to proceed according to the following apparent reaction
(CH 3 ) s NH HCN 4 CH< 4 H«.
6.The free energy of formation of di-methylamine has been calculated to be
ono = -7,382 cals*
Continuation of the work on the methylamines is contemplated.
BIBLIOGRAPHY
Adcock and Wells, Phil. Mag. 45,541 (1923).
Akin, Phil. Mag. 27,341,(1864).
Andrews, J»Chem«Ed» 1133-43 (1931)*
Andrews and Southard, Phys. Rev. 35, 670-71 (1930).
Ashby, Thesis, TJhiv. of Texas (1931).
Assman, Ann.Physik 85, 1, (1852).
Behn and Geiger, Verh.d.deut.Phys.Gel. 9,657 (1907).
Berthelot, Ann.Chim.Phys (5), £3,243, 252 (1881).
Bjerrum, Z.Physik Chem. 79, 513 (1912);87,641 (1914).
Blackett and Rideal, Mature, 125, 816 (1930).
Bone, Phil.Trans.A. 215,275 (1915).
Proc.Roy.Soc.A, 100, 67 (1921).
Brinkworth, Proc»Roy«Soc« 107 A, 510-43 (1925).
Brodersen, Z.Physik 62, 180 (1930)*
Bunsen, Ann.Physik.l3l, 161 (1867).
Callender, Proc.Roy.Soc.A, 67, 266 (1900).
Clement and Desormes, Jour, de Phys. 89,321,428 (1819)•
Crawford, Experiments and Obersvations on Animal Heat, 1778 •
Delaroche and Berard, Ann#de#Chim# 81, 98 (1812);83,106 (1812)*
Denham, Z# Phy sik# Chern# 72, 641 (1910).
Dittenberger, Forts• Phys. (iii) 53,334 (1897).
Dulong and Petit, Ann.Chim♦Phys. 10,395 (1819).
Escher, Diss.Marburg,l9l2; Ann.Physik,42,76l (1913).
Felsing and Thomas, J.lnd.Eng.Chern, 21,1269 (1929).
Feising and Wohlford, J.Am.Chem.Soc. 54, 1442 (1932).
Francois, Compt.rend. 44,567 (1907);J. pharm.Chim.67,25,517 (1907).
Gay Lussac, Mem»d<Arcueil, 1, 180 (1807).
Grßneisen and Merkel, Ann.Physik 66, 344 (1921), 4, 72,193 (1923).
Haycroft, Trans.Roy.Soc.Edin. 10, 195 (1826)
Ann.Chim.et Phys. 26, 298 (1824).
Hartmann, Ann.Physik, 18, 252 (1905)
Henning and Justi, Z.Tech.Physik 11,191 (1930).
Holborn and Henning, Ann.Physik 23, 809 (1907).
Hsia, Zeit«Tech♦Physik 12,550, (1931)e.
Hebb, Trans♦RoyeSoc#Canada 13, 3, 101 (1919)#
Joly, Proe.Roy.Soc. A. 45,33 (1888); 48, 440 (1890);55,390 (1894)
Phil.Trans.A 182, 73 (1891).
Keeson and Itterbeek, Proc♦Acad»Sol# Arnsterdam 33, 440 (1930)«
Kirchoff, Ann.Physik (2) 103, 177 (1858)
Kundt, Pogg.Ann. 127, 497 (1866); 135, 337,527 (1868).
Kundt and Warburg, Ann.Physik (2) 157, 353 (1876).
Leduc, Chern Rev. 6, 1 (1929).
Lemoult, Ann.Chim.Phys. 10, 403 (1907).
Lewis and Randall, Thermodynamics, Ist Ed. McGraw Hill Book Co.
N.Y. 1923, pg 80, 590.
Lochte and Wilde, (1925).
Mallard and LeChatelier, Ann, des Mines 4, 379 (1883).
Martini, Nuov.Cim.(ii) 11, 11, (1882); VII 4, 1113 (1893).
Mayer, Ann♦Physik 42>233 (1842)
McCollum, J.Am»Chem«Soc» 49, 28 (1927) ♦
Moody, Phys* Rev* 34, 275 (1912); Phys.Zelt* 13, 383 (1912).
Muller, Bull * Soc * Chem* (2) 45, 439 (1886).
Muller 9 Ann »Chlm ♦ Phys* 20, 116 (1910) ♦
Muller, Ann*Physik 18, 94 (1883).
Nernst, 96 (1910).
Niemeyer, Diss•Halle, 1902♦
Oldfather, Thesis, Univ* of Texas (1929)•
Parks and Ruffmann,
Partington and Shilling, The Specific Heat of Gases, Benn,London 1924, pg. 22; Phil.Mag* 45, 416 (1923)*
Petavel, Phil.Trans* A. 205, 363 (1905).
Pier, Z.Eleotrochem. 15, 536 (1909); 16, 897 (1910).
Planck and Vohl, Ports Geb« Ingenierw. A 2, 11 (1931)*
Ramsey, Jour .Chern. So c. 67, 684 (1895).
Randall and Gerard, J*lnd*Eng.Chem. 20, 1335 (1928)*
Regnau.lt, Mem* de I 9 Acad* 26, 1, (1862)*
Rinkel, Physik*Z* 30, 805 (1929).
Robertson and LaMer, J.Phys.Chem. 35, 1953 (1931)*
Ro th and Nae se r, Z • Electrochem, 31 461 (1925).
Ross ini, B,S»J•Re asearch t 6, 34 (1931)*
Saha, Indi an J our * Phys * 6, 445 (1931)*
Sauermann. Ann*Physlk 41, 474, (1837).
Scheel and Reuse, Ann*Physik 37, 79 (1912);40, 473, (1913) 59, 86 (1919)*
SchBl er, Aim.Ph.ysik, 45, 913 (1914) •
Shields, Phys*Rev* 10 535 (1917)*
Swann ♦, Proc*Roy*Soc*A* 82, 147(1909)*
Swearingen, Ph.D.Thesis, Univ, of Texas (1933).
Swietoslawski and Popov, J.Chem.Phys. 22, 395 (1925).
Taylor, J.Phys.Chern, 36, 1960 (1932).
Thayer and Haas, J.Phys.Chem. 36, 2127 (1932).
Thayer and Stegman, J .Phy .Chern 36. 1504 (1931).
Thiesen, Ann.Physlk, 24, 401 (1907); 25, 506 (1908).
Trautz and Grosskinsky, Ann.Physlk 67, 462 (1922).
Trautz and Hebbel, Ann.Physlk, 74 285 (1924).
Trautz and Kaufmann, Ann.Physlk (5) 5, 581-605 (1930).
Tsutsui, Tokyo Scientific Papers, Institute of Physics Chemical Reasearch, 11 93 (1929).
Vieille, Compt.rend. 95, 1280 (1882); 96, 116 (1883); 115,1268 (1892).
VBrlander, Ber, 44, 2455 (1911).
Wiedemann, Ann.Physik 157, 1 (1876); 2, 195 (1877).
Wohl, Z.Electrochem. 30, 36 (1924).
Will Ine r, Wled«Ann« 4, 321 (1878)«