Michael J. Joncich, Bruce H. Solko, ond John E. Bower
Northern Illinois University DeKolb, Illinois 601 IS
The Thermodynamic Properties of Ammonium Carbamate An experiment in heterogeneous equilibrium
T h e determination of changes of the Gibbs free energy (AG), entropy ( A S ) , and enthalpy ( A H ) from measurements of the dissociation pressures of pure solid compounds has been applied to oxides ( I ) , nitrides (t),carbonates ( S ) , and other compounds (4). Experimentally, this involves simply the measurement of the equilibrium pressure of the gas above the solid a t a series of temperatures. For instructional purposes the dissociation pressure as a function of temperature of carbonates (5) and halides (6) has been used but these experiments require high temperature furnaces, thermocouples, and potentiometers for temperature measurement and reach equilibrium very slowly. An experiment for determination of the properties of ammonium
carbamate utilizing- an inner isoteniscope has been described (7). We have recently introduced in the instructional nhvsical chemistrv laboratow an ex~erimentof this " type involving the decomposition of ammonium carbamate in which measurements are made in the range 30-5O0C with an ordinary 0-50°C degree) thermometer and utilizing an all glass apparatus. Very reproducible results are easily obtaiued in one laboratory period. With the apparatus shown in Figure 1, equilibrium is reached in approximately 30 min.
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~
~
Ammonium Carbamate Equilibrium
Measurements of the dissociation pressure of ammonium carbamate which proceeds by the reaction:
* 2NHdg) + COdg)
NH4CO1NHds)
have been carried out by a number of investigators (8I S ) . The most recent study of this compound by Janjic (14) provided the incentive for including such an experiment in our laboratory. We have experimented with several different designs based on that of Janjic. The one we have chosen is simple to construct, inexpensive, easy to manipulate and is applicable to the study of other equilibria of this type. Further, it has the advantage that all of the solid and gas are a t thermal equilibrium with the constant temperature bath. The dissociation of ammonium carbamate is treated in detail in many elementary physical chemistry texts ( 1 5 ) . The equilibrium constant for the reaction is: K,
=~'~NH~PCOZ
(1)
from which it follows that:
where P., is the total equilibrium pressure starting with pure solid only. The equilibrium may also be studied by admitting definite known initial pressures of either NH3 or C 0 2 to the evacuated vessel together with the solid. In such a case, if x represents the initial pressure of NH3gas, it follows that
while if y represents an initial pressure of COz gas Figure 1 . Dissociation presruro measurement apparatus. A, meter stick; 8, 0-5O0C thermometer; C, " 0ring joint with clamp (not shown); D, =ample container; E, stopcock.
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Table 1.
Thermodynomic Considerations
The change in the standard Gihbs Free Energy AGOr is then determined through the relationship AG'T = -RT Ln K , (5)
Equilibrium Pressures at Various Temperatures, Log Equilibrium Constants, and AGTO
.
A --O D r
Temp.
(C")
Pressure (Tom)
Loe K.
cal mole-'
where K , is the thermodynamic equilibrium constant. The average enthalpy change is determined from the relationship
a",
I t follows that the average enthalpy change, may be obtained by graphing in K , versus 1/T and determining the slope, or from the equation
The entropy change may then he determined a t any temperature in this range through the relationship
The Experiment
Ammonium carbamate was used as purchased without further purification.' The water jacket surrounding the sample container consists of a glass bottle large enough to surround the necessary equipment (Fig. 1) as well as the clamp required to compress the "0" ring joint (C in Figure 1). The top of the bottle was fitted with a rubber stopper in which three holes of the appropriate size were drilled. The largest tubing is 20 mm in diameter; the reaction vessel is 15 rnrn in diameter. To keep the rubber stopper from springing out of place a clamp consisting of two wooden collars (which could be bolted together) may he necessary. Prior to introduction of the sample the water jacket is removed, the system is connected to a vacuum pump through stopcock E, and the system is flamed gently while being evacuated. The sample container is removed, several grams of solid ammonium carbamate added over a plug of glass wool, and the system is evacuated for 10 min. The stopcock is closed and the solid allowed to dissociate for 10 min. The system is evacuated again and the whole process repeated twice more. Finally, while under evacuation the stopcock is closed, the clamps and water jacket are put in place, and water circulation from the constant temperature (*O.Ol°C) bath is started. The bath is set for 30°C initially. Pressure readings may he taken at short intervals if it is desired to study the rate of approach to equilibrium. Otherwise only the final equilibrium pressure is recorded. Equilibrium is reached in approximately 30 min. Each equilibrium pressure is corrected for the temperature effect on the Hg column height. The exact temperature is read from the thermometer in proximity to the sample. The bath temperature is then raised by a small increment (3-5'C) and the series of equilibrium pressures from 30 to 50°C are obtained. Since the apparatus from one period to another does not actually require a new sample and re-evacuation, it is a t equilibrium at room temperature when the student We found that the ammonium carbamate obtained from K & K Laboratories, Plainville, N. Y., provided the best results. Samples from several other sources were tried.
i x to eight additional points can thus be obbegins. S tained in one laboratory period. It is possible to employ the time between points to perform another experiment simultaneously. A simpler system which may be used as a semipermanent setup was also devised. In this case the possibility of leakage through the "0" ring joint or the stopcock was eliminated. This system was identical to the other except that the "0" ring joint was not present and the sample was contained in glass tube D before it was sealed to the rest of the system. The purging cycle was carried out as described previously and the tubing was sealed off between D and E while under vacuum.
Results and Discussion
Table 1 and Figure 2 illustrate the experimental results of the average of five student experiments chosen at random. A11 P., points from these experiments were plotted versus T and the equilibrium pressures at 30,35, 40,45, and 50°C were taken from the smooth curve constructed. For each value of log K , the value of AGO was determined. A plot (Fig. 2) of log K , versus 1/T was then constructed.
Figure 2. Log K, *enus 1/T X 10' for emmonium carbarnolo in the ternperdure rongo of 25-50°C. Data ore for Janjic l14), rquares; Bennett, e l d.,(131, triangles; and student valuer, circle..
From the slope of the line in Figure 2, a0 is calculated to be 37.4 kcal mole-'. Employing eqn. (8), AS"a t 25' is calculated to be 108.8 cal mole-' deg.-I. In Table 2 values of AG0(25'C), AS,O and hRo are compared with values calculated from the data of Janjic (Ib), Bennett (I$), and with values calculated from thermodynamic data tables (16). The agreement is satisfactory. Our equilibrium pressures in many repeated trials were always larger than those of Janjic Volume 44, Number 10, October 1967
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Table 2.
Comparison of Student and Literature Values of AGO, ASo, and AP(at 25'C)
Student Values Janjic (14) Bennett (IS) Thermo. Tables (161
AGO
@
AS"
4943 5100 4840 4878
37.4 38.7 36.6 38.1
108.8 113 106.5 111.2
(14). Our data agree rather well with the results of Bennett (IS) except in the lower part of the temperature range where our results are slightly lower. The authors are grateful for the assistance of Mr. E. J. Hyland in the development of the equipment and to the Dean's Fund of Northern Illinois University. Literature Cited (1) OTTO,E. M., J. Electrochem. SOC.,112, 367 (1965). R., AND WOOLCOCK, J., Z. amrg. A11g. Chem., 176, (2) LORENZ, 280 (1928). 11.R.,AND JANZ, G. J., J . CHEM.EDUC.,40, 611 (3) LORENZ, (1963).
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journal o f Chemical Educafian
GREGORY, N. W., AND THACKREY, B. A,, J . Am. Chem. Soe., 72, 3176 (1950). CAMPBELL, J. A,, J. CHEM.EDUC.,42, 489 (1965). ROSE, J., "Advanced Physico-Chemical Experiments," John Wiley & Sons, Inc., New York, 1964, p. 304. SAL~BERQ, H. W., MORROW,J. I., AND COHEN,S. R., "Laboratory Course in Physical Chemistry," Academic Press, Inc., New York, 1966, pp. 242-3. BRINER,E., J . Chim. Phys., 4, 267 (1906). MATIGNON, C., AND FREJACQUES, M., Bull. Sac. Chim. France, 31, 307 (1922). BRIGGS,T. R., AND MIGIDICHIAN, ~.V., J. Phvs. Chem.,. 28, 1121 (1924). TOKUOKA, M., J . Agr. Chem. Soc. Japan, 10, 1333 (1934). EGAN.E. P.. P o n s . J. E.. AND POTTS.G. D.. Ind. Eno. ~
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BENNETT.R. N.., RITCRIE. P. -~ D.., Roannnnn. D.. , -~ ., A N D ~ n o & , J., T m s . Famday Soe., 49, 925 (1953). JANJE,D., Helv. Chim. Acte, 47, 1879 (1964). MARON, S. H., AND PRUTTON, C. F., "Principles of Physical Chemistry," 4th Ed., The Macmillan Ca., New York, 1965, pp. 246-7. "Selected Values of Chemicd Thermodynemics PropertiesPart 1." Natl. Bureau Std. Tech. Note 27Ckl. Washinston, D: C., 1961. ~
