T H E AMMONIUM CARBAMATE EQUILIBRIUM BY T. R. BRIGGS AND V. MIGRDICHIAN
The equilibrium between ammonia, carbon dioxide and ammonium carbamate has been made the subject of several investigations,l some of which, particularly those by Horstmann and by Isambert, are regarded as classic. A critical study of the data, however, reveals the fact that the latter are far from satisfactory and confirm the Mass Law only roughly.. That this should be the case is not so surprising when one considers that the data were obtained more than forty years ago; but it is surprising to find that nobody heretofore has taken the trouble to repeat the work with care and reasonable accuracy. Professor Bancroft brought this point to our attention, and the present investigation was undertaken. The experimertal procedure employed may be said briefly to consist in measuring, a t constant volume and at definite temperatures (IO', IS', 20°, z s ' , 30°, 35', 40°, 45') the pressure exerted by the vapor phase in equilibrium with solid ammonium carbamate, when the latter is brought into contact with a definite quantity of ammonia or of carbon dioxide.
Theoretical Solid ammonium carbamate is volatile at ordinary temperatures and Naumann,* from determinations of the vapor density, has ehown conclusively that the vapor consists wholly of ammonia and carbon dioxide, a t least above 37'. At higher temperatures (130') the solid carbamate loses water and changes to urea3; but a t the temperatures employed in this work (IO' to 45') the formation of urea may safely be regarded as inappreciable. When solid carbamate is vaporized and brought into equilibrium with the dissociated vapor, the state of the system may be represented as follows: N E T ~ N F ~ ' O ~ ~ Z ~ H ~ + ? ? % (1) For such a case, the Mass Law requires the following relation between tho partial pressures of ammonia and carbon dioxide : p2NH3.pCOZ=Kp (2) and since dissociation occurs with an absorption of heat, K, will increase as the temperature is raised. If one starts with pure carbamate and causes it partially to vaporize, the system solid and vapor is univariant and a t any one temperature there can 'Bineau: Ann. chim. phys. (2) 67, 240 (1838); Rose: Pogg. Ann. 46, 363 (1839); Naumann: Ann. 160, I (1871); Horstmann: Ibid. 187, 148 (1877); Isambert: Compt. rend. 92, 919; 93, 731 (1881); 96, 340 (1882); 97, 1212 (1883); Briner: J. Chim. phys. 4, 276 (1906). 2Ann. 160, I (1871). Basarow: Bull. (4) 32, 394 (1922).
I122
T. R . BRIGGS AND V. MIGRDICHIAN
be but one equilibrium pressure. This pressure is the normal dissociation pressure and it will be represented by ro. If the carbamate vapor is completely dissociated into ammonia and carbon dioxide, then r0, pNH3= 2and pC02 =
3
3
On substituting these values in (2), the following expression is obtained:
When, however, carbamate is vaporized into a, space containing either ammonia or carbon dioxide, (or both, in any volume-ratio other than 2 "3: I C02) the system solid and vapor is bivariant and there can be different equilibrium pressures a t any one temperature depending upon the composition of the vapor phase. Suppose one introduces solid carbamate into a space containing ammonia, the pressure of which is el. Let the total vapor pressure at equilibrium be represented by P. Then P-el is the partial pressure of the 'carbamate' vapor, and since the latter is presumed to be completely dissociated 2 (P- el) (4) +el .=2P+e1 pNH3=--3
3
P - el
=and p C 0 ~
3
providing, of course, the space occupied by the solid carbamate itself is small enough to be disregarded. On substituting t'hese expressions for pNHI and pC02 in (2), one arrives at the following working relation: = K,
When carbon dioxide a t a pressure e2 is used in place of ammonia, the relation becomes :
By employing Equations (3), (6) and (7), the equilibrium constant has been determined in this investigation under three different sets of experimental conditions-( I ) when the vapor consisted wholly of dissociated ammonium carbamate; ( 2 ) when the vapor contained ammonia in excess, (3) when the vapor contained carbon dioxide in excess. The first method necessitated careful redetermination of the normal dissociation pressure P, of pure ammonium carbamate, while the other two methods required the measurement of the total equilibrium pressure when the excess of ammonia or carbon dioxide was known. A further interesting relation may be brought out as follows. If the partial pressure of dissociated carbamate in the vapor be represented by r, then since r = P-el= P-ez,
THE AMMONIUM CARBAMATE EQUILIBRIUM
1123
and
Dividing both members of each equation by rO3, we obtain the following: 3ro
and
-+-) r e2
(
3ro
,To
27
=- 4 27
whence ro
3
and These equations in e/ro and r/r0 are independent of the equilibrium constant K, and therefore of the temperature at which equilibrium prevails. By assigning definite values between o and I to r,lr0,corresponding values of e / r o have been computed, and curves-one for ammonia and one for carbon dioxide-have been drawn with the data thus obtained. Each of these curves (Figs. 2 and 3) is therefore the graph of the Mass Law applied to the particular case and each suffices in theory for all temperatures. Similar curves have been displayed by Horstmann, but it is a particular purpose of this investigation to ascertain how closely the experimentally determined values of r/roand e/ro agree with those calculated from the Mass Law Equations (8) and (9).
Experimental Preparation of the Pure Materials The ammonia was obtained from cylinders of the compressed gas. It was dried with great care by passing it over calcium oxide, then over solid sodium hydroxide and finally over metallic sodium. The gas thus treated was found to contain less than one-tenth of one percent of residue unabsorbable by sulphuric acid. The carbon dioxide was prepared from pure marble in a specially designed generating apparatus, and was dried by being passed through two Friedrichs bottles containing sulphuric acid, followed by two U tubes filled with phosphorus pentoxide. The gas was found to be free from hydrochloric acid vapor and was absorbed completely by a solution of sodium hydroxide. Pure ammonium carbamate was prepared by allowing dry ammonia and dry carbon dioxide, in the proper volume-ratio, to react in a special chamber cooled to 0’. The carbamate was preserved in this chamber out of contact with moisture and air.
1124
T. R. BRIGGS AND V. MIGRDICHIAN
Apparatus and Procedure The general disposition of the dissociation apparatus is shown in Figure I . B is the reaction chamber and M I M z the manometer. The volume of B was maintained constant by means of the adjustable mercury seal U in the lower arm of the bulb. Sealed into B at its upper end was a capillary tube containing a glass stop cock, through which ammonia or carbon dioxide could
FIG.I
be introduced, as desired. Solid ammonium carbamate was stored in the side-arm A and was kept completely covered with mercury, by means of a procedure to be described later. The pressure in B (always less than one atmosphere) was measured by means of the manometer M I M Zand a carefully calibrated barometer. When the mercury in each arm of U was brought to the same level, the pressure
THE AMMONIUM CARBAMATE EQUILIBRIUM
112.5
above the mercury in M nwas exactly equal to the pressure in B and this in turn was found by subtracting from the barometric pressure the pressure of the column of mercury between M1 and Mz. The accurate adjustment of levels in U was performed by raising or lowering M2 by means of a special screw until the surfaces al and a2 were at exactly the same level, as ascertained by sighting along a horizontal line in a telescope. The length of the column of mercury between Ml and ill2was measured against a fixed scale by determining the position of the mercury in MI and Mz, with the aid of a cathetometer. The usual corrections for temperature were applied to all manometric and barometric readings. The reaction bulb B was immersed up to the stopcock in a water thermostat, electrically heated, stirred and regulated. The temperature seldom varied by more than 0.05' over a period of eight hours, six hours being found ample above 15' for the establishment of equilibrium. A thermometer, calibrated by the Bureau of Standards, and permitting readings of temperature to 0 . o I ', was immersed in the bath near the bulb B. Readings a t stated intervals were taken and tthesewere averaged in obtaining the equilibrium temperature. In order to carry out the necessary measurements with one of the gasesammonia or carbon dioxide-present in excess in the reaction chamber B, it was first necessary to obtain a sufficient supply of the dry solid carbamate in the side arm A , before the excess of gas was introduced into B. Carbamate was first sublimed into B by connecting the latter to the cylinder in which was stored the dry reagent prepared as previously stated. A small cooling jacket was then fitted about the side arm A and the whole apparatus was immersed in hot water. Carbamate soon gathered in the side arm and in a few hours appeared to have been eliminated completely from B and from U , and to have been localized wholly in A . Thereupon the carbamate in A was covered with a column of mercury and the last traces of carbamate in the rest of the apparatus were removed by repeated evacuation. The whole apparatus was then filled with mercury which had previously been freed from air and moisture by being heated to 200' under reduced pressure. A suitable quantity of ammonia or carbon dioxide was next introduced and enough mercury was left in the apparatus to serve as the seal and pressure indicator in U . The whole was then placed in the thermostat at 20' and the pressure of the gas determined. Care was taken to see that the carbamate in the side arm was covered with mercury to a sufficient depth so as to prevent sublimation into B. Since the pressure of the gas in B remained constant with time, no sublimation could have occurred, for had it done so, n marked increase in pressure would have been observed. The bulb B was next removed from the thermostat and the side arm A was heated carefully so as to distill carbamate back into the reaction chamber, after the latter had been filled with ammonia or carbon dioxide a t known pressure. A small quantity of the reagent passed into B , where it condensed
1126
T. R. BRIGGS AND V. MIGRDICHIAN
on the walls. Care was taken to heat locally the walls of the U tube containing the mercury seal, so as to free them from condensed carbamate. The apparatus was then returned to the thermostat and allowed to remain for several hours until the pressure became constant and equilibrium was presumably established. The total pressure in B was finally ascertained as carefully as possible. Different determinations of pressure varied by not more than 0 . 3 mm. Equilibrium pressures were determined at IOO, I ~ O ,zoo, 2 5 O , 30°, is', 40°, and 45'. In all, twelve such complete runs were carried out, six with ammonia in excess, five with carbon dioxide and one with no excess of either component. The complete investigation thus included some ninety independent determinations of the equilibrium pressure, although in a few cases several of the above temperatures were passed by. The pressure of the gas in excess, in the absence of carbamate, was determined at 20' for each of the twelve runs. From this value the pressure of the gas in excess was computed for the other temperatures by assuming that the pressure, at constant volume, varied directly with the absolute temperature. Special experiments showed that this was true, as the pressures were never very great. No correction was made for the expansion of the bulb, a8 these special experiments indicated that this was an unnecesary refinement under the conditions of the work. Special care was taken, however, to eliminate the errors that might be caused by air adsorbed in the carbamate or by the walls of the reaction chamber. The carbamate was stored in vacuo and no air was allowed a t any time to enter the reaction chamber, after the air had once been removed completely by heating under reduced pressure. Special experiments were also carried out for the purpose of redetermining the dissociation pressures of ammonium carbamate between IO' and 45'. These measurements were carried out in the equilibrium apparatus just described. Carbamate was sublimed into the reaction chamber B, and the latter was then filled with dry, air-free mercury. On closing the upper stopcock and withdrawing mercury, the carbamate was caused to vaporize in B, this process being hastened by heating. The vapor so formed was next condensed to the solid by compression, the bulb B was again filled with mercury and the slight trace of uncondensable gas was trapped in the upper capillary and expelled through the stopcock. The mercury was again run out and the carbamate was once more vaporized in the reaction chamber. The condensation to solid was repeated, and the cycle of evaporation and condensation was continued until no trace of uncondensable residue could be detected. The bulb B containing pure carbamate was then placed in the thermostat and the equilibrium pressure was determined. Needless to say, the glass stopcock was tested and was found to be free from leaks.
THE AMMONIUM CARBAMATE EQUILIBRIUM
1127
The Dissociation Pressure of Ammonium Carbamate The data, obtained w described, have been assembled in Table I. Pressure is stated in millimeters, temperature in degrees Centigrade.
TABLE I The Dissociation Pressure of Ammonium Carbamate Temp.
=o
Temp.
To
10.92 14.92 16.90 17.86 19.87
29.2 31.4 42.5 49.3 52.7 61.3
26.77 26.92 27.85
21.25
68.1
28.87
88.3 92.0 94.2 100.3 101.3 108.3 114.1
22.96
77.0
28.92
116.7
10.03
24.91 25.33 25.88
Temp.
29.83 29.96 30.91 32.10 32.91 33.90 34.89 35,91
To
124.5 124.5 133.6 I45,O 153.4 163.3 174.9 186.7
Temp.
To
-
36.90 199.1 37.88 2 1 2 . 9 38.87 226.7 39.89 2 4 2 . 5 41.91 276.3 44.86 331.6
The values of ro and t were next plotted and a pressure-temperature curve, several feet in length, was constructed, each centimeter on the temperature axis representing 0 .z0, and each centimeter on the ro axis a pressure of 5 mm. The individual determinations lay very close to a smooth curve, while the dissociation pressures reported by Horstmann, Naumann and Isambert, plotted for comparison, showed irregular variations and were in generalgreater than ours. By constructing the curve on so generous a scale it became possible to read from the curve values of ro with great precision (to 0 .2 mm.).
The Dissociation Pressure With One Component in Excess In accordance with the procedure described, twelve different series of determinatione were carried out, six of these with ammonia in excess, five with carbon dioxide, and one with pure carbamate as a check. The pressure of the gas in excess was measured a t 20' in each series and the pressure a t other temperatures was computed from this value. Each series was run in general at 5 O intervals from I O O to 45' inclusive. The data have been assembled in Table 11, the symbols having in every case the meaning already assigned to them. The series are numbered in the first column. The equilibrium constant Kp has been computed in two ways-in Column 8 from the product pWH3.p COZand in Column 9 from 4/27 rO3, the values of ro having been read from the dissociation pressure curve. The agreement is satisfactory, except, for the runs a t I O O , though in general the values of K,, computed from the product of the partial pressures are slightly smaller than those obtained from the dissociation curve. We do not feel justified in regarding this difference as significant a t the present time, since in general the variations in Kp that may be observed in the table do not greatly exceed the probable error involved in these measurements.
1128
T. R. BRIGGS AND V. MIGRDICHIAN
TABLE I1 Equilibrium Data and Dissociation Constants (1)
(2 J
(3)
(4)
(5)
(6)
(7)
(8)
"C
el
e2
P
pNHs
pCOn
Kp/103
1 5 8 ~ 3 158.0 132. I 132.2 57.2 55.6 56.4 53.9 36.3 32.7 27.1 34.3 29.2 19.4 39.6 13.5 10.2 48.7 97.1 6.7 165.1 4, i 166.9 5.2 162. I 165. I 136. I 137.1 60.0 63.3
0.26
6.5
0. I j
2.2
Exp. No.
Temp.
AI
10.04 10.08
157.5
10.01 IO.05 I O . 41 IO. 04 I O . 03 I O . 00 IO. 18 10.01 I O . 00
52.4 49.0
A2
A3 A4
-45 A6
A7 A8 A9
AIO AI I AIZ
BI
B2 B3 B4 B5 B6
B7 B8 B9
BIO
BII B12 CI c2
c7
c8 c9 CIO
CII CI2 DI D2
DIO DI I D12
25.5 12.7 0
159. I
14.89 14-93 14.92
160.2 134.1 53.3
14.93 14.88
25.9 12.9
15.00
14.85 14.92 15.00 15.00 14.91 19.93 19.93 19.92 19.89 19.94 19.89 20.00
0
0
19.7 34.0 88.6 160.9 161.9 163 . o 136.4 54.2 50.7 26.4
13.I 0
0
20.0
19.95 19.91 19.86 19.91 19.86
34.6 90. I 163.6 164.7
24 * 98 24.91 24.89
765.7 138.7 55.2
24.94 24.94
26.9 r3.3
24.88 24.88 24,86 24.94 24.89
0
19.3 33.4 87. I 158.0
10.06
25.00
D9
131.8
0
o 20.4
46.7' 42. I 43. I 48.6 58.0 105.7
173.1 174.5 166.6 141.7 75.9 73 - 0 64.2 63. I 61.8 66. I 74.4 118.3 184.9 185.3 176.4 152.4 98.1 89.4 88.1 88.5 90.2 97.4 137.3
35.2 91.7 166.5 2 0 1 . 1 1 6 7 . 5 202.4
39.8 32.4 28.7 19.3 16.0 11.4 8. I 8.4 16s.4 139.9 68.7 65.6 51.6 i6.4 41.2 30.7 26.5 18.8 14.2
13.7 172.8 147.8 83.8 68.6 63.2 59.0 46.5 41.5 30.4 23.1 23.3
(9)
5 To8/ IO3 27
1.0
18.5
3.7 3.8 3.7 3.7 4.1 3.7 3.7 3.7 3.9 3.7 3.7 3.8 11.3 11.3
3.3
11.9
11.3
10.9
11.3 11.3
1.6 2.5 3.6 7.2
9.7 26. I 38.5 90.4 160.4 161.7 0.63
6.9 9.7 14.4 29.3 42.0 94.3 165. o 166. I 1.2 I
.8
7.2
7.4 12.6 16.7 20.6 35.4 47.9 99.5 170.7 171~6
5.0
7.3 3.9 5.3 3.7 4.8 4.0 4.1 3.5 4.4 16.4
IO. 2
11.8 10.9 10.8 12.3 10.8
11.5 11.2 11 - 3 11.5
11.7
11.5 11.3
32.8 35.2 34.0 31.8 33.6 36.0 35.0 33.4 33.6 35.2 34.4 32.3
34.7 34.7 34.6 34.4 34.8 34.4 35.3 34.9 34.6 34.1 34.6 34.1
3.6 4.6 14-3
107.2
102.7
100.5
100.7
100.4
101. I
20.8 24.9 29.5 43.7 55.9 106.9 178.0 179.7
97.9 99.5 102.7 94.9 69 3 '98.8 95.0 97.2
101.5 101.5
103.3 99.8 99.8 99.2 101.5
99.9
THE AMMONIUM CARBAMATE EQUILIBRIUM
I
129
Table I1 (continued) (1)
EI E2
(6)
(2)
30.01 29-96 29.95 29.94 29 * 93 29.96 30.00 29.93 29 * 92 29.90 29.85 29.93
168.6 141. I
34.92 34.88 34.91
171.3 143.5 56.9
226.2 210.9 180.0
207.9 188.4
34.86 34.94 35.00 34.90 34.76 34.85 34.81 34.90
27.7 13.8
174.2 174.5 175.9 175.7 178.8
174. I I45.7 57.9 54.1 28.3 14.0
GIO GI I G12
39.89 39.90 39.94 39.87 39.84 39.85 40.00 39.90 39.87 39.80 39.85 39.87
HI H2
44.93 44.84
E3 E4
E5 E6
E7
E8 g9 Ero
EI I E12 FI
F2 F3
194.2 174.2 132.2 129.5 125.4 124.9 0 125.0 20.7 126.8 3 5 . 8 132.4 9 3 . 3 165.9 169.2 226.6 170.4 227,3
56.1 52.5 27.3 13.6 0
185.7
163.2 106.8 103.8 92 * 7 87.8 83.3
70.7 64.4 48.4 38.3 37.9
(7) 8.5 11.0
25.4 25.7
(8)
293 293 289 277
32..7 37.1 41.7 56.1 68.0
281 286 289 280
II7.5
275 276
188.3 189.4
282
F5
F7
F8 F9 Fro
FI I F12
GI G2 G3 G4 G5 G6
G7 G8 G9
H3 H4 H5 H6
H7
H8 H9
HIO HI I H12
44.84 44.84 44.89 45.00 44.88 44.82 44.85 44.97 44 * 83
294 291 289 289 288 290 293 288 287 285
272
283 288
139.0
18.3 22.5 41.0
791 799 792
798 790 796
48.8 53.6 58.6 72.6 83.9 129.3 202.6 203.9
767 783 806 771 756 758
263.7 265.2
125.4 120.9 117.3 103,7 94.9 78.9 61.1 61.3
789 800 810 794 7 73 787
279.8 270.9 246.4 244.3 241 * 5 240.9 244.3 243.5 246.6 268.7 319.5 320. I
244.6 229.2 183.6 181.3 170.4 165.3 162.9 148.0 139.7 114.9 96.4 96.0
35.2 41.7 62.8 63.0
2106 2190
2120
2117 2071
2 136 2 108
2096
224.1
2065 2066 2160 2091 2086 2030 2073 2065
176.8 148. I
358.8 352.5
298. I 284.4
60.7 68.1
5508
5394
5476 5384
55.0
i32.9 332.2 331.7 0 334.4 21.8 332.0 38.7 333.0 98.0 351.0 177.8 397.9 178.9 3 9 6 . 8
240.3 231.3 225.9
5347 5441 5399 . 5540 5354 5290 5188 5407 5310
5384 5384 543 6 5545 5426 5363 5395 5515 5374
F4 F6
(91
0
0
21.1
36.4 94.8 172.0 173.2
0
'
0
21.4 37.0 96.4 174.9 176. I
28.7 14.3 0
208.2
71.1
75.6 81.4 95.5 106.9 153.8 223.1
92.6
2 2 2 .Q
101.7 105.8 111.5
206.8 196.5 168.7 146.7 I45,3
125.2 137.0 182.3 251 2 251.5
757 767
780 794 2116
2100
2160 2120
2108 2080 2 IO0 2 1c8
'
I
130
T. R. BRIGGS AND V. MIGRDICHIAN
Values of e/Ro and r / r ocomputed from the experimental data of Table I1 have been assembled in Table 111. For convenience the number of each experiment has been repeated in the first column of data, and likewise the values of el and e2 in Columns 2 and 3.
TABLE I11 ii-
Comparison between E Found, and ?r, Required by Mass Law ?r,
(1)
Exp. No.
(2)
(3)
e1
ea
(4
(5)
ii-
To
(7)
(6) C -
?r -
=o
T O
AI A2 A3 A4
A5 A6 A7
0
AIO AII A12
B5 B6
B7
160.2 134.1 53.3
0
BIO BII B12 CI c3
c4 C5 C6
c7
0
17.1 I2 * 2
12.6
22.,.3
37.8 5o.c
0
20.0
c9
34.6 90. I 163.6 164.7
CII CI2
20.8 29.2 43. T 28.9 24.0
3.6 5.3 21.7
C8 CIO
7.1 7.8
10.0
163.0 136.4 54.2 50.7 26.4 13. I 0
IO. I
1.9
19.7 34.0 88.6 160.9 161.9
B9
4.8 7.4 10.8 21.6 29.2 20.3 15.3
3.0
25.9 12.9
B8
c2
0
19.3 33.4 87. I 158.0 159.1
A9
B3 B4
0.4
12.7
A8
BI B2
0.8
157.5 131.8 52.4 49.0 25.5
61.8 46. I 39.8 28.2 21.:5
20.6
29.1 29.2 29.0 29. I 30.0 29.1 29.0 29.0 29.5 29.0 29.0 29.2
5.42 4.52 1.81 1.68
42.4 42.5 42.5 42 * 5 42.4 42.8 42.3 42.5 42.8 42.8 42.5 61.7 61.7 61.7 61.5 61.8 61 5 62.0 61.8 61.6 61.5 61.6 61.5
0.85 0.44
Found 0.03
(8) ?r R,
Mass Lnw 0.01
0.01
0.02
0.17
0.13 0.14 0.37 0.62
0.25
0.36 0.74
0
I
1
0.67 I . 13 3.00 5.44 5.44
0.70 0.52 0.35
0.62 0.51 0.33
0.25 0.27
0.25 0.25
3.78 3-15 1.25
0.05
0.03
0.07
0.05
0.24
0.23
0.61 0.30
0.49 0.69
0.50 0.73
0
I
1
0.47 0.80
0.68 0.57 0.40 0.29 0.30
0.69 0.58 0.39 0.30 0.30 0.06
2.07
3.75 3.78
0.21
0.06 0.09 0.35 0.36 0.61 0.82
0
1
1
0.32 0.56 1' 47 2.64 2.67
0.75
0.76 0.65 0.45 0.35
2.64 2.21
0.88 0.83 0.43
0.65 0.4.6
0.35 0.34
0.09
0.36 0.39 0.62 0.80
0..34
1131
THE AMMONIUM CARBAMATE EQUILIBRIUM
Table I11 (continued) (5)
16)
(7)
(8)
89.0 88.5 88.5
1.86 1.57 0.62
0. I 2
0. I1
13.7 42.9
0.16 0.48
0.16 0.49
62.5 74.8 88.5 69.8 62.2 45.6 34.6 34.9
88.7 88.7 89.0 88.4 88.4 88.3 88.7 88.5
0.30
0.71 0.84
0.73 0.86
25.6 33.1 76. I 98. I 111.3 125.0 0 106. I 20.7 96.6 35.8 72.6 93.3 169.2 57.4. 56.9 170.4
125 * 5 125.0 125.0 125.0 124.7 125.0 125,5 124.7 124.7 124.5 124.2 124.7
171.3 143.5 56.9
54..9 67.4 123.1
27.7 13.3
146.5 160.7 175.9 154.6 142.4 113.4 91.7 92.0
(1)
(2)
DI D2
165.7 138.7 55.2
D3 D4
D5 D6
D7
0
DIO DI I n12
168.6 141. I 56. I 52.5 27.3 13.6 0
E8 E9
E10 EI I E12
FI Fz F3 F4 F5 F6
F7
0
Ii'8
173.2
G6
G7
0
G3 G4
G5 G8 G9 GIO
GI I G12
0 21.1
172.0
174.1 145.7 57.9 54. I 28.3 r4.o
7
77.0
36.4 94.8
F9
FIO FI I FI 2 GI G2
0
20.4 35.2 91.7 166.5 167.5
D9
E7
IO.
26.9 13.3
D8
EI E2
(4)
(3)
105.7
0
21.4 37.0 96.4 r74 9 176. I
-
125.2 188.5 189.2 213.2 226.9 244.3 221. I
209,6 172.3 144.6 144.0
0.15 0
I
1
0.24 0.40 I .04 1.88 1.90
0.79 0.70 0.52 0.39 0.39
0.82
1.34 I . 13 0.45 0.42
0.20
0.21 0.27
0.22 0. I1 0
0.26 0.61 0.62 0.79 0.89
0.72 0.53 0.40 0.40
0.61 0.63 0.80 0.89
I
1
0.17 0.29 0.75 1.36 1.37
0.85
0.86 0.78 0.59 0.47 0.47
175.2 174.8 175.0
0.92 0.82 0.33
0.31 0.39 0.70
0.32 0.39 0.71
174.5 175.5 176.2
0.16 '0.08
0.84 0.92
0.85 0.92
0
I
1
175.0
0.12 0.21
0.89 0.82 0.65 0.53 0.53
0.90
0.83 0.66 0.53 0.53
0.44 o.5r 0.77 0.78 0.88 0.94
0'44 0.51 0.78 0.80 0.89 0.94
173.5 174.5 174.0 175.0 242.5 243.0 243.5
0.54 0.99 0.99 0.72
0.60 0.24
232.3
0.22
242.0 242.0 244.4 243.0 242.3 241.2 242.0 242.3
0.12
0.06
0.77
0.59 0.47 0 46
0
I
1
0.09 0.15
0.91 0.87
0.92 0.87
0.40
0.72
0.72
0.72 0.73
0.60
0.60
0.59
0.60
1132
HI H2
T. R. BRIGGS AND V. MIGRDICHIAN
176.8 148. I
182.0
204.4
333 331
0.53 0.45
0.54
33= 331 332 334.5 332 331 331.5 334 331
0.17
0.84
0.09 0.04
0.92 0.96
H3 55.0
H4 H5 H6
28.7 14.3
H7
0
H8
277.9
0
21.8
H9
HIO HI I HI^
303.5 3I7.4 334.4 310.2
38.7 294.8 98.0 253.0 177.8 220.1 r78.9
217.7
0.62
0.55 0.61
0.85 0.92 0.96
0
I
I
0.07
0.94 0.89 0.76 0.66 0.66
0.94 0.90
0.12
0.30 0.53 0.54
0.78 0.67 0.66
I n Figure 2 (and also in Figure 3) the graphs of Equations (8) and ( 9 ) have been displayed in accordance with the statement made during the discussion of the theory. From these curves, therefore, may be read values of r / a o corresponding in theory to the various experimental values of e/ro. The theoretical values of r/rothus read from the curves have been assembled
0.8-
FIG.2
in the last column of data in Table 111, where they may be compared with the values of r/ro obtained by experiment. The close agreement between the two sets of values shows how nearly the experimental data are in accord with the Mass Law. e To bring out, this point more strikingly, the values of r/a, and TO
obtained by experiment have been plotted in Figure
2,
ammonia in excess
.
THE AMMONIUM CARBAMATE EQUILIBRIUM
I
I33
being distinguished from carbon dioxide in excess by the full black circles. It will be seen that the points lie on, or very close to, the corresponding Mass Law curves. The results a t 10' are less satisfactory and have not been plotted in Figure 2, since equilibrium was possibly not attained in this series of determinations. It should also be stated that the values of e / r o and r/roin Table I11 have been rounded off as regards the third decimal.
FIG.3
An interesting point is brought out by the curves shown in Figure 2. For small values of e / r o r particularly when e represents the excess of ammonia, e/ro = I -r/ro(approximately), whence e = ro- r (approximately), and since P=r+e, P = ro (approximately). That is, the total equilibrium pressure obtained when the solid carbamate is in contact with vapor containing a small 'relative' excess of ammonia or carbon dioxide (e/ro less than 0 .I ) is approximately equal to the normal dissociation pressure of the pure carbamate. It follows from this that a t high temperatures one may add a fairly large amount of ammonia or carbon dioxide to carbamate in contact with its vapor without causing any marked increase in the total pressure of t,he vapor. A glance a t the values of P (Table 11, Column 5 ) show that such is the case a t the higher temperatures when e is
T. R. BRIGGS AND V. MIGRDICHIAN
1134
small. As a matter of fact however, the Mass Law requires that P be a minimum when e is zero, as Brinerl has pointed out. For the purpose of comparison, values of e/ro and r/r0 computed from Horstmann’s data have been plotted in Figure 3 on the same scale as that employed in Figure 2, the full black circles representing a.mmonia in excess, as before. It is evident that these values, all of which were obtained in the neighborhood of 2 0 ° , are not satisfactory, particularly when ammonia is present in excess, though the values with carbon dioxide are in better agreement with the theory. Isambert’s results have also been displayed in Figure 3, the values of e / r o and r/rohaving been calculated from the original data.2 A glance will suffice to show that these data, likewise, can hardly be looked upon as confirming the Mass Law. Isambert3 at a later date reported results that were much more accurately obtained. Unfortunately the experimental data were not reported, but only values of ro computed from the relation:
TABLE IV x, from Dissociation
Curve
Temp.
34.0 37.2 41.8 46.9 52.6
170
165
211
20.5
272
268 372 522
375 524
167 206 266 3 76 524
181
165
2 16
2 04
275 378 526
274
ir0from Dissociation Curve
Temp.
61.9 88.2 124.5 174.5 242.7 333.2
20.0 25.0
30.0 35 . o 40.0 45.0
61.4 87.7 124.8 174.9 243 * 5 333.0
61.6 88.5 125 5 175.9 243 7 333.8 +
J. Chim. phys. 4, 276 (1906). Compt. rend. 93, 731 (1881);Ostwald: “Lehrbuch”, 11 8 Compt. rend. 97, 1212 (1883).
a
62,.0
60.9 88.0 125.0 176.8 243.7 332.9
(2)
89.0
125.5 176.2 244.4 334.5
523.
THE AMMONIUM CARBAMATE EQUILIBRIUM
1135
In Table I V are recorded Isambert's values of ro calculated from Equation and for comparison some values computed in a like manner from the data obtained in the present investigation, by employing the same equation. It should be noted that the values of K, = p2NH3.pCOz (taken from Column 8 of Table 11) have been reduced to the proper temperature by adding a correction ascertained from the temperature variation in the values of 4/,,r: recorded in Column g of Table 11. The values of ro have been computed from determinations in which either carbon dioxide or ammonia was in excess as stated. All values are expressed in mm. These later determinations by Isambert agree much more closely with the Mass Law, and in some cases remarkably so. Nevertheless Isambert's calculated values of ro differ among themselves rather widely, much more so than do the values of r, computed from the equilibrium pressures' in this investigation, though the latter values in general are slightly smaller than the normal dissociation pressures obtained directly with carbamate alone. Briner's data have not been considered because they were obtained at rather high temperatures and are not very numerous. They can be regarded, however, as approximately confirming the Mass Law. (IO),
(I).
summary Previous investigations of the ammonium carbamate equilibrium
from the point of view of the Mass Law have for the most part yielded incomplete or unsatisfactory results. 7 he ammonium carbamate equilibrium has been studied a t low pres(2). sures and a t several temperatures between IO' and 45'. (3). The dissociation pressures of pure ammonium carbamate have been redetermined with great care between IO' and 45'. (4). Except at the lowest temperature employed, the ammonium carbamate equilibrium has been found to conform to the Mass Law, within the limits of experimental accuracy. Cornell Universitu March, 1934
