The Molecular State of Acetic Acid Vapor An Experiment in Gaseous Equilibrium R. H . WRIGHT University of New Brunswick, Fredericton, New Brunswick, Canoh
T.
HE USUAL textbook examples of gaseous equilibnum suffer from the disadvantage that they cannot easily be assigned for study by students in the undergraduate laboratory. Thus, PC15 and NzO,, both classical examples involve highly corrosive gases which attack both mercury and stopcock grease and hence call for apparatus that is both complicated and fragile, and in the intricacies of this apparatus beginners are likely to lose sight forever of the fundamental chemical principles a t stake. This paper describes an experiment on the equilibrium between monomeric and dimeric molecules of acetic acid in the vapor state. The apparatus is simple to operate so that, in the course of a single laboratory period, the equilibrium can be investigated fully a t each of a number of temperatures and so both the reaction isotherm and the reaction isochore can be verified.
ZNor, and the total number of mols of gas present is the or). Assuming that each molecsum of these, or N ( l ular species conforms to the ideal gas law, (that is, the van der Waals' effects can be neglected), then we can write:
+
PV = N ( l
+ a)RT
Hence, in order to evaluate or, it is necessary to measure separately: P, the total pressure of the gas; V, its volume; T, its temperature; and N , the number of mols of acetic acid, reckoned as (C2H402)4present in the volume, V. That is, = weight of gas
120 INTRODUCTION
Gases may deviate from the ideal gas law either as a result of the molecular attractive forces and the molecular volume effects, or as a result of some chemical reaction causing the total number of molecules in the system to change. By means of van der Waals' equation and other equations of state, the effects of molecular attraction and volume can be estimated with some precision and deviations from ideal behavior that cannot thus be accounted for can generally be traced to a chemical change causing the total number of molecules in the system to change. This illustrates one of the prime functions of physical chemistry: to use deviations from normal physical behavior to reveal otherwise unsuspected chemical processes. The deviations of acetic acid vapor from the ideal gas law are of this second type as will be seen from the results of the experiment described below, that is, they can be attributed to the reversible chemical reaction
These measurements are described in the next section. Applying the Mass Law to the equilibrium, we have
where P is the total pressure of the gas. If the substitution of corresponding values of P and o! a t a fixed temperature leads to a reasonably constant value of K,, then the deviations of acetic acid vapor from the ideal behavior will have been satisfactorily interpreted in texms of a chemical equilibrium between two molecular species existing in the gas. It will be seen that the above treatment takes the Mass Law as given and uses the data to verify the hypothesis of a reversible chemical change in the gas. Alternatively, we can take the association-dissociation reaction as given and regard the experiment as a test of the Mass Law. I t can be shown thermodynamically that
2CnH4On = (CTH~OJ?
I
For puiposes of quantitative formulation, this reaction can be regarded either as a dimerization of single molecules or as a dissociation of double molecules. The latter course leads to somewhat simpler formulas. Suppose we have N mols (120 N grams) of ( G H r O& contained in a volume V and that a fraction or of these are dissociated thus, I
(C~HIOJP= 2C9H*02
then a t equilibrium the number of mols of (CtHr 02)%and of GHn02are, respectively, N(l - or) and
or, changing to common logarithms and integrating with the assumption that AH is independent of the temperature, AH log K, = const. - 2 ~ T (4) By plottinglog K, against 1/T, a straight line should result whose slope is equal to - AH/2.303R, and from this A H can be calculated for the reaction (C2H402)~= 2C.H10%.
APPARATUS AND EXPERIMENTAL METHOD
Figure 1 shows a photograph of the apparatus, while its essential parts are sketched in Figure 2. The apparatus is divided into two parts by the stopcock, X. To the right of this stopcock it consists of a pumping system and manifold carrying a mercury manometer, M ,and a McLeod gage, G. Evacuation is effected by means of a mercury vapor pump hacked by a Hyvac.
This part of the apparatus can he used in the determination of gas density by the ordinary procedure of weighing the detachable bulb, B, when empty and when filled with gas a t a known temperature and pressure. This experiment serves as a useful preliminary to what follows by providing a simple introduction to the apparatus. The part of the apparatus lying to the left of the tap, X, is used with the acetic acid. It consists of a eudiometer tuhe, E, connected with a leveling cup, L, and to the rest of the apparatus through the tube, A . Sealed to the top of the eudiometer is a short length of fine capillary tube, C, taken from a broken thermometer. Before attaching this capillary, its internal volume per degree was found by introducing a thread
of mercury into it, observing the length of the thread in "degrees," and then weighing the mercury. The eudiometer and its connecting tube, A are mounted inside a length of 10-cm. pyrex tubing, T , which serves as a thermostat. It is closed a t the bottom by a cup made from sheet copper, the glass-tometal joint being sealed with electrician's rubber splicing tape. The glass tuhe leading to the ?eveling cup passes out through a rubber stopper and a drain-cock is attached a t D. The thermostat is stirred by a series of paddles soldered to a piece of brass pipe which rests in a bearing soldered to the inside of the cup. The heating element consists of a long spiral of nichrome wire contained in a length of 15-mm. pyrex tubing filled with heavy oil, and the temperature is regulated by adjusting the current through the heater by means of a lamp hank or rheostat. Temperatures are measured by a thermometer attached to the side of the eudiometer, E. The procedure in making a run is as follows. The leveling cup, L, is lowered until the eudiometer is open to the tube, A , and the whole system is exhausted to a pressure of about 10-5 mm. Tap X is then closed and acetic acid vapor is admitted from the storage bulb, R. The leveling cup is then raised until the vapor in E is isolated, and the tube, A , is evacuated. Tap X is then closed and the pump shut off. The thermostat has meanwhile been filled with hot water and the current through the heating element adjusted so that the temperature remains reasonably constant at some point between 50°C. and 95'C The leveling cup, L, is then set a t a series of different positions and the corresponding volumes and pressures in E are observed. The pressures are determined by means of a meter stick situated outside the thermostat and provided with a metal slide so that the level of the mercury in E and A can be observed with a minimum of error due to parallax. A cathetometer would enable much more precise results to be obtained. When it is desired to change the temperature of the bath, some of the water is drained out through D and replaced with hot or cold water as needed. In this way, sets of values of P, V, and T can be obtained for substitution in equation (1). To determine N, part of the water is drained out of the thermostat until the greater part of the capillary, C, is no longer immersed. A tube is then let down into the top of the thermostat until its end is within an inch or two of the water surface, and compressed air is blown in for 10 or 1.5 minutes. This serves to cool the upper part of the capillary while its lower end and the eudiometer are still kept hot by the water remaining in the thermostat. On slowly raising the leveling cup, L, the acetic acid is made to condense in the cool upper part of the capillary where it is confined by the rising mercury. The rest of the water is then drained out and replaced by water a t 25'C. or some other temperature for which the density of liquid acetic acid is known, and the volume of the condensed vapor is read off in terms of the degree marks on the thermometer stem
'
from which the capillary, C, was made. Knowing the volume of the capillary per degree and the density of the acetic acid, N can then be calculated from equation (2). The acetic acid in R was purified by distillation with potassium dichromate followed by fractionally freezing it a number of times until the melting point of the residue was about 15.5'C. This corresponds to less than one per cent of w t e r . After introducing the liquid into R, it was freed from dissolved air by freezing it with an ice-salt mixture, pumping off the residual gas, allowing the solid to melt, and then repeating the freezing and pumping a number of times. The following corrections may be applied to the results. 1. I n attach'mg the capillary tube, C, to the eudiometer, a constant amount was added to the volume. This amount was determined a t the time the apparatus was built by inverting the tube, E, and running a known volume of water into it from a burette. In this way it was found that the volumes etched on the stem of E must he increased by 0.15 cc. 2. Since the standard atmosphere (which is incorporated into the constant, R, in equation (1))is defined as the pressure of a column of mercury 76 cm. high when the mercury is at O°C., and since, in this experiment, the mercury is a t a considerably higher temperature, the observed difference in level between E and A is not the true pressure of the gas. If the expansion of the mercury is given by the formula VZ= VO( 1
+ Bt)
where fl is the cubical coefficient of expansion of mercury and t its temperature in OC., then since the density varies inversely as the volume and since @ is small,
a,
= do(l
- Bt)
and the corrected pressure is given by
A somewhat similar correction, but in the opposite direction, may be applied to allow for the expansion of the meter stick. As a result of its expansion, the indicated difference of level tends to be too small. If #'
FIGURE 3.-SHOWINGRELATION OP LOGKp TO RECIPROCAL TEMPEMTURE. RESULTS O F DETERMINATION, OPEN C I R C L ~ SMACDOUGALL'S ; VALUES,BLACKCIRCLES
OF
is the temperature of the meter stick and 0' its linear coefficient of expansion, then the correction to be applied for the expansion of the stick is given by
+
Po,. (1 B't') Combining the two corrections, we have Pa.,.
=
PC,,. = Po,,. (1 - Bt) ( 1
+ B't')
and, because @ and p' are small, this simplifies to PC.,.= Po,. (1 - Bt
+ B't')
Since @ is 0.000182 and @' (the linear expansion coefficient of maple wood) is 0.0000064, this correction amounts to about two per cent a t the highest temperatures, and i t may, if desired, be neglected. However, inasmuch as it involves the multiplication of each pressure by a factor which is constant at each temperature, it is convenient to include it with the constant factor, R, in equation (1) and with the constant, 4, in equation (3). 3. Owing to the expansion of the glass, the volume of the eudiometer changes as a result of its expansion. Since, however, the cubical coefficient of glass is only about 0.000028, this correction amounts to no more than 0.2 per cent a t 90°C. and it can generally be neglected. RESULTS
The results of a single afternoon's experimenting are given in Table 1. The pressures shown are uncorrected for the expansion of the mercury and meter stick. but this correction has been included in calculating a and K,, as described in the preceding section. The
volumes shown were corrected for the change in volume of the eudiometer as a result of attaching tube, C, but not for its change in volume as a result of thermal expansion. The condensed acetic acid occupied 57.0 divisions in the capillary and the volume of the capillary is 5.23 X lo-' cc. per division. Taking the density of acetic acid a t 25'C. as 1.03, the number of mols of (C~HIO&was, from equation (2), N =
from which A H = 15,000 cal. for the reaction (CZH~OI)~ = 2CnH102
This value of AH may well be in error by 1000 cal. or more. TABLE 2
5.23 X 1 0 - W 57.0 X 1.03 120
TABLE 1
v,cc.
1°K.
K ~ In, ,
30.95 22.'10 10.15 9.35 5.35 3.95 38.40 20.15 17.90 10.25 7.55 4.50 38.50 25.80 19.15 12.55 8.15 0.30 38.60 29.20 19.50 14.10 9.90 7.35 41.55 29.05 22.50 17.65 13.25 10.85
366.1 366.1 365.2 366.1 360.1 366.00 355.1 355.1 355.1 355.1 355.0 354.8 318.4 348.2 348.1 348.2 348.2 348.3 338.8 338.8 338.7 338.5 338.4 338.3 330.5 330.0 329.9 330.1 330.2 330.3
113.8 137.1 116.2 103.1 106.2
9"
--.A
The mean values of K, a t each temperature are given in Table 2, and Figure 3 (open circles) shows the result of plotting log K, against 1/T. The data can be represented by the equation (compare equation (4)) log K p = 10.996 -
3275
93.0 82.0 75.1 65.5 57.1
112.6 56.1 40.0 21.2 12.3
PC.
40.0 35.0 30.0 25.0
'
log K, = 11.789
Kp, mm.
.
2.08 1.37 0.909 0.547
- 3590 7
from which A H = 16,400 cal. with a possible error of 800 cal. The present results are therefore in satisfactory agreement with MacDougall's more precise data, particulaxly when it is recalled that the acetic acid used here had not been completely freed from water. CONCLUSION
1
22.7 20.2 19.5 10.8 12.5 13.4 12.9 13.0 11.4 ~- -
Kp.mm.
The molecular state of acetic acid vapor has been investigated between 25°C. and 40°C. by F. H. MacDougalll and his "best values" of K, are given in Table 3 and shown in Figure 3 by the black circles. According to MacDougall, his results can be represented by the formula
. 62.0 53.1 50.9 50.1 48.0 41.2 42.5 39.5 36.7 37.7 20.6 22.2
TABLE 3
PC.
An apparatus and experimental procedure are described with which it is possible in a short time to investigate the pressure-volume relationships of acetic acid vapor a t a number of temperatures. The results can be regarded either as a verification of the Mass Law or of the hypothesis that acetic acid v a ~ o rcontains two mole&ar species, CzH,Oz and ('&H,o~),, in chemical equilibrium. Application of the reaction isochore gives a value of the heat of reaction agreeing satisfactorily with that given in the literature. The experiment should have considerable instructional value in the undergraduate laboratory.
-
I.Am. Chem. Soc., 58,25852591
(1936).
