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The enthalpy of mixing of (acetone + trichloromethane) vapour
M-l 144 J Chem.
Therm&namics
1981, 13, 261-272
The enthalpy of mixing of (acetone + trichloromethane) J. A. DOYLE, D. J. HUTCHINGS, C. J. WORMALD
J. C. MAYR,
vapour and
School of Chemistry. The University, Bristol BSB ITS. U.K. (Received 10 December 1979; in revised.form II August 1980) Measurements of the excess enthalpy of (acetone + trichloromethane) vapour have been made using a new differential flow calorimeter. The measurements cover the range 323.3 to 393.2 K at pressures between 34.3 and 104.5 kPa. The accuracy of the measurements is _+2 per cent. Crossterm second virial coefficients B,, derived from the measurements are in good agreement with B,,‘s obtained from excess-volume measurements.
1. Introduction The first measurements of the excess enthalpy HE of fxCH,COCH, + (1 - x)CHCl,) vapour previously reported”) were made using a flow calorimetric apparatus which has subsequently been greatly improved. The interpretation of the HE measurements requires an accurate knowledge of either the second virial coefficient B or of the isothermal Joule-Thomson coefficient 4 of the pure components. While virial coefficient measurements for both acetone and trichloromethane are subject to errors due to adsorption and to reaction with mercury, measurements of 4 are not and, for acetone and trichloromethane, measurements of 4 have been reported recently.‘2’ Measurements of E = B,,- (B, 1+ B,,)/2, for (CH,COCH, + CHCl,) have also been reported recently. (3) New measurements of HE for {xCH,COCH, + (I- x)CHCl,} vapour have now been made, and a better method for the analysis of the results than was used originally”) has been developed. 2. The flow system A new flow calorimetric apparatus, incorporating several features of an apparatust4’ developed for the measurement of Joule-Thomson coefficients, has been built and is shown in figure 1. Vapour is produced in boiler 1. The way in which the boiler operates to degas the liquid and produce air-free vapour has been described.t4’ Vapour flows through heat-exchange coil 2 and needle valve 3 which are mounted in a small thermostatted bath. Valve 3 controls the flow rate. The vapour then flows through heat-exchange coil 4 and enters the mixing calorimeter in the main thermostat which is held constant to kO.005 K. A similar boiler and valve supply the second component vapour to heat-exchange coil 5. The vapours mix in calorimeter 6 0021-9614/81/030261+
12 %01.00/O
t‘ 1981 Academic Press Inc. (London) Ltd.
262
J. A. DOYLE
ET AL.
where the temperature is sensed by a four-junction thermopile. When the mixing is endothermic, as with the (methane + n-alkane) mixtures reported previously!” the power supplied to a heater fixed in the centre of the mixing chamber is adjusted until the temperature of the outflowing mixture equals that of the inflowing pure components. The pressure in the calorimeter is measured by a mercury manometer connected at 7. To prevent condensation of vapour on the mercury surface, the manometer is heated. The mixture next flows through heat exchanger 8, the stream is split at 9, and the mixture enters a second calorimeter 10 which was constructed to be as nearly identical with the first calorimeter as possible. The thermocouples of the first calorimeter 6 can be connected in series with those of second calorimeter 10. The advantage of this arrangement when it was used previouslyC5’ was that any unwanted effects, such as the Joule-Thomson effect, due to pressure gradients in the mixing -
15
14
1 FIGURE 1. The flow system and differential calorimeter.
calorimeter were cancelled out. The advantage in the present work is that the enthalpy of exothermic processes can be measured. When acetone and trichloromethane vapours are mixed, the temperature rise is sensed by the thermocouples of the first calorimeter. The vapour is restored to thermostat temperature by heat-exchange coil 8 and power is supplied to the heater of the second calorimeter until the temperature rise in this calorimeter matches that in the first calorimeter. With the thermocouples of the two calorimeters connected in series so that the e.m.f.‘s oppose each other (differential mode), this condition is indicated when the attached galvanometer reads zero. The mixture leaving calorimeter 10 is condensed at 11, and the volumetric flow rate is measured in calibrated bulbs 12. The bulbs can be drained into vessel 13 from which a sample of condensate can be removed and the composition of the mixture determined by density. The outlet pressure is measured on manometer 14, and a vacuum pump and controller are connected at 15. While the previous apparatusC5’ operated only at atmospheric pressure, the present apparatus works at pressures below atmospheric. As the saturation pressure of the least-volatile component determines the minimum temperature, this apparatus can work at lower temperatures than previously.
EXCESS ENTHALPIES
OF (ACETONE
263
+ TRICHLOROMETHANE)
3. Construction and testing of the differential flow calorimeter The design of the calorimeters is shown in figure 2 and is inherently better than that described previously. (V Mixing of the components occurs in the centre of the calorimeter over heater 1, the flow is reversed over the outside of the heater by a cylindrical tufnol baflle 2, and is reversed again over the outside of the baffle. The mixture is forced to take a spiral path over the outside of the baffle by a length of woven glass sleeve 3 wound in a helix around the baffle. This design ensures that temperature gradients are confined to the centre of the calorimeter and, for endothermic processes, the mixture in contact with the calorimeter wall is almost at the thermostat temperature. Copper gauze discs 4 ensure that the gas stream flows over thermocouples 5 at uniform speed, and that any heat conducted up electrical lead 6 is returned to the gas stream. The calorimeter body is made of glass and is surrounded by a silvered vacuum jacket 7. Two calorimeters were constructed simultaneously so that a well-matched pair was obtained. Before the calorimeters were sealed into their vacuum jackets the pressure drop across each was measured when air was passed through at a rate of 0.3 dm3 s- ‘. Small adjustments were then made to the calorimeters so that the pressure drop across the first differed by no more than 2 per cent from that across the second. The first test of the differential arrangement was to pass acetone vapour through the two calorimeters at a flow rate approximately three times as fast as was used for mixing runs. As acetone has a large Joule-Thomson coefficient, it is an excellent fluid with which to test for the presence of Joule-Thomson effects in the calorimeter. When the thermocouples of each calorimeter were connected in turn to a galvanometer, a small Joule-Thomson effect was detected. However, when thermocouples were connected in differential mode, the galvanometer deflection was negligible. The second test was again done using acetone vapour. While power was supplied at a constant rate to the heater of the first calorimeter, the power supplied to the second calorimeter was adjusted until the galvanometer connected to the differential thermocouples was restored to zero. This test was repeated over a range of flow rate ; particular care was taken with measurements at low flow rates. The power supplied to the two calorimeters was never found to differ by more than 0.5 per cent. This test not
0
,
.
.
FIGURE 2. Construction of the mixing calorimeter.
.
5cm I
J. A. DOYLE
264
ET
A.!,.
only confirms that the heat leaks in the two calorimeters are near enough the same. but also confirms that the heat-exchange coil 8 linking the two calorimeters is efficient.
4. Experimental results Acetone and trichloromethane were purified as described previously!” The chloroform was stabilized by the addition of 1 mole per cent of ethanol. It was shown previously (‘) that vapour leaving the boiler contained less than 0.1 mole per cent of ethanol and that the error introduced was negligible. Runs were done at flow rates between 0.7 and 1.9 mmol s- ’ and no dependence of HE upon flow rate was found. The results of our measurements are listed in table 1. The table includes TABLE 1. Results of measurements of {xCH,COCH, + (1 -x)CHCl,j. Results at 353.2, 363.2, and 373.2 K and at a pressure of 101.3 kPa were obtained using a previous apparatus (reference 1)
x
HE Jmol-’
P kPa
HE/4x(l
-x)
x
J mol-’
HE/4x(l- u)
HE
P
J mol-’
kPa
J mol-’
323.3 K 0.392 0.395 0.470
- 123.8 - 118.4 - 122.2
46.1 44.9 43.1
- 125.3 - 122.7 - 126.5
0.502 0.619 0.625
- 117.0 - 108.6 -113.6
44.1 43.5 45.2
- 118.0 - 117.8 - 119.2
0.401 0.408 0.496
-84.4 -88.7 -91.9
43.2 44.9 42.6
-87.8 -88.4 -93.1
0.508 0.547 0.567
-94.4 - 86.7 -82.7
44.4 42.4 42.6
-91.8 -89.1 -85.3
0.562
- 111.8
60.8
- 114.2
0.578
- 111.5
60.8
-113.5
0.427 0.431 0.432 0.443
-62.8 -63.1 - 64.9 -64.6
38.2 39.5 40.1 39.7
- 66.0 -64.0 -64.8 -64.7
0.481 0.506 0.569 0.599
-63.6 -64.7 - 64.4 -63.9
38.2 40.1 38.9 39.9
-65.5 -63.4 - 66.2 -65.4
0.349 0.410 0.416
- 127.2 - 136.7 - 135.1
87.8 87.4 87.4
- 139.7 - 141.6 - 139.4
0.426 0.443 0.476
- 136.8 - 137.2 - 139.5
87.4 87.7 87.8
- 140.2 - 138.7 - 139.5
0.454 0.466 0.483 0.500
-48.6 -49.5 -46.1 -47.4
34.0 36.1 34.2 33.9
-49.9 -47.2 -46.4 -48.0
0.531 0.565 0.593
-46.5 -46.4 -46.6
34.3 34.0 33.8
- 46.7 -47.6 -49.0
0.396 0.427 0.446 0.473
-61.8 - 64.4 -64.1 -64.5
44.3 45.4 45.9 46.1
-67.1 - 66.5 -64.8 -64.4
0.498 0.514 0.525 0.559
-67.1 -66.1 -65.5 -63.7
46.8 47.3 46.0 45.5
- 65.8 -64.3 -65.6 -65.2
327.8 K
333.2 K
336.5 K
338.2 K
343.2 K
EXCESS
ENTHALPIES
OF
(ACETONE
TABLE
.x
HE Jmol-’
0.401 0.432 0.477 0.494
-93.8 -95.9 -95.1 -93.6
P kPa
HE/4x(l
-x
265
+ TRICHLOROMETHANE)
l-continued I
HE
HE/4x(l
--x)
J mol-’
P kPa
0.503 0.526 0.536 0.595
-93.5 -95.3 -94.6 -90.8
66.3 66.5 67.0 66.6
-94.7 -96.5 -95.2 -94.9
127.0 127.1 127.1 127.5
0.476 0.484 0.399
- 126.9 - 126.2 - 121.7
88.0 88.0 88.5
- 127.7 - 126.8 - 126.5
- 151.5 - 152.4 - 152.9
0.531 0.544 0.575
- 153.1 - 150.7 - 148.2
105.0 103.9 104.0
- 153.0 - 152.8 - 152.3
J mol-’
68.1 69.0 67.2 66.5
-96.2 -95.1 -95.3 -94.5
x
Jmol-’
0.432 0.434 0.455 0.468
-
125.5 125.8 125.6 126.5
88.9 88.9 88.0 88.0
0.448 0.493 0.496
- 149.8 - 152.4 - 153.8
104.5 104.5 105.1
0.467 0.512 0.526
-96.5 -97.1 -98.0
86.2 86.2 86.5
-97.1 -97.3 -98.1
0.532 0.536 0.547
-99.7 -98.6 -96.2
86.1 86.2 86.2
- 100.4 -99.2 -97.1
0.244 0.283 0.350 0.352 0.423 0.439 0.467
- 84.2 -90.3 - 103.0 - 101.6 - 108.9 - 109.7 .- 110.3
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 114.1 -111.6 - 113.2 -111.3 -111.5 -111.3 - 110.8
0.474 0.484 0.529 0.533 0.599 0.652 0.675
- 112.6 -113.3 -111.3 - 112.1 - 108.9 - 101.2 -97.9
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 112.9 - 113.4 -111.7 - 112.5 - 113.3 -111.5 - Ill.6
0.321 0.394 0.439 0.489 0.503
- 76.8 -85.7 -92.5 -93.8 -91.3
101.3 101.3 101.3 101.3 101.3
-88.0 -89.7 -93.9 -93.8 -91.4
0.554 0.560 0.662 0.732
-91.2 - 89.5 -82.0 - 70.8
101.3 101.3 101.3 101.3
-92.2 -90.8 -91.6 -90.2
0.276 0.334 0.385 0.451 0.487 0.542 0.543
- 54.7 - 62.2 - 69.9 -72.1 - 74.6 -73.1 -71.5
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 68.4 - 69.9 -73.8 - 72.8 - 74.6 -73.6 - 72.0
0.556 0.578 0.582 0.644 0.647 0.664 0.720
- 69.0 -67.6 - 69.0 - 65.0 -60.0 - 63.6 - 54.7
101.3 101.3 101.3 101.3 101.3 101.3 101.3
-69.8 - 69.3 - 70.9 - 70.9 -65.7 -71.2 - 67.8
0.477 0.482
-53.7 - 54.0
81.8 81.6
-53.7 -54.1
0.545 0.554
- 50.5 - 52.3
81.7 81.7
- 50.9 - 52.9
0.471 0.482 0.522
- 36.0 - 37.1 - 36.4
80.2 80.2 80.0
-36.1 -37.1 - 36.5
0.533 0.551
- 36.3 -33.6
80.0 80.1
- 36.4 -33.9
-
353.2 K
363.2 K
373.2 K
378.2 K
393.2 K
266
J. A. DOYLE
ET
AL
measurements which were made using a previous(‘) apparatus, and these are all at a pressure of 101.3 kPa. The pressure at which each measurement was made is listed. and the mean pressure for each set is given in table 2. As graphs of 25” against x are almost parabolic, the simplest way to find H” at x = 0.5 is to calculate HE/4.x(1 -.u) for each measurement and take the mean. The values of H”/4x( 1 - x) listed in table 1 were all calculated after first correcting the experimental values of HE to the mean pressure for each set. At 343.2 K a series of measurements was made at 5 pressures. The measurements at 104.5 kPa were done by slightly pressurising the vapour generators. Table 2 summarizes the results. TABLE T
2. HE and standard
E
(P> kPa
323.3 327.8 333.2 336.5 338.2 343.2 343.2 343.2
44.5 43.5 60.8 39.3 87.6 34.3 45.9 66.9
deviations HE(0.5) J mol-’ - 121.6 -89.2 -113.9 - 65.0 - 139.8 -47.8 -65.5 -95.3
CTfor (O.SCH,COCH, 0 J mol-’ 3.8 2.8 2.0 1.0 1.0 1.3 1.0 0.7
+ OSCHCI,) T
at the mean
(p)
pressure
(P> kPa
HE(0.5)
I?
E
J mol-’
J mol-’
343.2 343.2 353.2 353.2 363.2 373.2 378.2 393.2
88.3 104.5 86.4 101.3 101.3 101.3 81.7 80.1
- 127.1 - 152.5 -98.2 -111.6 -91.3 -71.2 - 52.9 - 36.0
0.4 0.6 1.4 1.5 1.9 2.5 1.4 1.2
5. Analysis of the measurements The excess enthalpy of a binary gaseous mixture densities is given by the equation:c5) HE = XIX,P(~~I,-~,,
-~22)-(p2/RT)(B,~,-xlB11~11
of components
1 and 2 at low
-~2B22$22),
(1)
where 4 = B-TdBfdT, B, = x:.B,,+2x,x,B,,+x~B,,,
(2) (3)
and 4, is given by an expression similar to (3). As 4r r , B, r , &22, and B,, for acetone and trichloromethane have been measuredt2) the only unknowns in equations (1) and (3) are B,, and 412. While 4r1 and 422 for the pure components can be fitted with the Stockmayer potential, +r2 for (CH,COCH, + CHCI,) is much more negative than 4 for either of the pure components and cannot be fitted using this potential. To obtain B12 and A2, a modification of the method employed by Al-Bizreh and Wormald’4r to obtain values of B from measurements of 4 was used. Deviations of the second virial coefficients of n-alkanes from the principle of corresponding states were correlated by McGlashan and Potter@) using a parameter N which is the number of carbon atoms in the alkane. Guggenheim and Wormald”) noted that for substances other than alkanes an effective value of N could be chosen. We extend the method of Al-Bizreh
EXCESS ENTHALPIES
and Wormald’*’
OF (ACETONE
to mixtures by defining pseudo-critical
parameters:
v;, = {(v,“l)1’3+(v;2)l’3}3/8.
T2 = VT1m1’2, The deviation equation :
267
+ TRICHLOROMETHANE)
of B12 from the principle
of corresponding
(4)
states is expressed by the
= O.O375(N- NT&/T)?
(B,, -BJVf2
(5)
where B,, is the second virial coefficient of a fluid which obeys the principle, and h are adjustable parameters. B,, is calculated from the equation:‘“’
and N
B,,/I’f/,‘, = 0.430 - 0.886(T,“,/T) - 0.694( T;JT)‘.
(6)
From equations (2) and (5) it follows that (d)lz-#cs)/V,c, = 0.0375(1 +bW-
1)(T;2/Wb,
(7)
where 4,, is obtained from (6) using equation (2). The p2 term in equation (1) is small compared with the term in p and, to a first approximation, it can be neglected. Using and 422 for CH,COCH, and CHC13’2’ and the HE’s listed in table 1, 4 11 approximate $Q~‘s were calculated. Parameters b and N which fitted values of (4r 2 - ticS)/Vf2 were found, and B, 2’s were calculated from equation (5). The p2 term in equation (1) was next calculated, subtracted from HE, and new values of +r2 were obtained. Four cycles of this iterative procedure were required before constant values and the parameters b and N were obtained. With Tf2 = 522.9 K and of 429 4127 Vt, = 224.1 cm 3 mol -l, the final values of b and N were 7.0 and 5.26 respectively. The results of the analysis are summarized in table 3. The HE(l)% are calculated from the experimental values of the excess enthalpy at x = 0.5 given in table 2 and are obtained by scaling these values up to a pressure of 101.325 kPa using equation ( 1) to TABLE 3. Results of the analysis of the HE measurements. HE(l ) is obtained from the experimental results listed in table 1 by interpolation to x = 0.5 and extrapolation to a pressure of 101.325 kPa. HE(O) is obtained by subtracting the p2 term in equation (1) from HE(l). o is calculated from column 4 of table 2 and is the standard deviation on HE(l ) T
HE(l)
K
J rnol-.t
323.3 327.8 333.2 336.5 338.2 343.2 353.2 363.2 373.2 378.2 393.2
- 276.8 - 217.0 - 193.8 - 172.3 - 162.7 - 147.2” -113.3b -91.3 -71.2 -62.4 -45.7
CJ
-J mol-’ 8.9 6.8 3.4 2.6 1.2 1.7 1.6 1.9 2.5 1.5 1.5
HE(O)
J mol-’ -
259.6 202.8 182.6 162.5 153.6 139.7 108.1 -87.7 -68.6 - 60.2 -44.4
~- 4 12 cm3 mol-’ - 10591 -9143 - 8399 -7812 -7523 - 7002 - 5906 -5118 -4409 -4096 -3411
WI2
cm3 molJ’
___--B I?. cm3 mol-’
285 246 163 143 127 119 107 105 111 90 81
’ Calculated from the measurements at the 5 pressures listed in table 2. ’ Calculated from the two sets of measurements at 353.2 K listed in table 2. 17
-
1735 1543 1439 1358 1319 1243 1087 -971 - 866 -819 -712
___.@I, cm3 molt ’ 40
34 23 20 17 17 15 15 17 14 13
268
J. A. DOYLE
ET
AL
calculate the pz term. HE(O) is obtained by subtracting the p* term of equation (1) from HE(l) and facilitates easy calculation of 4,2. At 323.3 K the p* term is 7 per cent ofHE and at 393.2 K it is 2.8 per cent. Values of 41 1 and 422 were calculated using parameters of the Stockmayer potential fitted to measurements of # for acetone and trichloromethane.“) The uncertainty 61$,, on $,2 was calculated from the standard deviation 0 on HE(l) together with an uncertainty on both 41 1 and $2r of 2 per cent. In the calculation of the p2 term it was assumed that contributions from third virial coefficients are negligible. If this is not so, an additional termc5’ must be included in equation (1). Measurements of the pressure dependence of 4 for CH,COCH, and CHCl, made previously suggest that (C-0.5TdC/dT) for the pure components is small. To investigate the contribution to HE arising from cross-term third virial coefficients, a series of careful measurements of HE was made at 343.2 K over a range of pressure. Figure 3 shows these measurements, interpolated to x = 0.5, plotted against pressure. The solid curve in the figure is calculated from equation (1) and the dashed straight line is the first term of equation (1) only. At pressures below 50 kPa the error on the measurements is greater than the difference between the two lines. The contribution of the p2 term can be seen more clearly on a plot of HE/p against p as shown in figure 4. The error bars in the figure are calculated from the standard deviations d listed in table 2, and the way in which the uncertainty in HE/p increases at low pressure is clearly shown. The solid line is calculated from equation (1) and the horizontal lower dashed line is the first term of this equation only. The upper dashed
FIGURE 3. Comparison of the excess enthalpies HE for (O.SCH,COCH, + OXHCI,) in table 2 with equation (1). The solid curve is calculated from equation (1) and calculated from the first term of the equation.
at 343.2 K listed the broken line is
EXCESS ENTHALPIES
OF (ACETONE
+ TRICHLOROMETHANE)
269
FIGURE 4. Comparison of HE/p for (O.SCH,COCH, + O.SCHCI,) at 343.2 K listed in table 2 with equation (1). The solid line is calculated from equation (1) while the horizontal broken line is calculated from the first term of this equation. The upper broken line is a least-squares fit to the experimental points.
line is a least-squares line through the points. The solid line is not coincident with the least-squares line because results at all temperatures were used to determine the parameters of equation (1) whereas only results at 343.2 K were used to obtain the least-squares line. The important feature of figure 4 is that the least-squares line through the points is almost parallel to the solid line calculated using the pz term in equation (1). If the contribution of third virial coefficients to HE is zero, the leastsquares line should be exactly parallel to the solid line. We conclude that to within the accuracy of our measurements the contribution of third virial coefficients is negligible. Figure 4 illustrates a further point. From equation (1) the zero-pressure limit of ME/p = x1x2(24,, -C#J~~-c#J~~). This implies that, at each temperature, measurements of HE should be made over a range of pressure and the zero-pressure limit obtained. That this is not a good procedure is shown by the way in which the uncertainty in HE/p increases as the pressure is reduced. Our procedure of measuring HE in the region of atmospheric pressure and obtaining HE(O) subtracting the p2 term is more accurate and requires fewer measurements. 6. Cross-term
second virial
coefficients
Values of RI2 were obtained from the 4lZ’s listed in table 3 using equation (7) with b = 7.0. At each temperature 412 was put into equation (7), a value of N was obtained, and B, Z was calculated from equation (5). The B, *‘s are listed in table 3. An
J. A. DOYLE
270
ET AL.
equation for B,, can be obtained by combining and b= 7.0: &,/cm3
mol-’
= 96.4- 1.038 x 105(K/T)-4.253
equations (5) and (6) with N = 5.26 x lO’(K/T)’ -3.789 x lO*‘(K/T)‘.
The uncertainty
SB,, in B,, arising from the uncertainty
(8)
&$I,, in 4r2 is given by
= s#l,(dB,,/dT)(d~,,/dT)‘. (9) The temperature derivatives in equation (9) were calculated from equation (8). The uncertainties U?,, are listed in table 3 and are between 2 and 3 per cent. 642
7. Comparison with other work The first measurements of excess enthalpy for (acetone + trichloromethane)(‘) reported in 1969 were made using a simpler calorimeter and flow system. The 1969 HE(0.5) measurements made at temperatures of 353.2, 363.2, and 373.2 K are -(113+2), -(92f2), and -(73+2)Jmol-‘. The excellent agreement with the present work is shown in figure 5. The solid line in this figure is calculated from equation (1).
FIGURE 5. The excess enthalpy HE of (O.SCH,COCH, + OSCHCI,) calculated from equation (1) compared with experiment. 0. this work. a, reference 1.
EXCESS ENTHALPIES
j./
OF (ACETONE
, 300
+ TRICHLOROMETHANE)
, 340
,
271
; 380
T/K FIGURE 6. The cross-term second virial coefficient B,, calculated from equation (8) compared with experiment. 0, this work. 0, reference 3. A, reference 8.
Comparison of B,,‘s calculated from our measurements with other work is shown in figure 6 where the solid line is calculated from equation (8). While the results of Zaalishvili and Kolysko@) are in fair agreement with this work the B, 2’s obtained by Pasco, Handa, Scott, and Knobler’3’ obtained by direct measurement of the excess second virial coefficient are in very close agreement, well within the limits of error on both measurements. Pasco, Handa, Scott, and Knoblerc3’ analysed their excess virial-coefficient measurements in terms of an association treatment”’ and obtained AHe = -20 kJ mol-’ for the standard enthalpy of formation of the acetone + trichloromethane hydrogen bond which they compare with the enthalpy of mixing measurements of Mayhew”‘) who obtained -(21+3) kJ mol-’ at 323 K and - (19+3) kJ mol-’ at 343 K. If we use this approach we obtain AHe = -(19.4&0.5) kJ mol-’ and for the equilibrium constant we obtain K, = 1.503 MPa-’ at 298.15 K.
REFERENCES 1 Wormald, C. J. Proceedings of the 1st Internarional Conference Calorimetry and Thermodynamics. Polish Scientific Publishers : Warsaw. 1969,601. 2. WormaId, C. J. J. Chem. Thermodynamics 1979, 11, 1127. 3. Pasco, N. F.; Handa, Y. P.; Scott, R. L.; Knobler, C. M. J. Chem. Thermodynamics 1980, 1, 11. 4. Al-Bizreh, N.; Wormald, C. J. J. Chem. Thermodymzmics 1978, 10, 231. 5. Hutchings, D. J.; Lewis, E. J.; Wormald, C. J. J. Chem. Thermodynamics 1978, 10, 559. 6 McGlashan, M. L.; Potter, D. J. B. Proc. R. Sot. London Ser. A. 1962, 267,478.
272
J. A. DOYLE
ET AL.
7. Guggenheim, E. A.; Wormald. C. J. J. Chem. Phys. 1%5, 42, 3776. 8. Zaalishvili, Sh. D.: Kolysko, L. E. Russ. J. Phys. Chem. 1961, 35, 1291. 9. Lambert, J. D.: Roberts, G. A. H.; Rowlinson. J. W.; Wilkinson, V. J. Proc. R. .Soc London 1949, 196, 113. 10. Mayhew, C. J. Ph.D. Thesis, University of Canterbury, N.Z. 1978.
Ser. .4
Therm&namics
1981, 13, 261-272
The enthalpy of mixing of (acetone + trichloromethane) J. A. DOYLE, D. J. HUTCHINGS, C. J. WORMALD
J. C. MAYR,
vapour and
School of Chemistry. The University, Bristol BSB ITS. U.K. (Received 10 December 1979; in revised.form II August 1980) Measurements of the excess enthalpy of (acetone + trichloromethane) vapour have been made using a new differential flow calorimeter. The measurements cover the range 323.3 to 393.2 K at pressures between 34.3 and 104.5 kPa. The accuracy of the measurements is _+2 per cent. Crossterm second virial coefficients B,, derived from the measurements are in good agreement with B,,‘s obtained from excess-volume measurements.
1. Introduction The first measurements of the excess enthalpy HE of fxCH,COCH, + (1 - x)CHCl,) vapour previously reported”) were made using a flow calorimetric apparatus which has subsequently been greatly improved. The interpretation of the HE measurements requires an accurate knowledge of either the second virial coefficient B or of the isothermal Joule-Thomson coefficient 4 of the pure components. While virial coefficient measurements for both acetone and trichloromethane are subject to errors due to adsorption and to reaction with mercury, measurements of 4 are not and, for acetone and trichloromethane, measurements of 4 have been reported recently.‘2’ Measurements of E = B,,- (B, 1+ B,,)/2, for (CH,COCH, + CHCl,) have also been reported recently. (3) New measurements of HE for {xCH,COCH, + (I- x)CHCl,} vapour have now been made, and a better method for the analysis of the results than was used originally”) has been developed. 2. The flow system A new flow calorimetric apparatus, incorporating several features of an apparatust4’ developed for the measurement of Joule-Thomson coefficients, has been built and is shown in figure 1. Vapour is produced in boiler 1. The way in which the boiler operates to degas the liquid and produce air-free vapour has been described.t4’ Vapour flows through heat-exchange coil 2 and needle valve 3 which are mounted in a small thermostatted bath. Valve 3 controls the flow rate. The vapour then flows through heat-exchange coil 4 and enters the mixing calorimeter in the main thermostat which is held constant to kO.005 K. A similar boiler and valve supply the second component vapour to heat-exchange coil 5. The vapours mix in calorimeter 6 0021-9614/81/030261+
12 %01.00/O
t‘ 1981 Academic Press Inc. (London) Ltd.
262
J. A. DOYLE
ET AL.
where the temperature is sensed by a four-junction thermopile. When the mixing is endothermic, as with the (methane + n-alkane) mixtures reported previously!” the power supplied to a heater fixed in the centre of the mixing chamber is adjusted until the temperature of the outflowing mixture equals that of the inflowing pure components. The pressure in the calorimeter is measured by a mercury manometer connected at 7. To prevent condensation of vapour on the mercury surface, the manometer is heated. The mixture next flows through heat exchanger 8, the stream is split at 9, and the mixture enters a second calorimeter 10 which was constructed to be as nearly identical with the first calorimeter as possible. The thermocouples of the first calorimeter 6 can be connected in series with those of second calorimeter 10. The advantage of this arrangement when it was used previouslyC5’ was that any unwanted effects, such as the Joule-Thomson effect, due to pressure gradients in the mixing -
15
14
1 FIGURE 1. The flow system and differential calorimeter.
calorimeter were cancelled out. The advantage in the present work is that the enthalpy of exothermic processes can be measured. When acetone and trichloromethane vapours are mixed, the temperature rise is sensed by the thermocouples of the first calorimeter. The vapour is restored to thermostat temperature by heat-exchange coil 8 and power is supplied to the heater of the second calorimeter until the temperature rise in this calorimeter matches that in the first calorimeter. With the thermocouples of the two calorimeters connected in series so that the e.m.f.‘s oppose each other (differential mode), this condition is indicated when the attached galvanometer reads zero. The mixture leaving calorimeter 10 is condensed at 11, and the volumetric flow rate is measured in calibrated bulbs 12. The bulbs can be drained into vessel 13 from which a sample of condensate can be removed and the composition of the mixture determined by density. The outlet pressure is measured on manometer 14, and a vacuum pump and controller are connected at 15. While the previous apparatusC5’ operated only at atmospheric pressure, the present apparatus works at pressures below atmospheric. As the saturation pressure of the least-volatile component determines the minimum temperature, this apparatus can work at lower temperatures than previously.
EXCESS ENTHALPIES
OF (ACETONE
263
+ TRICHLOROMETHANE)
3. Construction and testing of the differential flow calorimeter The design of the calorimeters is shown in figure 2 and is inherently better than that described previously. (V Mixing of the components occurs in the centre of the calorimeter over heater 1, the flow is reversed over the outside of the heater by a cylindrical tufnol baflle 2, and is reversed again over the outside of the baffle. The mixture is forced to take a spiral path over the outside of the baffle by a length of woven glass sleeve 3 wound in a helix around the baffle. This design ensures that temperature gradients are confined to the centre of the calorimeter and, for endothermic processes, the mixture in contact with the calorimeter wall is almost at the thermostat temperature. Copper gauze discs 4 ensure that the gas stream flows over thermocouples 5 at uniform speed, and that any heat conducted up electrical lead 6 is returned to the gas stream. The calorimeter body is made of glass and is surrounded by a silvered vacuum jacket 7. Two calorimeters were constructed simultaneously so that a well-matched pair was obtained. Before the calorimeters were sealed into their vacuum jackets the pressure drop across each was measured when air was passed through at a rate of 0.3 dm3 s- ‘. Small adjustments were then made to the calorimeters so that the pressure drop across the first differed by no more than 2 per cent from that across the second. The first test of the differential arrangement was to pass acetone vapour through the two calorimeters at a flow rate approximately three times as fast as was used for mixing runs. As acetone has a large Joule-Thomson coefficient, it is an excellent fluid with which to test for the presence of Joule-Thomson effects in the calorimeter. When the thermocouples of each calorimeter were connected in turn to a galvanometer, a small Joule-Thomson effect was detected. However, when thermocouples were connected in differential mode, the galvanometer deflection was negligible. The second test was again done using acetone vapour. While power was supplied at a constant rate to the heater of the first calorimeter, the power supplied to the second calorimeter was adjusted until the galvanometer connected to the differential thermocouples was restored to zero. This test was repeated over a range of flow rate ; particular care was taken with measurements at low flow rates. The power supplied to the two calorimeters was never found to differ by more than 0.5 per cent. This test not
0
,
.
.
FIGURE 2. Construction of the mixing calorimeter.
.
5cm I
J. A. DOYLE
264
ET
A.!,.
only confirms that the heat leaks in the two calorimeters are near enough the same. but also confirms that the heat-exchange coil 8 linking the two calorimeters is efficient.
4. Experimental results Acetone and trichloromethane were purified as described previously!” The chloroform was stabilized by the addition of 1 mole per cent of ethanol. It was shown previously (‘) that vapour leaving the boiler contained less than 0.1 mole per cent of ethanol and that the error introduced was negligible. Runs were done at flow rates between 0.7 and 1.9 mmol s- ’ and no dependence of HE upon flow rate was found. The results of our measurements are listed in table 1. The table includes TABLE 1. Results of measurements of {xCH,COCH, + (1 -x)CHCl,j. Results at 353.2, 363.2, and 373.2 K and at a pressure of 101.3 kPa were obtained using a previous apparatus (reference 1)
x
HE Jmol-’
P kPa
HE/4x(l
-x)
x
J mol-’
HE/4x(l- u)
HE
P
J mol-’
kPa
J mol-’
323.3 K 0.392 0.395 0.470
- 123.8 - 118.4 - 122.2
46.1 44.9 43.1
- 125.3 - 122.7 - 126.5
0.502 0.619 0.625
- 117.0 - 108.6 -113.6
44.1 43.5 45.2
- 118.0 - 117.8 - 119.2
0.401 0.408 0.496
-84.4 -88.7 -91.9
43.2 44.9 42.6
-87.8 -88.4 -93.1
0.508 0.547 0.567
-94.4 - 86.7 -82.7
44.4 42.4 42.6
-91.8 -89.1 -85.3
0.562
- 111.8
60.8
- 114.2
0.578
- 111.5
60.8
-113.5
0.427 0.431 0.432 0.443
-62.8 -63.1 - 64.9 -64.6
38.2 39.5 40.1 39.7
- 66.0 -64.0 -64.8 -64.7
0.481 0.506 0.569 0.599
-63.6 -64.7 - 64.4 -63.9
38.2 40.1 38.9 39.9
-65.5 -63.4 - 66.2 -65.4
0.349 0.410 0.416
- 127.2 - 136.7 - 135.1
87.8 87.4 87.4
- 139.7 - 141.6 - 139.4
0.426 0.443 0.476
- 136.8 - 137.2 - 139.5
87.4 87.7 87.8
- 140.2 - 138.7 - 139.5
0.454 0.466 0.483 0.500
-48.6 -49.5 -46.1 -47.4
34.0 36.1 34.2 33.9
-49.9 -47.2 -46.4 -48.0
0.531 0.565 0.593
-46.5 -46.4 -46.6
34.3 34.0 33.8
- 46.7 -47.6 -49.0
0.396 0.427 0.446 0.473
-61.8 - 64.4 -64.1 -64.5
44.3 45.4 45.9 46.1
-67.1 - 66.5 -64.8 -64.4
0.498 0.514 0.525 0.559
-67.1 -66.1 -65.5 -63.7
46.8 47.3 46.0 45.5
- 65.8 -64.3 -65.6 -65.2
327.8 K
333.2 K
336.5 K
338.2 K
343.2 K
EXCESS
ENTHALPIES
OF
(ACETONE
TABLE
.x
HE Jmol-’
0.401 0.432 0.477 0.494
-93.8 -95.9 -95.1 -93.6
P kPa
HE/4x(l
-x
265
+ TRICHLOROMETHANE)
l-continued I
HE
HE/4x(l
--x)
J mol-’
P kPa
0.503 0.526 0.536 0.595
-93.5 -95.3 -94.6 -90.8
66.3 66.5 67.0 66.6
-94.7 -96.5 -95.2 -94.9
127.0 127.1 127.1 127.5
0.476 0.484 0.399
- 126.9 - 126.2 - 121.7
88.0 88.0 88.5
- 127.7 - 126.8 - 126.5
- 151.5 - 152.4 - 152.9
0.531 0.544 0.575
- 153.1 - 150.7 - 148.2
105.0 103.9 104.0
- 153.0 - 152.8 - 152.3
J mol-’
68.1 69.0 67.2 66.5
-96.2 -95.1 -95.3 -94.5
x
Jmol-’
0.432 0.434 0.455 0.468
-
125.5 125.8 125.6 126.5
88.9 88.9 88.0 88.0
0.448 0.493 0.496
- 149.8 - 152.4 - 153.8
104.5 104.5 105.1
0.467 0.512 0.526
-96.5 -97.1 -98.0
86.2 86.2 86.5
-97.1 -97.3 -98.1
0.532 0.536 0.547
-99.7 -98.6 -96.2
86.1 86.2 86.2
- 100.4 -99.2 -97.1
0.244 0.283 0.350 0.352 0.423 0.439 0.467
- 84.2 -90.3 - 103.0 - 101.6 - 108.9 - 109.7 .- 110.3
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 114.1 -111.6 - 113.2 -111.3 -111.5 -111.3 - 110.8
0.474 0.484 0.529 0.533 0.599 0.652 0.675
- 112.6 -113.3 -111.3 - 112.1 - 108.9 - 101.2 -97.9
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 112.9 - 113.4 -111.7 - 112.5 - 113.3 -111.5 - Ill.6
0.321 0.394 0.439 0.489 0.503
- 76.8 -85.7 -92.5 -93.8 -91.3
101.3 101.3 101.3 101.3 101.3
-88.0 -89.7 -93.9 -93.8 -91.4
0.554 0.560 0.662 0.732
-91.2 - 89.5 -82.0 - 70.8
101.3 101.3 101.3 101.3
-92.2 -90.8 -91.6 -90.2
0.276 0.334 0.385 0.451 0.487 0.542 0.543
- 54.7 - 62.2 - 69.9 -72.1 - 74.6 -73.1 -71.5
101.3 101.3 101.3 101.3 101.3 101.3 101.3
- 68.4 - 69.9 -73.8 - 72.8 - 74.6 -73.6 - 72.0
0.556 0.578 0.582 0.644 0.647 0.664 0.720
- 69.0 -67.6 - 69.0 - 65.0 -60.0 - 63.6 - 54.7
101.3 101.3 101.3 101.3 101.3 101.3 101.3
-69.8 - 69.3 - 70.9 - 70.9 -65.7 -71.2 - 67.8
0.477 0.482
-53.7 - 54.0
81.8 81.6
-53.7 -54.1
0.545 0.554
- 50.5 - 52.3
81.7 81.7
- 50.9 - 52.9
0.471 0.482 0.522
- 36.0 - 37.1 - 36.4
80.2 80.2 80.0
-36.1 -37.1 - 36.5
0.533 0.551
- 36.3 -33.6
80.0 80.1
- 36.4 -33.9
-
353.2 K
363.2 K
373.2 K
378.2 K
393.2 K
266
J. A. DOYLE
ET
AL
measurements which were made using a previous(‘) apparatus, and these are all at a pressure of 101.3 kPa. The pressure at which each measurement was made is listed. and the mean pressure for each set is given in table 2. As graphs of 25” against x are almost parabolic, the simplest way to find H” at x = 0.5 is to calculate HE/4.x(1 -.u) for each measurement and take the mean. The values of H”/4x( 1 - x) listed in table 1 were all calculated after first correcting the experimental values of HE to the mean pressure for each set. At 343.2 K a series of measurements was made at 5 pressures. The measurements at 104.5 kPa were done by slightly pressurising the vapour generators. Table 2 summarizes the results. TABLE T
2. HE and standard
E
(P> kPa
323.3 327.8 333.2 336.5 338.2 343.2 343.2 343.2
44.5 43.5 60.8 39.3 87.6 34.3 45.9 66.9
deviations HE(0.5) J mol-’ - 121.6 -89.2 -113.9 - 65.0 - 139.8 -47.8 -65.5 -95.3
CTfor (O.SCH,COCH, 0 J mol-’ 3.8 2.8 2.0 1.0 1.0 1.3 1.0 0.7
+ OSCHCI,) T
at the mean
(p)
pressure
(P> kPa
HE(0.5)
I?
E
J mol-’
J mol-’
343.2 343.2 353.2 353.2 363.2 373.2 378.2 393.2
88.3 104.5 86.4 101.3 101.3 101.3 81.7 80.1
- 127.1 - 152.5 -98.2 -111.6 -91.3 -71.2 - 52.9 - 36.0
0.4 0.6 1.4 1.5 1.9 2.5 1.4 1.2
5. Analysis of the measurements The excess enthalpy of a binary gaseous mixture densities is given by the equation:c5) HE = XIX,P(~~I,-~,,
-~22)-(p2/RT)(B,~,-xlB11~11
of components
1 and 2 at low
-~2B22$22),
(1)
where 4 = B-TdBfdT, B, = x:.B,,+2x,x,B,,+x~B,,,
(2) (3)
and 4, is given by an expression similar to (3). As 4r r , B, r , &22, and B,, for acetone and trichloromethane have been measuredt2) the only unknowns in equations (1) and (3) are B,, and 412. While 4r1 and 422 for the pure components can be fitted with the Stockmayer potential, +r2 for (CH,COCH, + CHCI,) is much more negative than 4 for either of the pure components and cannot be fitted using this potential. To obtain B12 and A2, a modification of the method employed by Al-Bizreh and Wormald’4r to obtain values of B from measurements of 4 was used. Deviations of the second virial coefficients of n-alkanes from the principle of corresponding states were correlated by McGlashan and Potter@) using a parameter N which is the number of carbon atoms in the alkane. Guggenheim and Wormald”) noted that for substances other than alkanes an effective value of N could be chosen. We extend the method of Al-Bizreh
EXCESS ENTHALPIES
and Wormald’*’
OF (ACETONE
to mixtures by defining pseudo-critical
parameters:
v;, = {(v,“l)1’3+(v;2)l’3}3/8.
T2 = VT1m1’2, The deviation equation :
267
+ TRICHLOROMETHANE)
of B12 from the principle
of corresponding
(4)
states is expressed by the
= O.O375(N- NT&/T)?
(B,, -BJVf2
(5)
where B,, is the second virial coefficient of a fluid which obeys the principle, and h are adjustable parameters. B,, is calculated from the equation:‘“’
and N
B,,/I’f/,‘, = 0.430 - 0.886(T,“,/T) - 0.694( T;JT)‘.
(6)
From equations (2) and (5) it follows that (d)lz-#cs)/V,c, = 0.0375(1 +bW-
1)(T;2/Wb,
(7)
where 4,, is obtained from (6) using equation (2). The p2 term in equation (1) is small compared with the term in p and, to a first approximation, it can be neglected. Using and 422 for CH,COCH, and CHC13’2’ and the HE’s listed in table 1, 4 11 approximate $Q~‘s were calculated. Parameters b and N which fitted values of (4r 2 - ticS)/Vf2 were found, and B, 2’s were calculated from equation (5). The p2 term in equation (1) was next calculated, subtracted from HE, and new values of +r2 were obtained. Four cycles of this iterative procedure were required before constant values and the parameters b and N were obtained. With Tf2 = 522.9 K and of 429 4127 Vt, = 224.1 cm 3 mol -l, the final values of b and N were 7.0 and 5.26 respectively. The results of the analysis are summarized in table 3. The HE(l)% are calculated from the experimental values of the excess enthalpy at x = 0.5 given in table 2 and are obtained by scaling these values up to a pressure of 101.325 kPa using equation ( 1) to TABLE 3. Results of the analysis of the HE measurements. HE(l ) is obtained from the experimental results listed in table 1 by interpolation to x = 0.5 and extrapolation to a pressure of 101.325 kPa. HE(O) is obtained by subtracting the p2 term in equation (1) from HE(l). o is calculated from column 4 of table 2 and is the standard deviation on HE(l ) T
HE(l)
K
J rnol-.t
323.3 327.8 333.2 336.5 338.2 343.2 353.2 363.2 373.2 378.2 393.2
- 276.8 - 217.0 - 193.8 - 172.3 - 162.7 - 147.2” -113.3b -91.3 -71.2 -62.4 -45.7
CJ
-J mol-’ 8.9 6.8 3.4 2.6 1.2 1.7 1.6 1.9 2.5 1.5 1.5
HE(O)
J mol-’ -
259.6 202.8 182.6 162.5 153.6 139.7 108.1 -87.7 -68.6 - 60.2 -44.4
~- 4 12 cm3 mol-’ - 10591 -9143 - 8399 -7812 -7523 - 7002 - 5906 -5118 -4409 -4096 -3411
WI2
cm3 molJ’
___--B I?. cm3 mol-’
285 246 163 143 127 119 107 105 111 90 81
’ Calculated from the measurements at the 5 pressures listed in table 2. ’ Calculated from the two sets of measurements at 353.2 K listed in table 2. 17
-
1735 1543 1439 1358 1319 1243 1087 -971 - 866 -819 -712
___.@I, cm3 molt ’ 40
34 23 20 17 17 15 15 17 14 13
268
J. A. DOYLE
ET
AL
calculate the pz term. HE(O) is obtained by subtracting the p* term of equation (1) from HE(l) and facilitates easy calculation of 4,2. At 323.3 K the p* term is 7 per cent ofHE and at 393.2 K it is 2.8 per cent. Values of 41 1 and 422 were calculated using parameters of the Stockmayer potential fitted to measurements of # for acetone and trichloromethane.“) The uncertainty 61$,, on $,2 was calculated from the standard deviation 0 on HE(l) together with an uncertainty on both 41 1 and $2r of 2 per cent. In the calculation of the p2 term it was assumed that contributions from third virial coefficients are negligible. If this is not so, an additional termc5’ must be included in equation (1). Measurements of the pressure dependence of 4 for CH,COCH, and CHCl, made previously suggest that (C-0.5TdC/dT) for the pure components is small. To investigate the contribution to HE arising from cross-term third virial coefficients, a series of careful measurements of HE was made at 343.2 K over a range of pressure. Figure 3 shows these measurements, interpolated to x = 0.5, plotted against pressure. The solid curve in the figure is calculated from equation (1) and the dashed straight line is the first term of equation (1) only. At pressures below 50 kPa the error on the measurements is greater than the difference between the two lines. The contribution of the p2 term can be seen more clearly on a plot of HE/p against p as shown in figure 4. The error bars in the figure are calculated from the standard deviations d listed in table 2, and the way in which the uncertainty in HE/p increases at low pressure is clearly shown. The solid line is calculated from equation (1) and the horizontal lower dashed line is the first term of this equation only. The upper dashed
FIGURE 3. Comparison of the excess enthalpies HE for (O.SCH,COCH, + OXHCI,) in table 2 with equation (1). The solid curve is calculated from equation (1) and calculated from the first term of the equation.
at 343.2 K listed the broken line is
EXCESS ENTHALPIES
OF (ACETONE
+ TRICHLOROMETHANE)
269
FIGURE 4. Comparison of HE/p for (O.SCH,COCH, + O.SCHCI,) at 343.2 K listed in table 2 with equation (1). The solid line is calculated from equation (1) while the horizontal broken line is calculated from the first term of this equation. The upper broken line is a least-squares fit to the experimental points.
line is a least-squares line through the points. The solid line is not coincident with the least-squares line because results at all temperatures were used to determine the parameters of equation (1) whereas only results at 343.2 K were used to obtain the least-squares line. The important feature of figure 4 is that the least-squares line through the points is almost parallel to the solid line calculated using the pz term in equation (1). If the contribution of third virial coefficients to HE is zero, the leastsquares line should be exactly parallel to the solid line. We conclude that to within the accuracy of our measurements the contribution of third virial coefficients is negligible. Figure 4 illustrates a further point. From equation (1) the zero-pressure limit of ME/p = x1x2(24,, -C#J~~-c#J~~). This implies that, at each temperature, measurements of HE should be made over a range of pressure and the zero-pressure limit obtained. That this is not a good procedure is shown by the way in which the uncertainty in HE/p increases as the pressure is reduced. Our procedure of measuring HE in the region of atmospheric pressure and obtaining HE(O) subtracting the p2 term is more accurate and requires fewer measurements. 6. Cross-term
second virial
coefficients
Values of RI2 were obtained from the 4lZ’s listed in table 3 using equation (7) with b = 7.0. At each temperature 412 was put into equation (7), a value of N was obtained, and B, Z was calculated from equation (5). The B, *‘s are listed in table 3. An
J. A. DOYLE
270
ET AL.
equation for B,, can be obtained by combining and b= 7.0: &,/cm3
mol-’
= 96.4- 1.038 x 105(K/T)-4.253
equations (5) and (6) with N = 5.26 x lO’(K/T)’ -3.789 x lO*‘(K/T)‘.
The uncertainty
SB,, in B,, arising from the uncertainty
(8)
&$I,, in 4r2 is given by
= s#l,(dB,,/dT)(d~,,/dT)‘. (9) The temperature derivatives in equation (9) were calculated from equation (8). The uncertainties U?,, are listed in table 3 and are between 2 and 3 per cent. 642
7. Comparison with other work The first measurements of excess enthalpy for (acetone + trichloromethane)(‘) reported in 1969 were made using a simpler calorimeter and flow system. The 1969 HE(0.5) measurements made at temperatures of 353.2, 363.2, and 373.2 K are -(113+2), -(92f2), and -(73+2)Jmol-‘. The excellent agreement with the present work is shown in figure 5. The solid line in this figure is calculated from equation (1).
FIGURE 5. The excess enthalpy HE of (O.SCH,COCH, + OSCHCI,) calculated from equation (1) compared with experiment. 0. this work. a, reference 1.
EXCESS ENTHALPIES
j./
OF (ACETONE
, 300
+ TRICHLOROMETHANE)
, 340
,
271
; 380
T/K FIGURE 6. The cross-term second virial coefficient B,, calculated from equation (8) compared with experiment. 0, this work. 0, reference 3. A, reference 8.
Comparison of B,,‘s calculated from our measurements with other work is shown in figure 6 where the solid line is calculated from equation (8). While the results of Zaalishvili and Kolysko@) are in fair agreement with this work the B, 2’s obtained by Pasco, Handa, Scott, and Knobler’3’ obtained by direct measurement of the excess second virial coefficient are in very close agreement, well within the limits of error on both measurements. Pasco, Handa, Scott, and Knoblerc3’ analysed their excess virial-coefficient measurements in terms of an association treatment”’ and obtained AHe = -20 kJ mol-’ for the standard enthalpy of formation of the acetone + trichloromethane hydrogen bond which they compare with the enthalpy of mixing measurements of Mayhew”‘) who obtained -(21+3) kJ mol-’ at 323 K and - (19+3) kJ mol-’ at 343 K. If we use this approach we obtain AHe = -(19.4&0.5) kJ mol-’ and for the equilibrium constant we obtain K, = 1.503 MPa-’ at 298.15 K.
REFERENCES 1 Wormald, C. J. Proceedings of the 1st Internarional Conference Calorimetry and Thermodynamics. Polish Scientific Publishers : Warsaw. 1969,601. 2. WormaId, C. J. J. Chem. Thermodynamics 1979, 11, 1127. 3. Pasco, N. F.; Handa, Y. P.; Scott, R. L.; Knobler, C. M. J. Chem. Thermodynamics 1980, 1, 11. 4. Al-Bizreh, N.; Wormald, C. J. J. Chem. Thermodymzmics 1978, 10, 231. 5. Hutchings, D. J.; Lewis, E. J.; Wormald, C. J. J. Chem. Thermodynamics 1978, 10, 559. 6 McGlashan, M. L.; Potter, D. J. B. Proc. R. Sot. London Ser. A. 1962, 267,478.
272
J. A. DOYLE
ET AL.
7. Guggenheim, E. A.; Wormald. C. J. J. Chem. Phys. 1%5, 42, 3776. 8. Zaalishvili, Sh. D.: Kolysko, L. E. Russ. J. Phys. Chem. 1961, 35, 1291. 9. Lambert, J. D.: Roberts, G. A. H.; Rowlinson. J. W.; Wilkinson, V. J. Proc. R. .Soc London 1949, 196, 113. 10. Mayhew, C. J. Ph.D. Thesis, University of Canterbury, N.Z. 1978.
Ser. .4