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Determination of activity coefficients at infinite dilution for each of 14 organic solutes in each of 3 organic solvents at 333.15 K by gas chromatography
M-21 17 J. Chem.
Thermodynamics
1988, 20,
119-123
Determination of activity coefficients at infinite dilution for each of 14 organic solutes in each of 3 organic solvents at 333.15 K by gas chromatography Lu HUI,” FU HAIZHANG,’
AND JIA YONGZHENb
Chemistry Department, Northwest Teachers’ College, Lunzhou, Gansu, The People’s Republic of China (Received 5 January 1987; in final form 27 May 1987) The activity coefficients of each of heptane, hexane, cyclohexane, tetrachloromethane, benzene, trichloromethane, diethyl ether, 2-propanol, I-propanol, ethanol, methanol, methyl ethanoate, propanone, and 2-butanone at infinite dilution in each of quinoline, di-n-butyl phthalate, and di-n-nonyl phthalate, have been measured at 333.15 K by g.l.c., and the molecular interactions of the components in these solutions have been discussed on the basis of the experimental results.
1. Iatrodwtion Activity coefficients at infinite dilution are important and useful properties to solution researchers. Their most interesting and successful application has been in the testing of various solution theories. This is possibly due to the infinite dilute condition-the distance between two solute molecules is infinitely great and solute-solute interactions can be neglected; we have only solute-solvent and solvent-solvent interactions, a situation which presents solution chemists with simpler theoretical treatments and fewer complications. Measuring activity coefficients at infinite dilution using g.l.c., because the results can be obtained so rapidly and accurately, has been one of the most important methods in solution research.‘rW3’
2. Experimental So that the apparatus would be suitable for physicochemical measurements the following modifications to a gas chromatograph (model 102G, Shanghai Analytical Equipment Factory, China) have been made. A precise temperature regulator (DWT-702, Jinshan Electronic Equipment Factory, Shanghai, China) was attached a Author to whom correspondence should be sent. b Students graduated from the Department in 1986. 0021-9614/88/010119+05
$02.00/O
0 1988 Acadtic
Press Limited
120
Lti
HUI.
FU HAIZHANG,
AND
JIA YONGZHEN
to the heating circuit of the apparatus, so that the temperature of the column could be controlled to within 0.02 K. The temperature distribution in the column oven was also checked by a self-installed device consisting of a thermal resistor and a Wheatstone bridge. The results showed that the temperature distribution in the column oven was no more than 0.02 K. A glass-walled manometer (i.d. 8 mm, so as to reduce the capillary effect) was placed just before the inlet of the column so as to determine the inlet pressure; the largest error was within 0.04 per cent. The outlet pressure was measured with a normal Fortin barometer. The carrier-gas flow rates were measured with a soap-film meter placed at the outlet of the detector; the error was up to 2 per cent in the worst case. Hydrogen was used as the carrier-gas with flow rates from 0.8 to 1.2 urn3. s- l. Silanized White 101 (60 to 80 mesh, Shanghai number 1 reagent factory, China) was used as the support. The temperature of the column was (333.15 f 0.02) K. Thermal conductivity was used for detection. The solutes employed were reagent-grade and the solvents used were chromatography-grade. The total mass of stationary phase (solvent) present in the column was determined as follows. Appropriate amounts of the support and stationary phases were weighed. The support was then loaded with stationary phase. Mass ratios of the solvent-to-support were about 0.25. The packing was then carefully introduced into the column without any loss. Thus the precise amount of stationary phase present in the column could be obtained. Furthermore, this amount was checked by weighing the total amount of the packing which was carefully obtained after the experiment, and the results showed that there was no loss of the stationary phase during the experiment. This was because the column temperatures were much lower than the maximum operating temperatures of the stationary phase. The ashing method was also used to determine the exact amount of stationary phase packed. (4*‘) It was shown that the deviations of both methods were nearly the same (about 0.006 g). Sample injections were made by firstly, taking up 0.4 to 0.8 pm3 of solute into the syringe; secondly, removing the syringe and withdrawing the plunger further to admit 3 to 4 pm3 of air; and finally, injecting the contents of the syringe through the septum into the vaporization chamber. The adjusted retention time t’ (see figure 1) was determined by starting the stopwatch at point A, recording the times t, at point B and t, at point C (points B and C lie at one-third of the height of the solute peak). Then the adjusted retention time was given by t’ = f(t1+ CJ. The points B, C could be predicted with adequate precision by repeated injections to enable the differences between peak heights to be no more than 2mm. This precision is enough to allow the measurement of t’. Actually, it is not necessary to measure points B, C one-third of the way up the leading edge of the elution peaks, because all elution peaks in the experiments were highly symmetric. The adjusted retention time t’ of a solute in one column was measured three times and the mean was taken; the absolute errors were within + 1 s, and the relative errors were within
121
VALUES OF A” BY G.C. Elution of solute peak Injection Elution of air
> C
A
h
V
V
t FIGURE 1. Plot of solute concentration c against time c.
0.1 per cent. Inlet pressures and carrier-gas flow rates were also measured three times and the means taken; relative errors of inlet pressures were within 0.05 per cent; relative errors of flow rates were within 0.4 per cent.
3. ~Results The activity coefficient of the solute 1 in a binary solution conditions is’@ ln(rP(T,
0)} = ln(RTm,/I/,p~M,)
-(B,,
under chromatographic
- I/:)p:/RT+(2B,,-
ViQ,/RTJ.
(2)
Here yr(T, 0) is the activity coefficient of solute (component 1) at infinite dilution in the stationary phase (component 2) at the column temperature and zero total pressure; J, given by J
is the pressure correction respectively;
=
4{@i/P33-
11/3{(PilPo)4- l>,
factor; pi and p, are column v, = u(l -p,/p,)Jt’T/T,,
(3)
inlet and outlet pressures (4)
is the net retention volume; u is the carrier-gas flow rate; T and Tf are column and flowmeter temperatures, respectively; p, is the saturated vapour pressure of water at the flowmeter temperature; m, is the solvent (component 2) mass and M, is the molar mass of the solvent; B, i and B, 3 are second virial coefficients characterizing interactions between two solute molecules and between a solute and a carrier-gas (component 3) molecule, respectively; V: is the molar volume of pure solute and V;m is the partial molar volume of solute at infinite dilution in the stationary phase; p: is the vapour pressure of the solute at the column temperature T. Table 1 lists the measured values of the adjusted retention times of each of 14 solutes in each of three
122
LU HUI, FU HAIZHANG,
AND JIA YONGZHEN
TABLE 1. Adjusted retention times t’ of each of 14 solutes in each of three solvents at 333.15 K Solvent
/’a \/ auinoline
heptane C,H,, hexane C,H,, cyclohexane C,H i r tetrachloromethane CCI, benzene C,H, trichloromethane CHCI, diethyl ether CH,CH,OCH$Hs 2-propanol (CH,),CHOH l-propanol CH,(CH,),OH ethanol CHsCH,OH methanol CHsOH methyl ethanoate CH,CO,CH, propanone CHsCOCH, 2-butanone CHsCHsCOCHs
di-n-nonyl phthalate
t’/min
di-n-butyl phthalate ‘%CJ% OAH, CL t’/min
5.80 2.23 5.23 10.38 14.13 16.63 2.05 15.86 36.65 14.37 9.29 5.38 5.55 13.77
7.72 3.18 6.70 10.86 14.91 14.94 2.29 6.59 12.81 5.07 2.89 5.17 5.13 12.15
13.56 5.41 10.44 13.40 16.45 15.98 2.88 6.22 11.97 4.62 2.49 5.22 4.79 11.78
t’lmin
solvents. Table 2 lists the activity coefficients of each of 14 solutes at infinite dilution in each of 3 solvents calculated from equation (2); absolute and relative errors derived from equation (2) according to error theory are also listed. It can be seen from table 2 that the absolute error of an activity coefficient is not larger than 0.02 and that the relative error is 1 per cent in the worst case. For the sake of comparison, all of the measured activity coefficients were taken 2 digits beyond the decimal point. TABLE 2. Dipole moments p and activity coefficients y with their measurement errors for each of 14 solutes infinite dilution in each of 3 solvents at 333.15 K Solvent Solute heptane hexane cyclohexane tetrachloromethane benzene trichloromethane diethyl ether 2-propanol I-propanol ethanol methanol methyl ethanoate propanone 2-butanone
quinoline
1030p/(C. m)(‘) y y 0 0 0 0 0 3.37 3.84 5.54 5.60 5.64 5.67 5.74 9.61 11.4
AY?”
6.73 0.007 6.28 -0.006 3.98 0.003 1.73 0.004 1.47 0.006 0.67 0.003 2.09 -0.002 1.79 0.009 1.53 0.02 1.63 0,007 1.40 0.003 1.79 0.002 4.04 0.004 1.53 0.006
di-n-butyl phthalate
AYF’IY?~ Y?
AY?‘”
0.1 2.45 0.004 -0.1 2.14 -0.001 0.07 1.48 0.001 0.3 0.79 0.002 0.4 0.68 0.003 0.5 0.36 0.001 -0.1 0.90 -0.001 0.5 2.09 0.002 1 2.13 0.007 0.4 2.19 0.001 0.2 2.13 -0.001 0.09 0.91 0.001 0.09 2.11 0.001 0.4 0.85 0.003
di-n-nonyl phthalate
AY?/Y?‘~ Y? 0.2 -0.05 0.1 0.3 0.4 0.4 -0.1 0.1 0.03 0.06 -0.06 0.1 0.05 0.3
at
1.16 1.05 0.81 0.54 0.51 0.28 0.60 1.86 1.90 2.05 2.10 0.74 1.89 0.72
AY?“
AY?‘/Y?‘” 0.004 0.4 o.Ocm3 0.03 0.002 0.2 0.002 0.3 0.002 0.5 0.001 0.4 -0.0007 -0.1 0.001 0.07 0.006 0.3 -0.ooO2 -0.01 -0.003 -0.1 0.0002 0.02 -0.0004 -0.02 0.002 0.3
0*b Ayy and AyF/yF are the absolute error and the relative error of an activity coefficient, respectively.
VALUES OF A” BY G.C.
123
4. Discussion We reach the following conclusions from table 2. For all of the four alcohols in all three solvents y: > 1 and is larger than for most of the other solutes in solvents, that is to say, the deviations from Raoult’s law are positive, which means that molecular interactions between alcohols are larger than those between an alcohol and a solvent. This is possibly due to the fact that alcohols can form intermolecular hydrogen bonds. As solvent polarities decrease from left to right in table 2, activity coefficients of a solute in a solvent decrease in that order. This means that interactions between these solutes and solvents increase from left to right, which shows that dispersion forces are possibly a main factor in these interactions, because molecular volumes of the solvents increase from left to right though the dipole moments of the solvents increase from left to right. One exception to this trend is the solutions of alcohols in quinoline; $ for alcohols in quinoline are smaller than those for alcohols in other solvents for quinoline is a base. As the polarities of the solutes increase from heptane to trichloromethane, the activity coefficients of solutes in one solvent decrease, which means that interactions between solutes and solvents increase from heptane to trichloromethane. This also shows that dispersion forces are a main factor in these solutions. Other interesting examples are (propanone + any of the three solvents) and (Zbutanone + any of the three solvents). The activity coefficient of 2-butanone is each of three solvents is larger than that of propanone in the same solvent, which can easily be explained-the dipole moment and molar volume of 2-butanone are both larger than those of propanone. The above trends are very similar to those in the authors’ former work.“’ Gas-liquid chromatography can provide more, and more precise, results in a short time, and as more and more results are produced, a rapid growth in our knowledge of molecular interactions in solutions can be expected. REFERENCES 1. McGlashan, M. L. Chemical Thermodynamics, A Specialist Periodical Report. Vol. 2, Chapter 2. The Chemical Society: London. 1978. 2. Conder, J. R.; Young, C. L. Physicochemical Measuremem by Gas Chromatography. Wiley: New York. 1979. 3. Rowlinson, J. S. Liquids and Liquid Mixtures. Butterworth: London. 1971. 4. Martire, D. E.; Riedl, P. J. Phys. Chem. 1968, 72, 3478. 5. Laub, R. J.; Pumell, J. H.; Williams, P. S. J. Chromalogr. 1978, 155, 233. 6. Everett, D. H.; Stoddart, C. T. H. Trans. Faraday Sot. 1961, 57, 746. 7. Weast, R. C. Handbook of Chemistry and Physics. C.R.C. Press: Cleveland. 57th edition. 19761977. 8. Lii Hui; FU Haizhang; Jia Yongzhen. Journal ofNorthwest Teachers College (in Chinese) 1987, 3, 86.
Thermodynamics
1988, 20,
119-123
Determination of activity coefficients at infinite dilution for each of 14 organic solutes in each of 3 organic solvents at 333.15 K by gas chromatography Lu HUI,” FU HAIZHANG,’
AND JIA YONGZHENb
Chemistry Department, Northwest Teachers’ College, Lunzhou, Gansu, The People’s Republic of China (Received 5 January 1987; in final form 27 May 1987) The activity coefficients of each of heptane, hexane, cyclohexane, tetrachloromethane, benzene, trichloromethane, diethyl ether, 2-propanol, I-propanol, ethanol, methanol, methyl ethanoate, propanone, and 2-butanone at infinite dilution in each of quinoline, di-n-butyl phthalate, and di-n-nonyl phthalate, have been measured at 333.15 K by g.l.c., and the molecular interactions of the components in these solutions have been discussed on the basis of the experimental results.
1. Iatrodwtion Activity coefficients at infinite dilution are important and useful properties to solution researchers. Their most interesting and successful application has been in the testing of various solution theories. This is possibly due to the infinite dilute condition-the distance between two solute molecules is infinitely great and solute-solute interactions can be neglected; we have only solute-solvent and solvent-solvent interactions, a situation which presents solution chemists with simpler theoretical treatments and fewer complications. Measuring activity coefficients at infinite dilution using g.l.c., because the results can be obtained so rapidly and accurately, has been one of the most important methods in solution research.‘rW3’
2. Experimental So that the apparatus would be suitable for physicochemical measurements the following modifications to a gas chromatograph (model 102G, Shanghai Analytical Equipment Factory, China) have been made. A precise temperature regulator (DWT-702, Jinshan Electronic Equipment Factory, Shanghai, China) was attached a Author to whom correspondence should be sent. b Students graduated from the Department in 1986. 0021-9614/88/010119+05
$02.00/O
0 1988 Acadtic
Press Limited
120
Lti
HUI.
FU HAIZHANG,
AND
JIA YONGZHEN
to the heating circuit of the apparatus, so that the temperature of the column could be controlled to within 0.02 K. The temperature distribution in the column oven was also checked by a self-installed device consisting of a thermal resistor and a Wheatstone bridge. The results showed that the temperature distribution in the column oven was no more than 0.02 K. A glass-walled manometer (i.d. 8 mm, so as to reduce the capillary effect) was placed just before the inlet of the column so as to determine the inlet pressure; the largest error was within 0.04 per cent. The outlet pressure was measured with a normal Fortin barometer. The carrier-gas flow rates were measured with a soap-film meter placed at the outlet of the detector; the error was up to 2 per cent in the worst case. Hydrogen was used as the carrier-gas with flow rates from 0.8 to 1.2 urn3. s- l. Silanized White 101 (60 to 80 mesh, Shanghai number 1 reagent factory, China) was used as the support. The temperature of the column was (333.15 f 0.02) K. Thermal conductivity was used for detection. The solutes employed were reagent-grade and the solvents used were chromatography-grade. The total mass of stationary phase (solvent) present in the column was determined as follows. Appropriate amounts of the support and stationary phases were weighed. The support was then loaded with stationary phase. Mass ratios of the solvent-to-support were about 0.25. The packing was then carefully introduced into the column without any loss. Thus the precise amount of stationary phase present in the column could be obtained. Furthermore, this amount was checked by weighing the total amount of the packing which was carefully obtained after the experiment, and the results showed that there was no loss of the stationary phase during the experiment. This was because the column temperatures were much lower than the maximum operating temperatures of the stationary phase. The ashing method was also used to determine the exact amount of stationary phase packed. (4*‘) It was shown that the deviations of both methods were nearly the same (about 0.006 g). Sample injections were made by firstly, taking up 0.4 to 0.8 pm3 of solute into the syringe; secondly, removing the syringe and withdrawing the plunger further to admit 3 to 4 pm3 of air; and finally, injecting the contents of the syringe through the septum into the vaporization chamber. The adjusted retention time t’ (see figure 1) was determined by starting the stopwatch at point A, recording the times t, at point B and t, at point C (points B and C lie at one-third of the height of the solute peak). Then the adjusted retention time was given by t’ = f(t1+ CJ. The points B, C could be predicted with adequate precision by repeated injections to enable the differences between peak heights to be no more than 2mm. This precision is enough to allow the measurement of t’. Actually, it is not necessary to measure points B, C one-third of the way up the leading edge of the elution peaks, because all elution peaks in the experiments were highly symmetric. The adjusted retention time t’ of a solute in one column was measured three times and the mean was taken; the absolute errors were within + 1 s, and the relative errors were within
121
VALUES OF A” BY G.C. Elution of solute peak Injection Elution of air
> C
A
h
V
V
t FIGURE 1. Plot of solute concentration c against time c.
0.1 per cent. Inlet pressures and carrier-gas flow rates were also measured three times and the means taken; relative errors of inlet pressures were within 0.05 per cent; relative errors of flow rates were within 0.4 per cent.
3. ~Results The activity coefficient of the solute 1 in a binary solution conditions is’@ ln(rP(T,
0)} = ln(RTm,/I/,p~M,)
-(B,,
under chromatographic
- I/:)p:/RT+(2B,,-
ViQ,/RTJ.
(2)
Here yr(T, 0) is the activity coefficient of solute (component 1) at infinite dilution in the stationary phase (component 2) at the column temperature and zero total pressure; J, given by J
is the pressure correction respectively;
=
4{@i/P33-
11/3{(PilPo)4- l>,
factor; pi and p, are column v, = u(l -p,/p,)Jt’T/T,,
(3)
inlet and outlet pressures (4)
is the net retention volume; u is the carrier-gas flow rate; T and Tf are column and flowmeter temperatures, respectively; p, is the saturated vapour pressure of water at the flowmeter temperature; m, is the solvent (component 2) mass and M, is the molar mass of the solvent; B, i and B, 3 are second virial coefficients characterizing interactions between two solute molecules and between a solute and a carrier-gas (component 3) molecule, respectively; V: is the molar volume of pure solute and V;m is the partial molar volume of solute at infinite dilution in the stationary phase; p: is the vapour pressure of the solute at the column temperature T. Table 1 lists the measured values of the adjusted retention times of each of 14 solutes in each of three
122
LU HUI, FU HAIZHANG,
AND JIA YONGZHEN
TABLE 1. Adjusted retention times t’ of each of 14 solutes in each of three solvents at 333.15 K Solvent
/’a \/ auinoline
heptane C,H,, hexane C,H,, cyclohexane C,H i r tetrachloromethane CCI, benzene C,H, trichloromethane CHCI, diethyl ether CH,CH,OCH$Hs 2-propanol (CH,),CHOH l-propanol CH,(CH,),OH ethanol CHsCH,OH methanol CHsOH methyl ethanoate CH,CO,CH, propanone CHsCOCH, 2-butanone CHsCHsCOCHs
di-n-nonyl phthalate
t’/min
di-n-butyl phthalate ‘%CJ% OAH, CL t’/min
5.80 2.23 5.23 10.38 14.13 16.63 2.05 15.86 36.65 14.37 9.29 5.38 5.55 13.77
7.72 3.18 6.70 10.86 14.91 14.94 2.29 6.59 12.81 5.07 2.89 5.17 5.13 12.15
13.56 5.41 10.44 13.40 16.45 15.98 2.88 6.22 11.97 4.62 2.49 5.22 4.79 11.78
t’lmin
solvents. Table 2 lists the activity coefficients of each of 14 solutes at infinite dilution in each of 3 solvents calculated from equation (2); absolute and relative errors derived from equation (2) according to error theory are also listed. It can be seen from table 2 that the absolute error of an activity coefficient is not larger than 0.02 and that the relative error is 1 per cent in the worst case. For the sake of comparison, all of the measured activity coefficients were taken 2 digits beyond the decimal point. TABLE 2. Dipole moments p and activity coefficients y with their measurement errors for each of 14 solutes infinite dilution in each of 3 solvents at 333.15 K Solvent Solute heptane hexane cyclohexane tetrachloromethane benzene trichloromethane diethyl ether 2-propanol I-propanol ethanol methanol methyl ethanoate propanone 2-butanone
quinoline
1030p/(C. m)(‘) y y 0 0 0 0 0 3.37 3.84 5.54 5.60 5.64 5.67 5.74 9.61 11.4
AY?”
6.73 0.007 6.28 -0.006 3.98 0.003 1.73 0.004 1.47 0.006 0.67 0.003 2.09 -0.002 1.79 0.009 1.53 0.02 1.63 0,007 1.40 0.003 1.79 0.002 4.04 0.004 1.53 0.006
di-n-butyl phthalate
AYF’IY?~ Y?
AY?‘”
0.1 2.45 0.004 -0.1 2.14 -0.001 0.07 1.48 0.001 0.3 0.79 0.002 0.4 0.68 0.003 0.5 0.36 0.001 -0.1 0.90 -0.001 0.5 2.09 0.002 1 2.13 0.007 0.4 2.19 0.001 0.2 2.13 -0.001 0.09 0.91 0.001 0.09 2.11 0.001 0.4 0.85 0.003
di-n-nonyl phthalate
AY?/Y?‘~ Y? 0.2 -0.05 0.1 0.3 0.4 0.4 -0.1 0.1 0.03 0.06 -0.06 0.1 0.05 0.3
at
1.16 1.05 0.81 0.54 0.51 0.28 0.60 1.86 1.90 2.05 2.10 0.74 1.89 0.72
AY?“
AY?‘/Y?‘” 0.004 0.4 o.Ocm3 0.03 0.002 0.2 0.002 0.3 0.002 0.5 0.001 0.4 -0.0007 -0.1 0.001 0.07 0.006 0.3 -0.ooO2 -0.01 -0.003 -0.1 0.0002 0.02 -0.0004 -0.02 0.002 0.3
0*b Ayy and AyF/yF are the absolute error and the relative error of an activity coefficient, respectively.
VALUES OF A” BY G.C.
123
4. Discussion We reach the following conclusions from table 2. For all of the four alcohols in all three solvents y: > 1 and is larger than for most of the other solutes in solvents, that is to say, the deviations from Raoult’s law are positive, which means that molecular interactions between alcohols are larger than those between an alcohol and a solvent. This is possibly due to the fact that alcohols can form intermolecular hydrogen bonds. As solvent polarities decrease from left to right in table 2, activity coefficients of a solute in a solvent decrease in that order. This means that interactions between these solutes and solvents increase from left to right, which shows that dispersion forces are possibly a main factor in these interactions, because molecular volumes of the solvents increase from left to right though the dipole moments of the solvents increase from left to right. One exception to this trend is the solutions of alcohols in quinoline; $ for alcohols in quinoline are smaller than those for alcohols in other solvents for quinoline is a base. As the polarities of the solutes increase from heptane to trichloromethane, the activity coefficients of solutes in one solvent decrease, which means that interactions between solutes and solvents increase from heptane to trichloromethane. This also shows that dispersion forces are a main factor in these solutions. Other interesting examples are (propanone + any of the three solvents) and (Zbutanone + any of the three solvents). The activity coefficient of 2-butanone is each of three solvents is larger than that of propanone in the same solvent, which can easily be explained-the dipole moment and molar volume of 2-butanone are both larger than those of propanone. The above trends are very similar to those in the authors’ former work.“’ Gas-liquid chromatography can provide more, and more precise, results in a short time, and as more and more results are produced, a rapid growth in our knowledge of molecular interactions in solutions can be expected. REFERENCES 1. McGlashan, M. L. Chemical Thermodynamics, A Specialist Periodical Report. Vol. 2, Chapter 2. The Chemical Society: London. 1978. 2. Conder, J. R.; Young, C. L. Physicochemical Measuremem by Gas Chromatography. Wiley: New York. 1979. 3. Rowlinson, J. S. Liquids and Liquid Mixtures. Butterworth: London. 1971. 4. Martire, D. E.; Riedl, P. J. Phys. Chem. 1968, 72, 3478. 5. Laub, R. J.; Pumell, J. H.; Williams, P. S. J. Chromalogr. 1978, 155, 233. 6. Everett, D. H.; Stoddart, C. T. H. Trans. Faraday Sot. 1961, 57, 746. 7. Weast, R. C. Handbook of Chemistry and Physics. C.R.C. Press: Cleveland. 57th edition. 19761977. 8. Lii Hui; FU Haizhang; Jia Yongzhen. Journal ofNorthwest Teachers College (in Chinese) 1987, 3, 86.