Determination of Activity Coefficients by Gas-Liquid Chromatography
Rachel Pollack
11-05-02
Partner: Greg Sebring
Chemistry 4541: Section #002
Abstract
The activity coefficients of benzene, cyclohexane, and cyclohexene were all
determined experimentally. The method used in this experiment was Gas-Liquid
chromatography and was performed on a GLC column. The activity coefficients for
benzene, cyclohexane, and cyclohexene were found to be 0.524, 0.831, and 0.683,
respectively. These coefficients did not differ significantly from the literature values of
0.511 for benzene, 0.644 for cyclohexene, and 0.838. Therefore, the experimentally
determined values were accepted as reasonable activity coefficients.
Introduction
Chromatography was used to separate components of a mixture of liquids using
gas-liquid chromatography (GLC) in this experiment. These liquids included
cyclohexane, cyclohexene, and benzene. Certain properties of each liquid were
determined from the chromatogram data, such as, the activity coefficient 2. On the
chromatogram for the mixture of the three solutes, there were three different peaks
representing each liquid. The retention time of each solute, which was the time between
injection and the peak, yielded data to find the 2.
The average flow rate of the carrier gas, dinonyl phthalate, was obtained first in
this experiment. From the flow rate, the air peak retention time could be deduced from
the chart on the GLC column, due to the column not recording this value on the
chromatogram. The carrier gas was used as a solvent for the liquids after they had been
vaporized almost immediately upon injection into the GLC column. The measurement of
the pressure drop from the column to the atmosphere deltaP was vital in later calculations.
Six different runs were done on the GLC column to produce peaks. Three of the
runs included all three of the compounds, while the other three runs only included one of
the liquids in solution yielding only one peak. From the peaks observed on the single
liquid trials, the identities of each peak on the mixture chromatograms were determined.
Cyclohexane had the shortest retention time, cyclohexene had the retention time in the
middle, and benzene had the longest retention time.
From the measured flow rate Fm and the column temperature Tc, the corrected
flow rate was calculated from the following equation:
F = Fm * Tc / T * (P – Pw) / P
(1)
Where T was the room temperature, P was the atmospheric pressure, and Pw was the
vapor pressure of water at T. Next, the second correction was applied to the flow rate to
yield the Favg:
Favg = F * P / Pavg
(2)
Where the Pavg was the inlet pressure of the column Pi and the outlet pressure of the
column P averaged together. From the adjusted retention time Trr of each solute and the
Favg, the net retention volume Vn could be calculated. First, the Trr had to be calculated
by subtracting the air peak retention time Tra from the observed retention time Tr for
each solute. Once the Trr was calculated, the Vn could be calculated as well:
Vn = Favg * Trr
(3)
Once the Vn had been determined, the specific retention volume Vg could be calculated,
which took into account the flow of the gas:
Vg = (Vn * 273)/(G * Tc)
(4)
where G was the weight of the solvent on the column. Not only was the Vg needed to
find the activity coefficient, but also the vapor pressure of the pure liquid p2 was needed
for this calculation. The p2 of each of the liquids was calculated using Antoine’s
equation:
log(p2) = A – (B / t + C)
(5)
Where the coefficients A, B, and C were located in the lab handout, and t was the Tc.
The molecular weight M of the solvent was also necessary for the computation of the
activity coefficient:
2 = (273 * R) / (Vg * p2 * M)
(6)
where R was the gas constant. Therefore, from the above information, the activity
coefficient for each liquid could be determined from the chromatography data.
One other piece of information that was important to calculate was the number of
theoretical plates N in the column needed for each of the solutes. This calculation was
done through the following equation:
N = (4 * d / w) ^2
(7)
where d was the distance of the elution peak from the injection point, and w was the
width of the peak at its base. Overall, the most important aspect of this experiment was
to determine the activity coefficient experimentally.
Data
GLC Column Data:
Total Load of Column= 12.79 +/- .01g
16.0% by weight of dinonyl phthalate
Tc = 65 +/- .1 degrees C
deltaP = 595.3 +/- 0.5 mmHg
Room Data:
P = 627 +/- 1 mmHg
T = 22 degrees C
Flow Rates: Time for one bubble to travel 9mL
Before Experiment
1) 12.94 s
2) 13.02 s
3) 13.00 s
4) 13.09 s
5) 13.07 s
6) 12.99 s
Average Fm = 13.0 +/- .1 s
After Experiment
1) 13.04s
2) 13.00s
3) 13.08s
4) 13.06s
5) 12.99s
6) 13.10s
Average Fm = 13.1 (this value was within the margin of error of the original value,
therefore the original value was utilized for all calculations).
Retention Times:
Benzene
Cyclohexene
Cyclohexane
Tr5  14.3min
Tr5  12.0min
Tr5  9.3min
Tr1  13.5min
Tr1  11.3min
Tr1  8.7min
Tr6  14.3min
Tr6  12.0min
Tr6  9.4min
Tr2  14.1min
Tr4  12.0min
Tr3  9.2min
(See attached chromatograms for the 6 different runs)
Discussion and Systematic Error
The estimation of the uncertainty of γ2 for cyclohexane was 0.001. This
estimate was slightly too small because this uncertainty did not include the actual
value. Therefore, the uncertainty should have been estimated closer to 0.01 to include
the actual value in the range of error for the activity coefficient of cyclohexane. The
activity coefficients obtained in this experiment were fairly close to the actual
literature values. The experimentally determined values varied from the actual values
in the range of 0.007 to 0.04. Since this error was not greater than 6% for any of
these coefficients, they were reasonable values for the coefficients. On the other hand,
the coefficient for the cylohexane and the benzene were less than 2% error, therefore,
the coefficient for the cyclohexene could have been found by taking another set of
measurements to reduce the error from 6%.
The error in these coefficients was probably due to a few errors in the
experiment. For instance, during the first run of all three solutes, the drive button was
not turned on so that the paper would move as the data was coming in. Fortunately,
this button was only turned off for about thirty seconds, so none of the peaks would
have been disturbed in that error. This mistake would have only lowered the
retention time for each peak by a negligible amount. Also, on some individual solute
runs, there were still traces of the other compounds found on the chromatograms.
These solutes were represented by small peaks in comparison to the size of the peak
of the individual solute for that run. Traces of other compounds can affect the
retention time of the solute if there were attractive interactions between the solute
being studied in that run and the impurity (other solute from preceding run). These
attractions would have caused the retention time to have increased slightly due to the
interactions between the solutes stabilizing them.
The activity of a pure solution is equal to 1, ideal solution behavior. When a
mixture of solutes is present, each of the solutes behaves differently than when they
are pure. Hence, the activity coefficients for each of the solutes were not equal to one
because they were dissolved in a solvent. The activity coefficient was based upon the
interaction of the solutes with the solvent. When there was more of a solute dissolved
in the solution (more interaction) the coefficient was further away from one.
Therefore, the cyclohexane interacted less with the solvent (did not dissolve as well),
than the cyclohexene and the benzene, because its activity coefficient was closer to
one (ideal solution). Benzene interacted with the dinonyl phthalate more than the
other two solutes because the solvent was an inherently non-polar molecule with a
benzene ring, so the benzene coefficient was the furthest away from one.
Positive derivations from ideal solution behavior occurred when the ideal
solution had less repulsive actions than the real solution. This situation meant that
the solute/solvent mixture in the real solution repelled each other. Negative
derivations occurred when there were attractive forces between the solution and the
solvent, eg. benzene.
Equation 7 related to plate theory, in which the net retention volume was
related to the equilibrium constant of the solute in the liquid and gas phases and
related to the volume of the solvent. This equation was derived based upon the idea
that the solutes were moving along plates (column), and this phenomena caused the
difference in retention times. The choice of the solvent for the GLC column
depended upon the physical properties of the solutes to dissolve on the column in the
solvent. The solvent dissolved the different compounds on the column with different
affinity. Each compound dissolved with certain strength, and then eventually eluted
from the column, causing a peak to form. The more soluble the solute was in the
solvent, the longer the retention time, and the smaller the activity coefficient (less
ideal solution). A solvent must have a low vapor pressure, so it does not elute from
the column with the solutes, and it must also be able to dissolve the organic
compounds.
Conclusions
The activity coefficients were found in this experiment for each of the
compounds, and the ones that were dissolved more in the solvent did have the
longest retention time and the lowest activity coefficients.
References
1)
Handbook of Chemistry and Physics: 73rd edition (1993-1993).
http://dbhs.wvusd.k12.ca.us/GasLaw/Vapor-Pressure-Data.html. Online:
2002.
2)
“Determination of Activity Coefficients by Gas-Liquid Chromatography.”
Chemsitry 4541: University of Colorado at Boulder, Fall, 2002.
3)
S. Kenworthy, J. Miller, and D.E. Martire, Journal of Chemical Education, 40,
542 (1963).