**GAS CHROMATOGRAPHY**

__Background__

Gas chromatography is a powerful means of
performing qualitative and quantitative measurements of complex
mixtures of volatile substances. In this experiment you will use
gas chromatography for quantitative analysis of complex mixtures
and determine parameters used to optimize the separation. The
experiment uses common industrial solvents; cyclohexane (C_{6}H_{12}),
methylene chloride (CH_{2}Cl_{2}), and toluene (C_{2}H_{6}).
They are toxic, must be handled with respect, and must be
disposed of in appropriate containers.

*Theoretical Plates*

The separation process in gas
chromatography can be compared to a multiple distillation or a
fractional distillation using a reflux column. Gas chromatography
uses relatively long packed or open tubular capillary columns and
is subsequently far more efficient at separation than fractional
distillations with short reflux columns. In addition, gas
chromatography uses packing or *stationary phases* that can
be liquid or solid and may exhibit an affinity toward the
compounds being separated. The *column efficiency* of a gas
chromatography column is gauged by the *number of theoretical
plates*, *n*. The concept of a *plate* is a
carry-over from the first fractionating columns which used
discrete plates for separation. The chromatography column does
not have discrete plates. The number of theoretical plates is the
number of discrete distillations that would have to be performed
to obtain an equivalent separation. This number is commonly used
as a measure of separation efficiency and is a useful number to
use when comparing the performance of various chromatographic
columns. Gas chromatography columns normally have 1,000 to
1,000,000 theoretical plates as opposed to fractionating columns
which normally operate in the range of 5-100 plates.

The number of theoretical plates, *n,*
is a dimensionless number, which is related to the ratio between
the retention time, *t*_{r}, and the width of
the peak containing the compound. If the peaks are reasonably
symmetric, it can be assumed that they are Gaussian in shape. In
this case, *n* is found from:

*n*=5.45(*t*_{r}/*W*_{1/2})^{2}

The peak width at half height, *W*_{1/2},
is found by drawing a line vertically from the peak maximum to
the baseline, measuring half-way up the peak, drawing a
horizontal line, and measuring the length of the horizontal line.
The retention time, *t*_{r}, is measured at
the point where the vertical line drawn through the maximum
intersects the baseline. Both *t*_{r} and *W*_{1/2}
must be measured in the same units. Since the measurement is
usually made from a recorder chart, the units are usually in cm,
mm, or in. *n* varies depending on the compound as well as
the column packing material. So a column does not have a single *n*
value. *n* also varies with the flow rate, and the column
length. It is good practice to specify the column conditions and
the compound used to determine *n*.

*Height Equivalent to a Theoretical Plate*

Since *n* depends on the length of the
column, another parameter is used to express column efficiency.
It is the height (length of column) equivalent to a theoretical
plate, HETP, or just *H*

*H=L/n*

where *L* is the length of column in
cm or mm. Thus *H* is the length of column which represents
one theoretical plate in units of cm/plate or mm/plate.

The effect of flow on column efficiency is
usually shown by plotting *H* versus flow rate or linear
velocity. Such a plot is shown in the figure. Note that the *H*
line goes through a minimum. The minimum occurs at the optimum
flow velocity. The simplest equation for the curve in the *H*
versus *v* figure is the van Deemter equation:

*H*=*A*+*B*/*v*+*Cv*

A van Deemter plot for gas chromatography
can seen below. *A*, *B* and *C* are constants and
*v* is the linear velocity, the carrier gas flow rate. The
*A* term is independent of velocity and represents
"eddy" mixing. It is smallest when the packed column
particles are small and uniform. The *B* term represents
axial diffusion or the natural diffusion tendency of molecules.
This effect is diminished at high flow rates and so this term is
divided by *v*. The *C* term is due to kinetic
resistance to equilibrium in the separation process. The kinetic
resistance is the time lag involved in moving from the gas phase
to the packing stationary phase and back again. The greater the
flow of gas, the more a molecule on the packing tends to lag
behind molecules in the mobile phase. Thus this term is
proportional to *v*.

*Quantitative Analysis*

Chromatographic detectors have different responses to each compound. In order to determine quantitative amounts of various compounds in a separation mixture, the detector response must be calibrated using standards. Standard solutions of the analyte are injected and the detector response recorded. Comparison of the standard and sample retention times allows qualitative analysis of the sample. Comparison of the peak area of the standards with that of the sample allows quantitation of the analyte. The peak area can be determined by measuring it directly on the chart recorder output with a planimeter, or by carefully cutting out the peak and weighing it on an analytical balance. Chromatographic integrators which calculate the area automatically are also commonly used.

If the relationship between standard solution amount and detector response is nonlinear, the peak area versus amount data can be plotted to give a calibration curve. The amount of unknowns is then found determining their peak areas and reading the corresponding amounts from the calibration curve. If the relationship is linear, the data can be fitted by linear least squares to determine a response equation, or a conversion factor can be calculated for future use.

__Apparatus__

- Gas chromatograph with thermal conductivity detector (TCD).
- Digital flow meter and temperature monitors
- Computer data aquisition with peak-integration software
- Digital balance

__Instrument Settings__

- Column:
*L*x 1/4" DNP - Flow rate: 60 mL/min
- Temp. setting: 75
^{o}C - Attenuation: as required

__Procedure__

- Make 1 mL injections of each of pure cyclohexane, methylene chloride, and toluene. Measure retention times of each. Measure the peak areas of each via the "cut-and-weigh" method or directly with a chromatographic integrator if available.
- Prepare about 5 mL of a 1:1:1 by weight solution of cyclohexane, methylene chloride and toluene using a digital balance and a pipette. Inject a 1 mL sample of the mixture.
- Prepare four different mixtures (by weight) of toluene and cyclohexane, using equal amounts of cyclohexane but varying the amount of toluene (about .25:1, .5:1, .75:1, and 1:1 toluene to cyclohexane (w/w).) Inject 1 mL of each mixture.
- Obtain a toluene unknown mixture from the Teaching Assistant. Make 1 mL injections to determine the amount of toluene relative to cyclohexane.

__Calculations__

- Calculate the number of theoretical plates for cyclohexane, methylene chloride, and toluene at 60 mL/min flow.
- Determine the detector response for toluene and methylene chloride relative to cyclohexane as a ratio of peak areas.
- Determine the peak area ratio (toluene/cyclohexane) for each standard mixture using either the automatic integrator. Plot the relative detector response curve.
- Depending on the relationship between peak area and toluene standard solution concentration, plot a calibration curve or determine a linear conversion factor for converting peak area to concentration (w/w) in mg/g.
- Determine the concentration of toluene in the unknown based on the calibration step.

__Report__

Report the concentration of the toluene unknown in mg/g, the two relative detector response values at 60 mL/min flow. Your grade will be based 90% on unknown concentration and 10% on the detector response values.

__Reference__

Friday, October 03, 2003