Question

How can the peak area be used to quantitatively analyze a sample using GC?

Answer 1

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 (C₆H₁₂), methylene chloride (CH₂Cl₂), and toluene (C₂H₆). 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 orstationary 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 thenumber 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 ^oC
• Attenuation: as required

Procedure

1. 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.
2. 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.
3. 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.
4. Obtain a toluene unknown mixture from the Teaching Assistant. Make 1 mL injections to determine the amount of toluene relative to cyclohexane.

Calculations

1. Calculate the number of theoretical plates for cyclohexane, methylene chloride, and toluene at 60 mL/min flow.
2. Determine the detector response for toluene and methylene chloride relative to cyclohexane as a ratio of peak areas.
3. Determine the peak area ratio (toluene/cyclohexane) for each standard mixture using either the automatic integrator. Plot the relative detector response curve.
4. 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.
5. Determine the concentration of toluene in the unknown based on the calibration step.