Lesson 4 · 35 min

Gas and high-performance liquid chromatography

Oven temperature, carrier gas, stationary phase, mobile-phase strength and gradients: separate five solvents and a set of preservatives on the simulator, then use an internal standard to turn peak areas into blood-alcohol results.

In this lesson

  • Sketch a gas chromatograph and an HPLC system and describe the common detectors
  • Explain how oven temperature, stationary phase and mobile-phase strength change retention and selectivity, and calculate a retention index
  • Explain why temperature programming and gradient elution solve the general elution problem
  • Turn peak areas into concentrations with an internal standard and a response factor

A car is pulled over, the breath reading is suspicious, and a blood sample goes to the lab. There, 0.5 mL of blood is sealed in a vial with an internal-standard solution of 1-propanol, warmed, and the gas above it is injected into a gas chromatograph. Three minutes later the chromatogram shows two peaks, ethanol and 1-propanol, and the ratio of their areas decides whether the report reads “drink driving” or “drunk driving”. This lesson explains how that chromatogram is made and how it becomes a trustworthy number.

Predict first

On a nonpolar dimethylpolysiloxane (OV-101) column at 80 °C, benzene and 2-pentanone almost coincide (Rs ≈ 0.5). What separates them most effectively?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Gas chromatography: volatility sets the pace

A gas chromatograph has five parts: the carrier gas from a cylinder (He, H₂ or N₂); an injector that flashes the sample into vapour (split/splitless, or headspace as above); a capillary column in a thermostatted oven (a fused-silica tube of 0.25 mm i.d. and 15–60 m, coated inside with a 0.1–5 µm polymer film); a detector; and the data system.

Each detector has its niche: the flame ionisation detector (FID) responds to C–H compounds almost in proportion to their carbon atoms, with a linear range of 10⁷, and does most quantitation; the thermal conductivity detector (TCD) sees everything but insensitively; the electron-capture detector (ECD) is exquisitely sensitive to halogenated pesticides; a mass spectrometer (MS) adds structural information.

Retention in GC depends first on vapour pressure: the less volatile a solute, the longer it stays in the film. On a nonpolar column lg k of the n-alkanes is a straight line in carbon number, and compounds elute roughly in boiling-point order. Other compounds are placed by their retention index I, slotted between the neighbouring n-alkanes — n-heptane is 700, n-octane 800. The difference between a compound’s indices on two phases (the McReynolds constants) measures the polarity of a phase.

I=100[n+lg⁡t′R,x−lg⁡t′R,nlg⁡t′R,n+1−lg⁡t′R,n]I = 100\left[n + \frac{\lg t\prime_{\mathrm{R},x} - \lg t\prime_{\mathrm{R},n}}{\lg t\prime_{\mathrm{R},n+1} - \lg t\prime_{\mathrm{R},n}}\right]
Kováts retention index (isothermal). t′_R = t_R − t_M is the adjusted retention time; n is the carbon number of the n-alkane eluting just before x.
t′Rt\prime_\mathrm{R}
adjusted retention time t_R − t_M
n,n+1n, n+1
carbon numbers of the bracketing n-alkanes

Oven temperature is GC’s strongest knob: every 20–30 °C roughly halves k. When a mixture spans low and high boilers, no single temperature suits everyone — cool, and the early peaks separate but the late ones come out broad and slow; hot, and the late ones come out quickly but the early ones pile up. This is the general elution problem. Temperature programming ramps the oven linearly so each compound is driven off near “its own” temperature; the peaks come out evenly spaced and similarly narrow.

HPLC: the mobile phase joins the competition

Compounds that cannot be vaporised or would decompose — drugs, proteins, sugars, dyes — go to high-performance liquid chromatography (HPLC). A high-pressure pump drives 0.2–2 mL/min of mobile phase through a column packed with 1.7–5 µm particles (tens to over a thousand bar), an injection valve delivers a few microlitres of sample, and a UV/diode-array, fluorescence, refractive-index or mass-spectrometric detector reads the column effluent.

Most work uses reversed phase: the stationary phase is C18 chains bonded to silica (nonpolar), the mobile phase a mixture of water with methanol or acetonitrile (polar). Hydrophobic molecules prefer the C18 and are retained longer; the larger the organic fraction φ, the stronger the eluent. Over a wide range lg k is a straight line in φ (the linear solvent strength model), with S ≈ 3–5 for small molecules: 10 % more methanol cuts k by about a half to two-thirds. The counterpart of temperature programming is gradient elution, raising φ during the run.

lg⁡k=lg⁡kw−S φ\lg k = \lg k_\mathrm{w} - S\,\varphi
Linear solvent strength: k_w is the retention factor extrapolated to pure water, and S measures how sensitive the molecule is to the organic solvent.
φ\varphi
volume fraction of organic solvent in the mobile phase
kwk_\mathrm{w}
retention factor at φ = 0 (extrapolated)
SS
solvent-strength parameter, about 3–5 for small molecules
Retention from a thermodynamic model · peak widths from plate height

Chromatogram simulator

Particle size
Column length
Elution
t_M 1234505101520253035Time / minDetector response
Dead time t_M
1.62 min
Last peak
33.21 min
Critical pair
Rs = 14.69
Plates (last peak)
12200
Back-pressure
98 bar

All baseline-resolved

PeakCompoundt_R / mink (at elution)NRs to previous
1Caffeine2.210.36312200—
2Methylparaben5.332.291220022.86
3Ethylparaben9.204.681220014.69
4Propylparaben17.099.551220016.57
5Butylparaben33.2119.51220017.69
GC: n-alkanes partition by Raoult’s law, K = ρRT/(γ∞·p°·M), with p° from NIST Antoine fits; other compounds sit at their retention index I = I(squalane) + McReynolds constant (lg k is linear in carbon number). Temperature programmes are integrated step by step, dζ/dt = 1/(t_M(1 + k(T))). Plate heights come from Golay’s equation with Fuller diffusion coefficients. HPLC: linear solvent strength, lg k = lg k_w − S·φ (C18, methanol–water, teaching parameters), the reduced van Deemter equation, and ΔP = φ′ηLu/d_p². Peaks are Gaussians of equal area; γ∞, the mean column pressure and the LSS parameters are typical magnitudes, not measurements of one column; extra-column broadening, tailing and overload are ignored.
LC mode: at 60 % methanol all five peaks separate, but butylparaben takes over half an hour; at 40 % it does not come out within an hour. At 80 % everything elutes within 6 minutes, but caffeine and methylparaben have k below 0.5, hugging the dead time where unretained matrix components come out. Try a 10 min gradient from 30 % to 90 %: every peak now elutes near k ≈ 1. Then switch to 1.7 µm particles and watch the pressure. Finally go back to GC and program the oven for the n-alkanes.

From peak area to concentration: the internal standard

Peak area is proportional to the amount reaching the detector, but the constant differs between compounds (an FID responds less to ethanol than to 1-propanol) and every injection varies by a few per cent in volume. The internal-standard method fixes both: the same amount of an internal standard — a compound absent from the sample, chemically similar, and well separated — is added to every sample and standard, and quantitation uses the area ratio of analyte to standard. Inject a little more or less and both peaks change together; the ratio does not.

A standard of known concentration gives the response factor F, and the unknown’s area ratio then gives its concentration. Better still, make several standards and plot area ratio against concentration.

AX[X]=F AS[S]⇒[X]=AXAS⋅[S]F\frac{A_\mathrm{X}}{[\mathrm{X}]} = F\,\frac{A_\mathrm{S}}{[\mathrm{S}]}\qquad\Rightarrow\qquad [\mathrm{X}] = \frac{A_\mathrm{X}}{A_\mathrm{S}}\cdot\frac{[\mathrm{S}]}{F}
The internal-standard relation: F comes from a standard, and [S] is the concentration of added internal standard.
AX,ASA_\mathrm{X}, A_\mathrm{S}
peak areas of analyte and internal standard
FF
relative response factor
[S][\mathrm{S}]
concentration of internal standard in the sample
PEG column 15 m · 70 °C · FID · internal standard 1-propanol

Blood alcohol by headspace GC: the internal-standard method

Every vial: 0.50 mL of blood (or calibrator) + 2.00 mL of 1-propanol internal-standard solution (0.100 g/L), sealed; the headspace gas is injected.

① Calibrators (ethanol, mg/100 mL)

② Unknown blood sample #3

Chromatogram of the last injection

Ethanol1-Propanol00.511.522.533.54Time / minFID signal
Ethanol peak area alone · r² = 0.9980
050100150200Ethanol / (mg/100 mL)05001000
Area ratio A(ethanol)/A(propanol) · r² = 1.0000
050100150200Ethanol / (mg/100 mL)01234

Injection log

VialVolume injected (rel.)A(ethanol)A(propanol)Ratio
Cal 200.9811183140.3763
Cal 501.0553203370.9498
Cal 800.9404573001.5229
Cal 1201.0267473282.2776
Cal 2001.00212133193.8086
Retention times come from this unit’s GC model (PEG phase; retention indices ethanol 926, 1-propanol 1026, acetone 798, all estimates). Peak area = relative FID response (effective carbon number/molar mass: ethanol 1.4/46.07, propanol 2.4/60.10) × vial concentration × the injection’s volume factor; that factor is shared by every peak of one injection (6 % relative SD), plus 0.5 % independent integration scatter, all from a deterministic hash of the sample number. Headspace partitioning, matrix effects and evaporative loss of ethanol are not modelled.
Each of the five calibrators has been injected once. Compare the two calibration plots: ethanol area alone scatters with the injection volume (lower r²), while the area ratio falls almost on a line. Then inject the unknown twice and read its concentration; re-inject one calibrator a few times and compare how much the raw area and the ratio jump.

Worked example

Blood alcohol from a response factor

A calibrator containing 1.00 g/L ethanol, with the same 1-propanol internal standard as the samples (equivalent to 0.400 g/L), gives Aethanol=3040A_\text{ethanol} = 3040 and Apropanol=1596A_\text{propanol} = 1596. The unknown blood, treated identically, gives Aethanol=2270A_\text{ethanol} = 2270 and Apropanol=1612A_\text{propanol} = 1612. Find the blood ethanol in mg/100 mL.

Concept check

Why is 1-propanol a common internal standard for blood alcohol?

Try the calculation

In an isothermal run the adjusted retention times are 2.00 min for n-heptane, 4.20 min for n-octane and 3.10 min for an unknown. What is its retention index?

Key takeaways

  • GC separates by volatility and interaction with the film; 20–30 °C hotter roughly halves k; retention indices place compounds between n-alkanes.
  • In reversed-phase HPLC lg⁡k=lg⁡kw−Sφ\lg k = \lg k_\mathrm{w} - S\varphi: more organic solvent elutes faster.
  • Temperature programming and gradients solve the general elution problem; changing phases is the main way to change selectivity.
  • The internal-standard method quantifies by area ratio, cancelling injection-volume scatter; response factors must be measured with standards.
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Data and references

  1. D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), Ch. 24 (gas chromatography), Ch. 25 (HPLC), Ch. 5 (internal standards).
  2. W. O. McReynolds, “Characterization of some liquid phases”, J. Chromatogr. Sci. 8, 685–691 (1970); E. Kováts, Helv. Chim. Acta 41, 1915–1932 (1958).
  3. L. R. Snyder, J. W. Dolan, High-Performance Gradient Elution (Wiley, 2007); L. R. Snyder, J. J. Kirkland, J. W. Dolan, Introduction to Modern Liquid Chromatography, 3rd ed. (Wiley, 2010).
  4. J. T. Scanlon, D. E. Willis, “Calculation of flame ionization detector relative response factors using the effective carbon number concept”, J. Chromatogr. Sci. 23, 333–340 (1985).
  5. NIST Chemistry WebBook, SRD 69: Antoine parameters of the n-alkanes; gas-chromatographic retention indices.
  6. GB 19522-2010, Thresholds and test methods for blood and breath alcohol concentration of vehicle drivers (Standardization Administration of China).