Gas Chromatography (GC) Lecture Notes

CM2192 Analytical Experimentt 1: Experimen Gas Chromatography (GC) for Qualitative and Quantitative Analysis Prepared by Dr Emelyn Tan

Compound starts in mobile phase

Separation based on rate of analyte’s movement through stationary phase.

Column Chromatography: statio stationary nary phase is held in a narrow tube and the mobile phase is forced through the tube by gravity or under pressure. - Column, GC, HPLC and SCFC.

Type

GC

Stationary Phase

Liquid on solid or solid beads in column

Mobile Phase

Inert gas e.g. H 2 He or N2

Sample

Mixed in mobile phase (gas)

2

Schematic Diagram of GC

Requirements for the Analyte: - Volatile (low boiling point, high vapour pressure) - Thermal stability Separation depends on: a) Volatility (MAIN FACTOR): Higher volatility, shorter retention time (tR). b) Differential interaction between analytes and stationary phase: Weaker interaction (opposite polarity), shorter t R. No interaction with the mobile phase i.e. inert carrier gas.

T is regulated

Figure 31-1 Skoog 3

Instrument Parameters 1. Column type – Packed with Chromosorb W Chromosorb W is a white, polar, crumbled, naturally occurring, soft siliceous sedimentary rock and diatomaceous earth (contains a type of hard-shelled algae). 2.

Coating – 20% Free Fatty Acid Phase (FFAP): polyethylene glycol substituted with terephthalic acid

3.

Diameter of packing particle (mm) – 10 to 200 μm

4.

Inner diameter (mm) – 2 or 3 mm

5.

Length (cm) – 100 or 200 cm

6.

Temperature – isothermal at 150 °C

7.

Carrier gas – N2

8.

Linear flow rate (cm/s) – varied 4

Flame Ionisation Detector (FID) 

Figure 31-8 Skoog





Sample in

Effluent from the column is directed to H2-air flame. Organic compounds form cations and electrons when pyrolyzed at the temperature of the flame. Pyrolysis is a decomposition of organic material at elevated temperatures without the participation of oxygen. Collector electrode will capture the charge carriers (ions and electrons), the resulting current is measured by a picoammeter. The response is proportional to the number of the carbon atoms in the sample. This is related to the effective carbon number (ECN). 5

Plate Theory 



Plate theory supposes that the chromatographic column contains a large number of separate layers or plates, of a given plate height. This theory, which is adopted from a distillation column, is an assumption as there is actually insufficient time for equilibration in an chromatographic column. N = plate count or number of theoretical plates

N

L 

H

L = length of the column packing (cm) fixed H = plate height or Height Equivalent of Theoretical Plate (HETP) (cm)

Column efficiency and separation improves: Figure 30F-2 Skoog



as the plate count N increases



as the plate height H decreases 6

Column Efficiency, H Because the chromatographic peaks are usually Gaussian, the column efficiency is reflected by the breath of the peaks i.e. the variance s2, per unit length of the column. The plate height i.e. column efficiency H: H

σ

2



s2 = variance of Gaussian peak (cm 2)

L

Gaussian Distribution 1s = 34%

Plot showing distribution of molecules along the length of the column at the moment that the analyte peak reaches the end of the column/detector i.e. at the retention time, t R.

t x uo = L Figure 30-11 Skoog 7

Number of Theoretical Plates, N H

σ

2

N



L



4σ

H

L

N

Peak width at base, W



L2 

σ

2

L2 

2

(W 4)



16

No of theoretical plates:

L2 W

2

÷ linear flow

rate (cm / min)

N  16

Confidence Level = 95.4% tR

2

W

2

tR and W units are in minutes.

N  5.54 Peak width at ½ height (PWHH), W1/2, is used when W is difficult to be accurately determined.

W 68% =

2s

tR

2

W1/2

2

A larger N value represents better separation. Hence, a good separation is when narrow peaks are obtained.

8

Variables that affect Column Efficiency 



A decrease of H relates to an increase in column efficiency and separation, less peak/band broadening. Many variables affect H and various equations of H have been proposed that incorporate these complex physical interactions and effects.

k



t Stationary phase t Mobile phase

Skoog

Rate theory: The van Deemter equation In Plate theory, the number of theoretical plates, N, and plate height, H, is related closely to the efficiency of the chromatography column. Plate theory, however, does not provide any information on the effect of flow rate  on H, whereas Rate theory does.

The column efficiency can be approximated by:

H A

B u



(C s



CM ) u

A: coefficient that describes multiple path effects (eddy diffusion) B: longitudinal diffusion coefficient CS: mass transfer coefficient for stationary phase CM: mass transfer coefficient for mobile phase. At high flow rate, C M ≈ 0. u: linear flow velocity (cm/s) 10

The Multiple Path Effects: Eddy Diffusion A molecule can travel through a packed column using different paths, thus the residence times of each molecule is variable and band broadening occurs. This effect is called eddy diffusion. The heterogeneity in axial velocities is related to: - particle size and uniformity - geometry of packing Using small and uniform particles which give a tighter and more consistent packing will minimize this effect.

HA

B u

Molecule 2 will arrive later at B.  C su

Figure 30-14 Skoog 11

The Multiple Path Effects: Eddy Diffusion

l is packing factor, ranging from 0.8  – 1

Eddy Diffusion:

A



2 λ dp

l is a constant accounting for the consistency of the packing. A more consistent packing gives a smaller value for l which range from 0.8 to 1.

dp is the average diameter of the packing particles. 12

Longitudinal Diffusion

H A

B u



Csu

In chromatography, the diffusion results in movement of the solute from the concentrated center of a band to less concentrated regions on both sides. This results in band broadening and is more evident as time increases.

B



2 γ DM

g is a constant related to the column packing which range from 0.6 to 0.8.

DM is the solute’s diffusion coefficient in the mobile phase.

13

H A

Mass Transfer 



The Cu term comes from the finite time required for solute to equilibrate between the two phases. Thicker film on particles, smaller diffusion coefficient i.e. solute travels slower, larger Cs.

CS



B u

 C su

2

2k

df  2

3(k  1) DS

k: retention factor, t S/tM df : thickness of film on stationary phase DS: diffusion coefficient of solute on stationary phase

van Deemter equation H A

A



2 λ dp

B u

 C su

B  2 γ DM

CS



2

2k

df  2

3(k  1) DS 14

Part 1: Determination of HETP Analyte: ethylbenzene Run GC at different carrier gas flow rates cm 3/min

N

H



5.54

tR

20 cm3/min

2

W1/2

tR = 157.02 s

tR and W units are in seconds.

2

W1/2 = 11.99 s N = 950.13

L 

H = 200 / 950.13 = 0.210 cm

N 3

F



uo A



uo

 πr

2

F (cm /min)

uo (cm/s)

uo = F / πr2 = (20/60) / π0.152 = 4.72 cm/s

2

A (cm )

Plot HETP (or H) vs. Carrier gas linear flow rate (or u o)

Take 3 points, (uo, H), and solve simultaneously for A, B and C. H A

B u

 C su

http://math.cowpi.com/systemsolver/3x3.html

(uo, H) (4.72, 0.21)

0.21  A 

(2.83, 0.19)

0.19

(1.18, 0.19)

0.19

1 – 2

0.02  (

1 – 3

0.02  (

4 x (3.54/1.89) 4 x 1.873 6 – 5



A



A

B 4.72 B 4.72

0.0375  ( 0.0175  (

Sub B into 4, 5 or 6

B 2.52 B

2.52

B 4.72 B 2.83 B 1.18

 C s 4.72

1

 C s 2.83

2

 C s 1.18

3

B



2.83 B



1.18





C

)  C s 1.89

4

)  C s 3.54

5

)  C s 3.54

6

B 1.51 B 1.51 

)(

B 4.72



B 1.18

)

B  0.048

0.014 H  0.13 

Sub B and C into 1, 2 or 3

A



0.13

0.048 u

 0.014u

H A

B u

 C su

    )    m    c     (    H

Csu

Mass transfer

A

Eddy diffusion

B/u

Longitudinal diffusion

u (cm/s) Optimum linear flow rate and maximum column efficiency, when H and band broadening is minimum. 17

Part 2: Qualitative and Quantitative Analysis Sample A: equal volumes of toluene and ethylbenzene Sample B: 3 mL cyclohexane, 4 mL of n-propanol and 3 mL o-xylene Sample C: equal volumes of ethanol, n-propanol, n-butanol and n-pentanol Sample D: ??? Sample

Compound

Density / g mL-1

Mr

BP / oC

Vol / mL

Weight /g

Weight %

n

Mole %

Peak area %

toluene

0.8669

92.15

110.6

5 x 10-4

4.3345 x 10-4

50.01

4.704 x 10-6

53.55

49.69

ethylbenzene

0.8665

106.17

136.2

5 x 10-4

4.3325 x 10-4

49.99

4.081 x 10-6

46.45

50.31

A

Inject 1 mL

n

m 

Mr

Weight = Density x Vol

Weight %

Weight 

Total Weight

Mole %

n 

x 100 %

Total n

x 100 % 18

Sample

Compound

Density / g mL-1

Mr

BP / oC

Vol / mL

Weight /g

Weight %

n

Mole %

Peak area %

toluene

0.8669

92.15

110.6

5 x 10-4

4.3345 x 10-4

50.01

4.704 x 10-6

53.55

49.69

ethylbenzene

0.8665

106.17

136.2

5 x 10-4

4.3325 x 10-4

49.99

4.081 x 10-6

46.45

50.31

A

Sample A: toluene and ethylbenzene have similar polarity. Hence elution order is dependent on boiling point. Peak area %

toluene

Peak area 

Total peak area

x 100 %

ethylbenzene Retention time, t R 19

Sample C: equal volumes of ethanol, n-propanol, n-butanol and n-pentanol Retention Volume (mL) = volumetric flow rate (mL/min) x retention time (min) Sample

Compound

No. of C

tR

Retention volume/ mL

Logarithm of retention volume

ethanol

2

1.4

n-propanol

3

1.6

n-butanol

4

1.7

n-pentanol

5

1.9

C

2     ) 1.9    L    m 1.8     (    e 1.7    m    u 1.6     l    o    v 1.5    n    o 1.4    i    t    n 1.3    e    t    e    r 1.2    g 1.1    o    L 1

For n-hexanol : y = 0.16(6) + 1.09 = 2.05

y = 0.16x + 1.09 R² = 0.9846

Retention volume: 112 mL 0

1

2

3

4

5

6

Number of carbon atoms in the molecule

20

Sample A: equal volumes of toluene and ethylbenzene Sample B: 3 mL cyclohexane, 4 mL of n-propanol and 3 mL o-xylene Sample C: equal volumes of ethanol, n-propanol, n-butanol and n-pentanol Sample D: ??? Qualitative Analysis: identity of the analytes in Sample D can be determined by comparing the retention times, t R of the three unknown analytes in the Sample D’s chromatogram with the tR of nine known analytes in Sample A, B and C. Quantitative Analysis: Volume of analyte in Sample D sample

Peak area α Volume

sample Peak area of analyte in Sample D 

Peak area of analyte in Sample C standard

x Volume of analyte in Sample C standard

e.g. Analyte: n-propanol Volume of n-propanol in Sample D =

Vol % 

4 x 10

5

2 x 10

5

x 0.25 μL  0.5 μL

Volume Total Volume

x 100 % 21

Part 3: Effective Carbon Number Flame Ionisation Detector (FID)

Current signal

a

Number of ions produced for organic compounds

a

Number of reduced carbon atoms in the flame

Effective carbon number (ECN) = individual carbon atoms contributions + functional group contributions (Table 1-1 in lab manual). Atom

e.g. toluene

Type

ECN

C

Aliphatic

1.0

C

Aromatic

1.0

O

primary alcohol  –0.6

ECN: 6(1.0) + 1(1.0) = 7.0

e.g. ethanol

ECN: 2(1.0) + 1(-0.6) = 1.4 smallest ECN

Relative ECN ratio (expected): 7.0 / 1.4 = 5.00

Relative ECN ratio (expected): 1.4 / 1.4 = 1.00

Effective carbon number (ECN) (experimental) =

Peak area n

e.g. toluene

e.g. ethanol

ECN (experimen tal)

ECN (experimen tal)

7317915310.8 (from chromatogr am) 



-6

4.704 x 10 (previously calculated) 15

1.56 x 10

1324364458.4 (from chromatogr am) 



-6

4.274 x 10 (previously calculated) 14

3.10 x 10

smallest ECN (experimental) Relative ECN ratio (experimental): 1.56 x 1015 / 3.10 x 10 14 = 5.03

Relative ECN ratio (experimental): 3.10 x 1014 / 3.10 x 1014 = 1.00

Relative ECN ratio (expected): 7.0 / 1.4 = 5.00

Relative ECN ratio (expected): 1.4 / 1.4 = 1.00

% difference: 0.60 %

% difference: 0.00 %

23