11.4.2Chromatographic Behavior of Solutes

11.28

SECTION 11

k

tR

tM

VR

M V

tM

VM

Retention

time

may be expressed as

tR

tM

(1 k )

L

(1 k )

u

11.4.2.3

Relative Retention.

The relative retention

of two solutes, where solute 1 elutes before

solute 2, is given variously by

k 2

V R ,2

tR ,2

tR ,1

k 1

V R ,1

The relative retention is dependent on (1) the nature of the stationary and mobile phases and (2) the

column operating

temperature.

11.4.2.4

Column Efficiency.

Under

ideal conditions

the

profile of a solute band resembles that

given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is

expressed

by the

effective plate number

N

eff

, defined

from the chromatogram of a single band,

N

L

16

t

R

2

5.54

tR

2

eff

H

W

b

W

1/2

where

L

is

the column length,

H

is the

plate

height,

is theR adjusted time for elution of the band

center,

W b

is the width at the base of

the

peak

(Was bdetermined4 )from the

intersections of

tangents to the inflection points with the baseline, and

W 1/2is

the

width at

half

the peak

height.

Column efficiency, when expressed as the number of theoretical plates

N

theor

uses the

uncorrected

retention

time

in the foregoing expression. The

two

column

efficiencies are

related by

N eff

N theor

k

2

k

1

11.4.2.5

Band

Asymmetry.

The peak

asymmetry

factor

AF is often defined as the ratio of peak

half-widths at 10% of peak height, that is, the ratio

b/a, as shown in Fig. 11.2. When the asymmetry

ratio lies outside the range 0.95– 1.15 for a peak

of

the effectivek plate2, number

should be

calculated from

the expression

as the distance between band peaks (or centers) divided by the

average bandwidth using

W b , as

shown in Fig. 11.3.

Rs

tR ,2 tR ,1

0.5( W 2 W 1)

FIGURE 11.1

Profile of a solute band.

11.30

SECTION 11

FIGURE 11.2

Band asymmetry.

For reasonable quantitative accuracy, peak maxima must be at least 4

apart. If so, then Rs

1.0,

which corresponds approximately to a 3% overlap of peak areas. A

value of

(for 6

Rs 1.5

)

represents essentially complete resolution with only 0.2% overlap

of peak areas. These

criteria

pertain to roughly equal solute concentrations.

The fundamental resolution equation incorporates the terms involving the thermodynamics and

kinetics of the chromatographic system:

4 1 k H

Rs

1

1

k

L

1/2

, (2) a

Three separate factors affect resolution: (1) a column selectivity

factor that varies

with

capacity factor that varies with

k (taken usually as

k 2), and (3) an efficiency factor that depends on

the theoretical plate number.

FIGURE 11.3

Definition of resolution.

PRACTICAL LABORATORY INFORMATION

11.31

tR

16Rs

2 1

(k )2

u

2

(1 k )3

H

Now

tR

is a

minimum when

thatk is, when2,

TheretRis little3tM increase. in analysis time

when k lies between 1 and 10. A twofold increase in the mobile-phase velocity roughly halves the

analysis time (actually it is the ratio

H /u which influences

the analysis time). The ratio

H /u can be

obtained from the experimental plate height/velocity graph.

11.4.2.8

High-Performance Liquid Chromatography.

Typical performances for various exper-

imental

conditions are

given in Table

11.15. The

data

assume

these

reduced

parameters:

h 3,

v 4.5. The

reduced plate height

is

h

H

L

d p

Nd

p

The

reduced velocity

of the eluent

is

v

ud

p

Ld

p

DM

D

M

tM

In these

expressions,

d p is

the particle diameter of

the stationary

phase

that

constitutes

one

plate

height.

D M

is the

diffusion coefficient of

the solute in the mobile phase.

TABLE 11.15

Typical Performances in HPLC

for

Various Conditions

Performances

Column

parameters

N

t

M

, s

L , cm

d p , m

P

, atm (psi)

2 500

30

2.3

3

18.4 (270)

2 500

30

3.7

5

18.4 (270)

2 500

30

7.5

10

18.4 (270)

5 000

30

4.5

3

74 (1088)

5 000

30

7.5

5

74 (1088)

5 000

30

15.0

10

74 (1088)

10 000

30

9.0

3

300 (4410)

10 000

30

15.0

5

300 (4410)

10 000

30

30.0

10

300 (4410)

10 000

30

9.0

3

300 (4410)

10 000

60

9.0

3

150 (2200)

10 000

90

9.0

3

100 (1470)

15 000

90

2.3

3

223 (3275)

15 000

120

2.3

3

167 (2459)

11 100

30

10.0

3

369 (5420)

11 100

37

10.0

3

300 (4410)

11 100

101

10.0

3

100 (1470)

27 800

231

25.0

3

300 (4410)

Assumed reduced parameters:

,

h These3vare optimum4.5.values from a graph of reduced plate height versus reduced

linear velocity of the mobile phase.