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201Chapter 12 Chromatography and Electrophoresis
Chapter 12
1. (a) To calculate the number of theoretical plates we use equation 
12.15; thus
N w
t
16 16 0.15 min
8.04 min 46000 plates
2
A
A
r,A
2
# #= = =` aj k 
.N w
t
16 16 858 26
0.15 min
min 4 00 plates
2
B
r,B
2
B # #= = =` aj k
.N w
t
16 16
6
8 43 44
0.1 min
min 4 00 plates
2
C
r,C
2
C # #= = =` aj k
 he average number of theoretical plates is 46 300.
 (b) he height of a theoretical plate, H, is equal to L/N where L is 
the length of the column and N is the number of theoretical plates. 
Using the average number of theoretical plates from part (a) gives the 
average height as
H
46300 plates
20 m m
1000 mm
0.43 mm/plate
#
= =
 (c) heoretical plates do not really exist; they are, instead, an artiicial 
construct that is useful for modeling the variables that afect the width 
of a solute’s peak and its resolution relative to other solutes. As we see 
from equation 12.15, the number of theoretical plates for a solute is 
deined in terms of its retention time and its peak width. Two solutes 
may have identical retention times but diferent peak widths because 
retention time is a function of the equilibrium between the concen-
tration of solute in the mobile phase and the concentration of solute 
in the stationary phase, but peak width is a function, in part, of the 
kinetic efects that control how quickly the solute moves within the 
stationary phase and within the mobile phase.
2. Using equation 12.1, the resolution between solutes A and B is
( )
. .
( . . )
. .min min
min min
R w w
t t2
0 15 0 15
2 8 26 8 04
1 47 1 5AB
A B
r,B r,A
.=
+
-
=
+
-
=
 and the resolution between solutes B and C is
( )
. .
( . . )
. .
min min
min min
R w w
t t2
0 15 0 1
2 8 43 8
1 1
6
26
10 1BC
r,
B C
C r,B
.=
+
-
=
+
-
=
 To calculate selectivity factors or to calculate resolution using equa-
tion 12.19, we irst must calculate each solute’s retention factor using 
equation 12.8; thus
.
. . . .min
min mink t
t t
1 19
8 04 1 19 5 756 5 76A
m
r,A m
.=
-
=
-
=
.
. . . .min
min mink t
t t
1 19
8 1 19 5 5 9426 941
m
m
B
r,B
.=
-
=
-
=