Chromatographic Methods for Environmental Analysis - Fundamentals of Environmental Sampling and Analysis - page 256

(Eq. 10.3). In the equation below, subscript A denotes a rapidly eluted chemical with a
weak retention factor (refer to Fig. 10.2) so that a is always greater than 1.0.

k B
k A ¼

t rB t m
t rA t m

a ¼ ð10 : 4Þ

The separation factor represents the relative interaction between each of the solutes
and the stationary phase, and can be used to express the relative intermolecular
forces and the magnitude of their similarities or differences. In practice, it tells us
how difficult it is to separate these two solutes. The larger the value of a, the easier
the separation. Two compounds can be separated only if a is higher than 1.0 in the
selected phase system. For HPLC separation a should be 1.05 or higher.

Resolution

Resolution (R) is the measure of a column's ability to separate two peaks. The
column resolution of two adjacent peaks is defined as:

Peak separation
Average peak width ¼

t rB t rA
ðw A þw B Þ=

R ¼ ð10 : 5Þ

2

where t rA and t rB are the retention times of the two peaks (compound A elutes first),
and w A and w B are the baseline width of two peaks. Note that tangents are drawn to the
inflection points in order to determine the widths of peaks at their bases (Fig. 10.2).
The unit for w is the same as the time unit, hence resolution is a unitless parameter.
When a resolution (R) is equal to 1.0, two peaks of equal widths will have a
2.3% overlap and is considered to be the minimum for quantitative separation. A
resolution value of 1.5 results in only 0.1% overlap, and can be considered sufficient
for a complete baseline resolution. Strictly, Eq. 10.5 is valid only when two peaks
have the same heights. Typically an R value of greater than 1.5 is needed, depending
on the height ratio of the peaks. If a smaller peak is adjacent to its large neighbor,
then a higher resolution is necessary to achieve a good separation.

Number of Theoretical Plates

From the classical work of Martin and Synge (1941; 1952 Nobel Prize), a
chromatographic column with a length L is divided into equal length N theoretical
plates numbered from 1 to N. For each of these plates, the concentration of analyte in
the mobile phase reaches equilibrium with the concentration in the stationary phase.
The number of theoretical plates (N) can be calculated from a chromatogram on the
basis of the retention time (t r ) and the peak width (w).

2

t r
w

N ¼ 16 ð10 : 6Þ

Since one theoretical plate represents a single equilibrium step, a column with more
theoretical plates will have greater resolving power. Therefore, the plate number (N)
is a measure of the separation performance of a column, or the column efficiency.In