Question

A student researcher performed a chromatographic separation of caffeine and aspartame. The retention time for caffeine, is, was found to be 218.0 s with a baseline peak width, wc, of 14.4 s. The retention time for aspartame, 1., was 250.5 s with a baseline peak width, w of 21.1 s. The retention time for the unretained solvent methanol was 40.4 s. Calculate the average plate height, H, in micrometers for this separation, given that it was performed on a 27.7 cm long column. H = Calculate the resolution, R, for this separation using the widths of the peaks. Calculate the resolution if the number of theoretical plates were to increase by a factor of 2.5. RSNE

Answer 1

ANSWER:

Data:

• Caffeine:
  • t_C = 218.0 s
  • w_C = 14.4 s
• Aspartame:
  • t_A = 250.5 s
  • w_A = 21.1 s
• Column length (L): 27.7 cm

a) Average plate height

The plate height (H) is defined as:

$H=\frac{L}{N}$

where L = length column and N = number of plate

And the number of plate is

$N=16\left (\frac{t_{r}}{w} \right )^{2}$

then we can calculate the number of plate and the plate height for caffeine and aspartame:

	Caffeine	Aspartame
tR	218.0 s	250.5 s
w	14.4 s	21.1 s
N	$16\left (\frac{218.0\, s}{14.4\, s} \right )^{2}=\mathbf{3666.98}$	$16\left (\frac{250.5\, s}{21.1\, s} \right )^{2}=\mathbf{2255.12}$
H	$\frac{27.7\, cm}{3666.98}=7.554x10^{-3}\, cm=\mathbf{75.54\, \mu m}$	$\frac{27.7\, cm}{2255.12}=0.01228\, cm=\mathbf{122.8\, \mu m}$

then, the average plate height (H) is

$H=\frac{H_{C}+H_{A}}{2}=\frac{75.54\, \mu m+122.8\, \mu m}{2}$

$\mathbf{H=99.17\, \mu m}$

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b) Resolution

For this separation, the resolution is defined as

$R=\frac{2(t_{A}-t_{C})}{w_{C}+w_{A}}$

$R=\frac{2(250.5\, s-218.0\, s)}{14.4\, s+21.1\, s}=\mathbf{1.83}$

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c) Resolution - number of theoretical plates increased by a factor of 2.5

The resolution is related to number of plates in column as:

$R=\frac{\sqrt{N}}{4}\left ( \frac{\alpha -1}{\alpha } \right )\left ( \frac{1+k'_{A}}{k'_{A}} \right )$

where

• k'_A = capacity factor of aspartame => it could be changed by modifying temperature or mobile phase composition
• α = selectivity factor => it could be changed by modifying temperature, mobile phase composition or stationary phase composition

For this separation

$R=\frac{\sqrt{N}}{4}\left ( \frac{\alpha -1}{\alpha } \right )\left ( \frac{1+k'_{A}}{k'_{A}} \right )=1.83$

Then, if we increase N by a factor of 2.5 we have

$R_{2.5N}=\frac{\sqrt{2.5N}}{4}\left ( \frac{\alpha -1}{\alpha } \right )\left ( \frac{1+k'_{A}}{k'_{A}} \right )$

$R_{2.5N}=\sqrt{2.5} \left [\frac{\sqrt{N}}{4}\left ( \frac{\alpha -1}{\alpha } \right )\left ( \frac{1+k'_{A}}{k'_{A}} \right ) \right ]$

$R_{2.5N}=\sqrt{2.5} \times R=\sqrt{2.5} \times 1.83$

$\mathbf{R_{2.5N}=2.89}$