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A student researcher performed a chromatographic separation of caffeine and aspartame. The retention time for caffeine, t c , was found to be 216.7 s with a baseline peak width, w c , of 13.6 s. The retention time for aspartame, t a , was 267.1 s with a baseline peak width, w a , of 18.9 s. The retention time for the unretained solvent methanol was 45.2 s.

Calculate the average plate height, H , in micrometers for this separation, given that it was performed on a 24.1 cm long column.
H = μ m

Calculate the resolution, R , for this separation using the widths of the peaks.
R =

Calculate the resolution if the number of theoretical plates were to increase by a factor of 1.5 .
R 1.5 N =

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Answer:

Average plate height: 67,4μm

Resolution: 3,10

Resolutin with increase N by a factor of 1,5: 3,80

Explanation:

Average plate height is the average between plate height of aspartame and caffeine.

Plate height is:

[tex]H = \frac{L}{16(\frac{t_R}{W} )^2}[/tex]

For aspartame: [tex]H = \frac{0,241x10^{6}um}{16(\frac{267,1s}{18,9s} )^2}[/tex]

H = 75,4 μm

For caffeine: [tex]H = \frac{0,241x10^{6}um}{16(\frac{216,7s}{13,6s} )^2}[/tex]

H = 59,33 μm

Average plate height is:

(59,3μm + 75.4μm)/2= 67,4μm

The resolution formula is:

[tex]R = \frac{2(t_{R2}-t_{R1})}{(w_2+w_1)}[/tex]

Replacing:

[tex]R = \frac{2(267,1s-216,7s)}{(18,9s+13,6s)}[/tex]

R = 3,10

As resolution is proportional to the square root of the number of theoretical plates, the increasing of 1,5 in the number of theoretical plates increases the resolution by a factor of √1,5 ≈ 1,22

That means resolution would be:

R 1,5N = 3,10×√1,5= 3,80

I hope it helps!

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