A) How many moles of an analyte are present in a 10.0 micro-M solution that occu

Question

A) How many moles of an analyte are present in a 10.0 micro-M solution that occupies 1% of the length of a 25 micrometer internal diameter by 60.0 cm long capillary?

B) Assume that this particular analyte travels the entire length of the column at a rate of 3.22 mm/s with absolutely no natural diffusion. What would be the number of theoretical plates that one could obtain for this column (recall N = tr^2/W^2) where tr and W are the analyte retention time and peak width respectively? Note that both peak width and retention can be in time units.

Explanation / Answer

1.

First find volume.

For cylinder

V = (pi)r^2 x h

   = (pi)(25 x 10^-6 m) x (0.6 m)

   = 4.7 x 10^-5 m^3

1 m^3 = 1000 L

V = 4.7 x 10^-2 L

Analye takes up 1 % of this, so volume of analyte is 4.7 x 10^-2 x 0.01 L = 4.7 x 10^-4 L

Moles = concentration x volume

= 10x10^-6 mol/L x 4.7 x 10^-4 L

= 4.7 x 10^-9 mole

2.

Retention time is how long the analyte is in the column.

Peak width is how long it takes for the analyte to pass a certain point.

Analyte takes up 1 % of 60.0 cm = 600 mm column, thus it is 6 mm thick.

this moves at 3.22 mm/s

Retention time = 600mm / (3.22 mm/s) = 186 s

Peak width = 6 mm / (3.22 mm/s) = 1.86 s

N = rt^2/W^2

= 186^2/1.86^2

= 10000 plates

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