Question

An HPLC setup has an injection volume of 0.225 mL, a detector volume of 0.429 ml, and contains 31.0 cm of tubing, which has a diameter of 0.065 cm. The baseline width, wobs, of a band eluting from the column at a flow rate of 1.60 ml/min is observed to be 0.614 min. Assuming a diffusion coefficient of 8.9 x 10-9 m²/s, calculate the baseline width of the band, in minutes, if the column was the only source of broadening. Wcolumn = 1.548 x10–3 min

Answer 1

The values provided in the question are as follows: Injection volume = 0.225 ml Retention volume, VR = 0.429 ml Length of the column, L = 31.0 cm = 0.31 m Diameter of the column = 0.065 cm Flow rate of the band eluting from the column, Fe = 1.60 – min Observed baseline width, wobs = 0.614 min Diffusion coefficient, Dm = 8.9 x 10-9 -

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The longitudinal diffusion (B) can be calculated from the equation as follows: B= 2 X Y X Dm (Where Y is a constant =0.7) Now substituting the provided values in the above equation we get as follows:

B= 2 x (0.7) x (8.9 x 10-9) =B=1.246 x 10-8 m

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The retention time (tr) can be calculated from the equation as follows: tr = YES Now substituting the provided values in the above equation we get as follows:

0.429 R = 1.60 8 th = 0.2681 min 8 th = 16.086 s

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The linear velocity (u) can be calculated from the equation as follows: u blog Now substituting the provided values in the above equation we get as follows:

0.31 u= 16,086 u=0.0193

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The plate height (H) can be calculated from the Van Deemter equation as follows: Now substituting the provided values in the above equation we get as follows:

H =- 1.246 x 10-8 0.0193 H= 6.456 x 10-'m

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The number of theoretical plates (N) can be calculated from the equation as follows: N = 1 Now substituting the provided values in the above equation we get as follows:

0.31 N= 6.456 x 10-7 N= 4.8017 x 105

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Assuming that, if column was the only source of broadening, the baseline width (Wbase) of the band can be calculated from the equation as follows: N = 16x (white Now substituting the provided values in the above equation we get as follows:

4.8017 x 10 = 16 x = 16.0862 Wbase 16.0862 Wbase = 16 4.8017 x 105 → Wbase = 8.62226 x 10-3s = Wbase = 60 < (8.62226 x 10-3) min =W =0.5173 min

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The baseline width of the band is 0.5173 min, if the column was the only source of broadening.