Chapter 23: Q45P (page 631)

(a) For the asymmetric chromatogram in Figure 23-14, calculate the asymmetry factor, $\frac{B}{A}$ .(b) The asymmetric chromatogram in Figure 23-14 has a retention time equal to 15.0 min and a $w_{0.1}$ of 44s . Find the number of theoretical plates. (c) The width of a Gaussian peak at a height equal to $\frac{1}{10}$ of the peak height is $4.297 σ$ . Suppose that the peak in (b) is symmetric with $A = B = 22 s$ . Use Equations 23-30 and 23-32 to find the plate number.

Short Answer

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The solution is

$a) Asymmetry factor = 2 b) N = 5368 c) ρ = 10.24 s d) N = 7.72 \times 10^{3}$

Step by step solution

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a) For the asymmetric chromatogram in Figure 23-14, we shall calculate the

asymmetry factor (B/A) .

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A horizontal line was drawn across the peak at of the height, as shown in Figure

23-14:

- The quantities A and B are then determined by measuring the left half A and right half B of the peak width at 10% of the peak height - start with the left half and find that

the width is around 1 / 2(A).

- Next, look at the right-hand half; you can see that the width is roughly 1 / 1 ( B ).

We can calculate the asymmetry factor ( B / A ) from these findings, which is around:

Asymmetry factor $= \frac{1 / 1}{1 / 2} = 2$

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b) If the chromatogram is asymmetric, this is where we'll find the number of theoretical plates.

t_{r} = 15 \min = 900 s and a w_{0.1} = 44 s : N = \frac{41.7 {(t_{r} / w_{0.1})}^{2}}{(B / A) + 1.25}

Use the asymmetry factor from section a) but make sure to stick to the same time values (seconds).

$N = \frac{41.7 {(900 s / 44 s)}^{2}}{(2) + 1.25}$

$N = 5368$

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c) A Gaussian peak with a width of 4.297 $ρ$ has a height of 1/10 of the peak height.

We'll apply Equations 23-30 and 23-32 to find the plate number, assuming the

peak in (b) is symmetric with A = B = 22 s.

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If we know that the width at 1 / 10 is 22 s + 22 s = 44 s, we'll start by calculating the standard deviation.

$ρ = \frac{44 s}{4.297} = 10.24 s$

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We'll then figure out how many plates there are:

N = {(\frac{t_{r}}{ρ})}^{2} N = {(\frac{900 s}{10.24 s})}^{2} N = 7.72 \times 10^{3}

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