Question

A chromatogram with ideal Gaussian bands has${\mathbf{t}}_{\mathbf{r}}\mathbf{=}\mathbf{9}\mathbf{}\mathbf{min}$and
${\mathbf{w}}_{\mathbf{1}\mathbf{/}\mathbf{2}}\mathbf{=}\mathbf{2}\mathbf{}\mathbf{min}$.

(a) How many theoretical plates are present?

(b) Find the plate height if the column is 10cm long.

Short answer

The solution is

$$\begin{gathered} \mathrm{a})\mathrm{N}=112 \\ \mathrm{b})\mathrm{H}=0.089\mathrm{cm} \end{gathered}$$

Step-by-step solution

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We have a chromatogram with perfect Gaussian bands of ${\mathrm{t}}_{\mathrm{r}}=9\min$and ${\mathrm{w}}_{1/2}=2\min$in this task.

Because we have ${\mathrm{w}}_{1/2}$here, we used the half-width formula instead of Equation 23-30.

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a) Here we will find the number of theoretical plates present on a column:

$$\begin{gathered} \mathrm{N}=\frac{5.55{\mathrm{tr}}^2}{{\left({\mathrm{w}}_{1/2}\right)}^2} \\ \mathrm{N}=\frac{5.55\times {\left(9\min \right)}^2}{{\left(2\min \right)}^2} \\ \mathrm{N}=112 \end{gathered}$$

Because we have${\mathrm{W}}_{1/2}$ here, we used the half-width formula instead of Equation 23-30

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a)If the column is long, we will compute the plate height as follows:

$$\begin{gathered} \mathrm{H}=\frac{\mathrm{L}}{\mathrm{N}} \\ \mathrm{H}=\frac{10\mathrm{cm}}{112}=0.089\mathrm{cm} \end{gathered}$$