Question

23-32. Chromatograms of compounds A and B were obtained at the same flow rate with two columns of equal length. The value of ${\mathrm{t}}_{\mathbf{m}}$is 1.3m in both cases.

(a) Which column has more theoretical plates?

(b) Which column has a larger plate height?

(c) Which column gives higher resolution?

(d) Which column gives a greater relative retention?

(e) Which compound has a higher retention factor?

(f) Which compound has a greater partition coefficient?

(g) What is the numerical value of the retention factor of peak A?

(h) What is the numerical value of the retention factor of peak B?

(i) What is the numerical value of the relative retention?

Short answer

$$\begin{gathered} \mathrm{The}\mathrm{solution}\mathrm{is} \\ \mathrm{a})\mathrm{Column}1\mathrm{is}\mathrm{higher}\mathrm{due}\mathrm{to}\mathrm{higher}\mathrm{peaks}. \\ \mathrm{b})\mathrm{Column}2\mathrm{has}\mathrm{larger}\mathrm{peaks}\mathrm{due}\mathrm{to}\mathrm{the}\mathrm{big}\mathrm{plate}\mathrm{height},\mathrm{allowing}\mathrm{for}\mathrm{fewer}\mathrm{plates} \\ \mathrm{to}\mathrm{fit}\mathrm{in}\mathrm{a}\mathrm{column}. \\ \mathrm{c})\mathrm{Column}1:\mathrm{Because}\mathrm{the}\mathrm{peaks}\mathrm{are}\mathrm{separated}\mathrm{better},\mathrm{there}\mathrm{are}\mathrm{less}\mathrm{overlaps}. \\ \mathrm{d})\mathrm{neither},\mathrm{because}\mathrm{in}\mathrm{both}\mathrm{columns},\mathrm{the}\mathrm{retention}\mathrm{time}{\mathrm{t}}_{\mathrm{r}}\mathrm{and}\mathrm{the}\mathrm{mobile}\mathrm{phase} \\ \mathrm{elution}\mathrm{time}{\mathrm{t}}_{\mathrm{m}}\mathrm{are}\mathrm{the}\mathrm{same}. \\ \mathrm{e})\mathrm{Compound}\mathrm{B},\mathrm{due}\mathrm{to}\mathrm{the}\mathrm{fact}\mathrm{that}\mathrm{it}\mathrm{is}\mathrm{eluted}\mathrm{later}. \\ \mathrm{f})-\mathrm{Compound}\mathrm{B}\mathrm{is}\mathrm{eluted}\mathrm{later},\mathrm{indicating}\mathrm{that}\mathrm{it}\mathrm{has}\mathrm{a}\mathrm{longer}\mathrm{half}-\mathrm{life}\mathrm{has}\mathrm{a} \\ \mathrm{stronger}\mathrm{preference}\mathrm{for}\mathrm{the}\mathrm{stationary}\mathrm{phase} \\ \mathrm{g})\mathrm{k}=5.2 \\ \mathrm{h})\mathrm{k}=6.7 \\ \mathrm{i})\mathrm{\alpha }=1.3 \end{gathered}$$

Step-by-step solution

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We have chromatograms of chemicals A and B that were acquired at the same flow rate and with two columns of equal length in this work. In both circumstances, the value of ${\mathrm{t}}_{\mathrm{m}}=1.3\mathrm{m}$is the same.

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Please respond to the following questions:

(a) Which column has more theoretical plates?

- Column is higher due to higher peaks.

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(b) Which column has a larger plate height?

- Column 2 has larger peaks due to the big plate height, allowing for fewer plates to fit in a column.

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(c.) Which column gives higher resolution?

- Column : Because the peaks are separated better, there are less overlaps .

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(d) Which column gives a greater relative retention?

- neither, because in both columns, the retention time${\mathrm{t}}_{\mathrm{r}}$ and the mobile phase elution time ${\mathrm{t}}_{\mathrm{m}}$are the same.

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(e) Which compound has a higher retention factor?

- Compound B, due to the fact that it is eluted later.

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(f) Which compound has a greater partition coefficient?

- Compound B is eluted later, indicating that it has a longer half-life has a stronger preference for the stationary phase

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g) What is the numerical value of the retention factor of peak A?

- From the chromatogram, we can see that compound has a retention time of${\mathrm{t}}_{\mathrm{r}}=8$ minutes.

$$\begin{gathered} \mathrm{k}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}} \\ \mathrm{k}=\frac{8-1.3}{1.3} \\ \mathrm{k}=5.2 \end{gathered}$$

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h) What is the numerical value of the retention factor of peak B?

- From the chromatogram, we can see that compound B has a retention time of ${\mathrm{t}}_{\mathrm{r}}=10$minutes.

$$\begin{gathered} \mathrm{k}=\frac{{\mathrm{t}}_{\mathrm{r}}-{\mathrm{t}}_{\mathrm{m}}}{{\mathrm{t}}_{\mathrm{m}}} \\ \mathrm{k}=\frac{10-1.3}{1.3} \\ \mathrm{k}=6.7 \end{gathered}$$

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$$\begin{gathered} \mathrm{i})\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{numerical}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{relative}\mathrm{retention}? \\ \mathrm{\alpha }=\frac{{\mathrm{k}}_{\mathrm{B}}}{{\mathrm{k}}_{\mathrm{A}}} \\ \mathrm{\alpha }=\frac{6.7}{5.2} \\ \mathrm{\sigma }=1.3 \end{gathered}$$