91Ó°ÊÓ

$$\begin{gathered} \mathrm{Resolution}=\frac{\sqrt{\mathrm{N}\left(\mathrm{Î\pm }-1\right)}}{\mathrm{Î\pm }}\left(\frac{{\mathrm{k}}_2}{1+{\mathrm{k}}_2}\right) \\ \mathrm{Where}, \\ \mathrm{N}-\mathrm{number}\mathrm{of}\mathrm{theoretical}\mathrm{plates} \\ \mathrm{Î\pm }-\mathrm{relative}\mathrm{retention}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{peaks} \\ {\mathrm{k}}_2-\mathrm{retention}\mathrm{factor}\mathrm{of}\mathrm{the}\mathrm{more}\mathrm{retained}\mathrm{component} \\ \mathrm{The}\mathrm{above}\mathrm{equation}\mathrm{shows}\mathrm{that}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{resolution}\mathrm{is}\mathrm{proportional}\mathrm{to}\sqrt{\mathrm{N}} \end{gathered}$$

a)

The greatest and least retention of components in the mobile phase in reversed phase column chromatography, increasing the amount of organic solvent increases the mobile phase strength.

Acetonitrile at $40\%$yields the longest retention time. The retention time is the shortest at $60\%$.

Toluene and benzophenone are co-elutes at$51.6\%$acetonitrile

$$\begin{gathered} b) \\ \mathrm{Each}\mathrm{composition}\text{'}\mathrm{s}\mathrm{mobile}\mathrm{phase}\mathrm{is}\mathrm{separated}. \\ \mathrm{logk}\mathrm{to}\mathrm{retention}\mathrm{time}\mathrm{conversion}. \\ K=\frac{t_f\mathit{-}{t}_m}{t_m} \\ {\mathrm{t}}_{\mathrm{m}}×(1+\mathrm{K}) \\ {\mathrm{t}}_{\mathrm{m}}\mathrm{can}\mathrm{be}\mathrm{calculated}\mathrm{by}\mathrm{Equation}25-5~ \\ {\mathrm{t}}_{\mathrm{m}}≈\frac{1{{\mathrm{A}}_{\mathrm{C}}}^2}{2\mathrm{F}} \\ ≈\frac{15\mathrm{cm}×(0.46{\mathrm{cm}}^{2)}}{2×1.0\mathrm{mil}/\min } \\ =1.6\min \\ {\mathrm{t}}_{\mathrm{f}}=1.6\min ×(1+15.1) \\ =25.8\min \\ \mathrm{The}\mathrm{chromatogram}\mathrm{is}\mathrm{given}\mathrm{below}\mathrm{as} \end{gathered}$$

c)

Benzophenone and toluene, the chemicals with the closest peak, have the lowest resolution. These chemicals' retention factors are reported as

$$\begin{gathered} {10}^{0.13}=1.35 \\ {10}^{0.21}=1.62 \\ \mathrm{The}\mathrm{formula}\mathrm{for}\mathrm{calculating}\mathrm{relative}\mathrm{retention}\mathrm{is}\mathrm{as}\mathrm{follows}: \\ \mathrm{Î\pm }=\frac{{\mathit{K}}_{\mathit{2}}}{{\mathit{K}}_{\mathit{1}}} \\ =\frac{1.61}{1.35} \\ =1.20 \\ \mathrm{N}=\frac{3000.1\left(\mathrm{cm}\right)}{{\mathrm{d}}_{\mathrm{p}}\left(1\mathrm{m}\right)} \\ =\frac{3000×15}{5} \\ =9000 \\ \mathrm{Resolution} \\ =\frac{\sqrt{N}}{4}\frac{\left(\mathrm{Î\pm }-1\right)}{\mathrm{Î\pm }}\left[\frac{{\mathrm{k}}_{\mathit{2}}}{1+{\mathrm{k}}_{\mathit{2}}}\right] \\ =\frac{\sqrt{9000}}{4}\frac{\left(1.20-1\right)}{1.20}\left(\frac{1.62}{1+1.62}\right) \\ =2.4 \end{gathered}$$

d)

The requirements for good peak separation are as follows:

$$\begin{gathered} 0.5≤\mathrm{K}≤20 \\ Resoluctionâ‰\yen 2 \\ Operating\mathit{}pressure≤15\mathrm{MPa} \\ 0.9≤\mathrm{asymmetry}\mathrm{factor}≤1.5 \end{gathered}$$

All of the following requirements for excellent peak separation are met by the $60\%$

acetonitrile. Thus,$60\%$acetonitrile may be used to separate peaks, with the added benefit of a separation period of less than six minutes.