Question

Two peaks emerge from a reversed-phase chromatography column as sketched in the illustration.

According to Equation 23-33, resolution is given by

Resolution$\mathbf{=}\frac{\sqrt{\mathbf{N}}}{\mathbf{4}}\frac{(\alpha -1)}{\mathbf{\alpha }}\mathbf{\left(}\frac{{\mathbf{k}}_{\mathbf{2}}}{\mathbf{1}\mathbf{+}{\mathbf{k}}_{\mathbf{2}}}\mathbf{\right)}$

where $\mathit{N}$is plate number, $\mathbf{\alpha }$is relative retention (Equation23-20), and ${\mathbf{k}}_{\mathbf{2}}$ is the retention factor for the more retained component (Equation 23-16).

(a) If you decrease the amount of organic solvent in the mobile phase, you will increase retention. Sketch the chromatogram if retention factors increase but $\mathit{N}$and $\mathbf{\alpha }$are constant.

(b) If you change the solvent type or the stationary phase, you will change the relative retention. Sketch the chromatogram if$\mathbf{\alpha }$increases but $\mathit{N}$and${\mathit{k}}_{\mathbf{1}}$are constant.

(c) If you decrease particle size or increase column length, you can increase the plate number. Sketch the chromatogram if $\mathit{N}$increases by (i) decreasing particle size and (ii) increasing column length. Assume $\mathit{\alpha }$and ${\mathit{k}}_{\mathbf{2}}$are constant.

Short answer

a)The sketch of chromatogram if retention factors increase but $N$and $\alpha$are constant:

b) The sketch of chromatogram if $\mathrm{\alpha }$increases but $\mathrm{N}$and ${\mathrm{k}}_1$are constant:

c) The sketch of chromatogram if $N$increases by (i) decreasing particle size and (ii) increasing column length.

Step-by-step solution

Definition of retention factor.

The retention factor (Rf) is used in thin-layer chromatography to compare and identify substances. The distance travelled by the compound divided by the distance travelled by the solvent front gives the Rf value of a compound.

Step 2: The sketch of chromatogram if retention factors increase but   and  are constant.

a)

When the quantity of organic solvent in the mobile phase is reduced, the retention is automatically enhanced. As a result, if$N$and$\mathrm{\alpha }$are held constant, the chromatogram will look like this

Step 3: The sketch of chromatogram if αincreases butNandk1are constant.

b)

If the solvent or stationery phase is changed, the relative retention will vary. As a result, the chromatogram will look like this:

Step 4: The sketch of chromatogram if N increases by (i) decreasing particle size and (ii) increasing column length.

c)

The chromatogram can be produced as shown below if the particle size is reduced and the plate number is increased.

The chromatogram can be obtained as shown below if the column length is raised and the plate number is increased.