Given the following data, calculate the capacity factor for the solute.
Chart speed for recording the chromatogram is 1 cm/min
Mobile phase flow rate is 1.6 mL/min
Migration distance of the void volume indicator is 1.3 cm
Migration distance of the solute of interest is 13.2 cm

Question

Quizplus · Accepted Answer

The equation to calculate capacity factor is k' = Vₑ - Vₒ/Vₒ, where Vₑ is the elution volume and Vₒ is the void volume.A void volume indicator is used to determine the volume of mobile phase that is already on the column at the time the solute is injected into the system.This volume of mobile phase must come off of the column following injection of the sample before the solute can possibly elute from the column.This volume of mobile phase has no influence on the chromatography of the solute but will appear on the chromatogram from which results are derived.Therefore, this volume, the void volume, must be subtracted from the total elution volume measured in the elution of the solute.Thus the numerator of the capacity factor equation (Vₑ - Vₒ) could be considered as the corrected elution volume.The void volume is determined by measuring the elution volume of a solute (identified as a void volume indicator) known to not be retained by the stationary phase being used.The void volume indicator "rides the solvent front" of the mobile phase that carries it through the column, identifying how much mobile phase is on the column at the time of injection.To determine the elution volume for the solute, first determine retention time: tᵣ = distance migrated/chart speed; tᵣ = 13.2 cm/1 cm/min; tᵣ = 13.2 minutes.From this, determine the elution volume: Vₑ = tᵣ × mobile phase flow rate (F);
Vₑ = 13.2 min × 1.6 mL/min; Vₑ = 21.12 mL.This same method is used for determining the void volume, with the exception that the void volume is noted as Vₒ, and void time is noted as tₒ: tₒ = distance migrated/chart speed; tₒ = 1.3 cm/1 cm/min; tₒ = 1.3 minutes.Vₒ = 1.3 min × 1.6 mL/min; Vₒ = 2.08 mL.Considering the numerator of the capacity factor equation, Vₑ - Vₒ = 21.12 mL - 2.08 mL = 19.04.(Again, this could be considered as the corrected elution volume.)
Recall that the void volume is the volume of mobile phase in front of the solute at the time of injection.In other words, the void volume is the volume of one column capacity.Thus to determine the capacity factor, k', take the corrected elution volume (Vₑ - Vₒ) and divide by the volume of one column capacity, Vₒ.This will determine the number of column capacities necessary to elute the solute-known as the capacity factor: k' = Vₑ - Vₒ/Vₒ; k' = 21.12 mL - 2.08 mL/2.08 mL = 9.15.This same result can be determined by using tᵣ and tₒ in place of volume.

Given the Following Data, Calculate the Capacity Factor for the Solute