# Retention Factor Formula

Retention factor some\times called capacity factor is a very convenient chromatographic descriptor since it is dimensionless and independent of the mobile phase flow rate and column dimensions.

The formula for k is,

k = $\frac{t_{R} – t_{o}}{t_{o}}$ = $\frac{t_{R}}{t_{o}}$.
The capacity or retention factor has the advantage of being dimensionless and independent of the flow rate of the mobile phase or the dimensions of the column. According to the retention factor the non absorbed inert tracer is zero. As the most important quantity that can directly be obtained from the chromatogram, the retention factor has numerous meanings. It is a dimensionless partition or the distribution ratio given by,
k = $\frac{amount of an eluite in the stationary phase}{amount of that eluite in the mobile phase}$.

## Retention Factor Formula Problems

Some of the solved problems based on Retention Factor Formula are given below.

Question 1: If a 125 $\times$ 4.6 mm column and a flow rate of 1 mL min-1. Calculate the estimated dead time.

Solution:
tM = 0.1 $\times$ $\frac{12.5}{1}$ = 1.25

k = $\frac{t_{R}-t_{M}}{t_{M}}$ applies
Solving the equation for tR yields
tR = (tM + 1)k and thus tR = (1.25 + 1)4 = 9 min

Question 2: The k value is a multiple of the value of the dead time. How many \times the dead time is the retention time? For a substance that elutes after 4min on a 125$\times$4mm column at a flow rate of 1mL min-1, the k value is 4. If a flow rate of 2mL min-1 the substance would also elute after 4 min, the k value would be 8.

Solution:

tM in the first case,
tM = 0.08 $\frac{12.5}{1}$ = 1.25 retention time equals 4 \times the dead time 4$\times$1 = 4
tM in the second case,
tM = 0.08 $\frac{12.5}{2}$ = 0.5 retention time equals 8 \times the dead time 8$\times$0.5 = 4