Question

A sample containing anthracene dissolved in methane was separated using gas chromatography on a column with mobile phase (Vm) and stationary phase (Vs) volumes of 24 mL and 9.6 mL, respectively. For this particular column, anthracene has a retention volume (Vr) of 72.3 mL. Calculate the retention factor (k) and the partition coefficient (K) for anthracene in this separation.

I know that k=K(Vs/Vm) and K= Cs/Cm but how would you solve for both k and K?

Answer 1

I think that you are actually missing other values, like Concentrations or at least retention times.

However, I manage to find the following expressions which I will use to calculate k and K as an alternate solution, according to the data you are providing:

k can also be: k = tr - tm / tm = tr' / tm

Where tr is retention time, and tm is the hold up time in the column to elute. tr' is the adjusted retention time

Vr' = Vr - Vm

Vr' = 72.3 - 24 = 48.3 mL

Vr' is the adjusted retention volume

With this we also know that Fc = Vr/tr = Vm/tm = Vr'/tr'

Where Fc is the carrier gas flow in the column so:

Vm/tm = Vr'/tr'

tr'/tm = Vr'/Vm = k

k = 48.3 / 24 = 2.0125

With this, you can calculate now K solving for the equation you write of k:

k = K(Vs/Vm) ----> K = k(Vm/Vs)

K = 2.0125 * (24/9.6)

K = 5.03125

Hope this helps