Question

The following data was taken in a GC experiment: tr of air (non retained) = 33s, tr of benzene = 275s, tr of toluene = 342s. From the literature it is known that the partition coefficient of benzene for the stationary phase in your column and at your column temperature is 650. Calculate K for toluene.

Answer 1

Solution:

t _m:   the minimum possible time by which non-retained mobile phase travels

         through the column =33 s (given)

t _rB: retention time for Benzene =275 s (given)

t _rT: retention time for Toluene =342 s (given)

t’_rB: adjusted retention time for Benzene = (t _rB - t _m )=275 s - 33 s =242 s

t’_rT: adjusted retention time for Toluene = (t _rT - t _m) =342 s -33 s =309 s

k’_B:   capacity factor for Benzene= (t _rB - t _m)/ t _m=242 s/33s =7.33

k’_T: capacity factor for Toluene= (t _rT - t _m)/ t _m=309 s/33s =9.36

[The capacity factor is equivalent to the time the solute spends in the stationary phase over the mobile phase and can be related to the partition coefficient; k’=K (Vs/Vm)]

Where

K: partition coefficient

V s : Cross - sectional area of coating

V m: Cross - sectional area of column.

For benzene; k’_B= K _B(Vs/Vm) and for toluene; k’_T= K _T(Vs/Vm)

[where K_B: partition coefficient for Benzene = 650 and K_T: partition coefficient for toluene}

Relative retention can be related to retention time, capacity factor, and/or partition coefficient; α= t’_rB / t’_rT= k’_B / k’_T= K _B(Vs/Vm)/ K _T(Vs/Vm)= K _B/K _T

            Or t’_rB / t’_rT = K _B/K _T     ;           242s/309 s =650/ K _T

                K_T=(650 x309)/242 = 829.95 = round of to = 830

Answer: The partition coefficient of Toluene ( K_T) for the stationary phase = 830