An open tubular column with a diameter of 187 μm and a stationary phase thickness on the inner wall of 0.54 μm passes unretained solute through in 49 s. A particular solute has a retention time of 443 s. What is the partition coefficient for this solute?

a) 88.9% b) 2211

Explanation:

a)k = (443 – 49 s)/49 s = 8.04

K = Cs/Cm = k(Vm/Vs)

Vm = V cylinder = π(d²/4)L = π[(0.187 mm)²/4)L = 0.0275 mm²L

Vs = Vtube = Vouter cylinder – Vinner cylinder = π[(0.187 mm)²/4]L – π{[(0.187 mm – 2(0.00054 mm)]²/4}L

For a thin tube, Vtube = πtdL, where t = film thickness.

This same equation also can be derived from the first equation

(Vs = Vtube = Vouter cylinder – Vinner cylinder )

since Vtube = π[(0.187 mm)2/4]L – π[(0.187 mm)2/4]L + π(0.187 mm)(0.00054 mm)L – π(0.0054 mm)²L.

The first two terms cancel out and since 0.187 mm >> 0.00054 mm the last term is negligible.

Vs = Vtube = π(0.187 mm)(0.00054 mm)L = 0.0001 mm²L

K = k(Vm/Vs) = 8.04 x (0.0275 mm²L/0.0001 mm²L) = 2211

the L cancels out so the (0.0275column length is actually not needed

b) fraction of time spent in stationary phase = time spent in stationary phase/total time spent

fraction of time spent in stationary phase = (443 – 49 s)/443 s = 0.889 = 88.9%

The partition coefficient of the solute is 8.041. This means that the solute are properly separated.

Explanation: Partition coefficient of a solute is the ratio of concentration in the stationary phase to the mobile phase of the solute. It is equivalent to the "CAPACITY FACTOR" of the solute, which is the time the solute spends in the stationary phase to the time spent in the mobile phase.

K' = (tr-tm)/tm <--> Kd = Cs/Cm

That means we can use the capacity factor to define the partition coefficient.

Kd = K'

K' is the capacity factor

Kd is the partition coefficient

tr is the retention time

tm is the unretained time

Cs is the concentration of the solute in the stationary phase.

Cm is the concentration of solute in the mobile phase.

Find the capacity factor.

K' = (443 - 49) ÷ 49 = 8.041

Since capacity factor is equivalent to partition coefficient.

Therefore;

Kd = 8.041