Question

3. A capillary column for use in gas chromatography is 30.0 m long and has an internal diameter of 0.320 mm. The inside wall of the capillary is coated with the stationary phase. a. The phase ratio (B) is the ratio of the mobile phase volume to the stationary phase volume: B = Vm/Vs. For a particular separation, the desired phase ratio is B = 200. What should the thickness of the stationary phase be to obtain this phase ratio? b. When He is used at the mobile phase, theory predicts the optimal linear flow rate to be 25 cm/sec. What is the corresponding volume flow rate (in ml/min)?

Answer 1

3a. The phase ratio can also be given as

β = d_c/4d_f

where d_c is the column diameter and d_f is the film diameter or thickness of the stationary phase.

Given β = 200

internal diameter of the column, d_c = 0.320 mm

Therefore, from the equation thickness of the stationary phase can be calculated as

d_f = d_c/4 β

d_f = 0.320 mm/4 × 200

d_f = 0.320 mm/800

d_f = 0.0004 mm

3b. Volume flow rate, V can be calculated from linear flow rate, L as follows

F (mL/min) = () (cm/h) × column cross sectional area (cm²)

L 60

F (mL/min) = (
L 60
) ×
X d2 4
(cm²)

Where d is the column diameter in cm

Now we are given with d = 0.320 mm = 0.0320 cm

Linear flow rate, L = 25cm/sec = 89.99 × 10³ cm/h (By taking 1 sec = 1/3600 hour)

Therefore Volume Flow rate, F in mL/min is

F =
89.99 x 103 60
×
x (0.0320)2 TX 4

F =
89.99 x 103 60
×
3.14 X (0.0320)2 4

F = (1.499 × 10³) × 0.804 × 10^-3)

F = 1.21 mL/min