Calculations:
For each trial, calculate the VM, the mobile phase volume:
Trial 1:
VM = 0.5 πr2L = 0.5 x 3.14 x (0.50 cm)2 x 1.8 cm = 0.707 mL
Trial 2:
VM = 0.5 πr2L = 0.5 x 3.14 x (0.50cm)2 x 3.5cm = 1.37 mL
For each trial, calculate the band width for the two components:
Trial 1:
VR(start, red) = 1.2 mL
VR(end, red) = 1.3 mL
VR(start, blue) = 1.35 mL
VR(end, blue) = 2.0 mL
W(red)= VR(end, red) – VR(start, red) = 1.3 mL - 1.2 mL = 0.1 mL
W(blue)=VR(end, blue) – VR(start, blue) = 2.0 mL - 1.35 mL = 0.65 mL
Trial 2:
VR(start, red) = 1.8 mL
VR(end, red) = 2.3 mL
VR(start, blue) = 2.3 mL
VR(end, blue) = 4.3 mL
W(red)= VR(end, red) – VR(start, red) = 2.3 mL – 1.8 mL = 0.5 mL
W(blue)=VR(end, blue) – VR(start, blue) = 4.3 mL – 2.3 mL = 2.0 mL
For each trial, calculate the center of the bands for the two components:
Trial 1:
VR(avg, red) = VR(start, red) + 0.5 Wred= 1.2 mL + (0.5)(0.1 mL) = 1.25 mL
VR (avg, blue) = VR(start, blue) + 0.5 Wblue= 1.35 mL + (0.5)(0.65 mL) = 1.675 mL
Trial 2:
VR(avg,red) = VR(start, red) + 0.5 Wred= 1.8 mL + (0.5)(0.5 mL) = 2.05 mL
VR (avg, blue) = VR(start, blue) + 0.5 Wblue= 2.3 mL + (0.5)(2.0 mL) = 3.3 mL
For each tiral, calculate the retention factor k' for both components:
Trial 1:
k red’ = (VR(avg, red) - VM) = (1.25 mL – 0.707 mL) = 0.77 mL
(VM) (0.707 mL)
k blue’ = (VR(avg, blue) - VM) = (1.675 mL – 0.707 mL) = 1.37 mL
(VM) (0.707 mL)
Trial 2:
k red’ = (VR(avg, red) - VM) = (2.05 mL – 1.37 mL) = 0.50 mL
(VM) (1.37 mL)
k blue’ = (VR(avg,blue) - VM) = (3.3 mL – 1.37 mL) = 1.41 mL
(VM) (1.37 mL)
For each trial, calculate the selectivity, or seperation factor, a:
Trial 1:
a = k’ blue = 1.37 = 1.78
k' red 0.77
Trial 2:
a = k’ blue = 1.41 = 2.83
k' red 0.50
For each trial, calculate the number of theoretical plates, N, in the column:
Trial 1:
N = 16 [(VR(end,blue)]2 = 16 [2 mL]2 = 49.23 mL
[Wblue] [0.65 mL]
Trial 2:
N = 16[VR(end,blue)]2 = 16[4.3 mL]2 = 34.4 mL
[Wblue] [2.0 mL]
For each trial, calculate the resolution R, the major objective of a chromatographic seperation:
Trial 1:
R = 2(VR (avg, blue) - VR(avg,red)) = 2(1.675 mL – 1.25 mL) = 1.133 mL
Wred + Wblue (0.1 mL + 0.65 mL)
Trial 2:
R = 2(VR (avg, blue) - VR(avg,red)) = 2(3.3 mL – 2.05 mL) = 7.0 mL
Wred + Wblue (4.3 mL + 2.0 mL)
Calculate the average values for a, N, and R:
a = (trial 1 + trial 2) = (1.78 + 2.82) = 2.3
2 2
N = (trial 1 + trial 2) = (49.23 + 34.4) = 41.82
2 2
R = (trial 1 + trial 2) = (1.133 + 7.0) = 4.17
2 2