(a) Number of plates for each peak:
- Peak A: 483.53 plates
- Peak B: 705.95 plates
- Peak C: 666.26 plates
- Peak D: 1152.57 plates
(b) Mean and standard deviation for N:
- Mean (μ): 751.82
- Standard deviation (σ): 304.99
(c) Plate height for the column: 0.03 cm
For A, B, C, and D:
(a) Retention factor (k):
- Peak A: 0.74
- Peak B: 3.29
- Peak C: 3.55
- Peak D: 6.97
(b) Distribution constant (K): 8.35
(a) To calculate the number of plates from each peak, we can use the formula:
N = 5.54 * (tR / W)^2
where N is the number of plates, tR is the retention time, and W is the peak width at the base.
For peak A:
N = 5.54 * (5.4 / 0.41)^2 = 483.53
For peak B:
N = 5.54 * (13.3 / 1.07)^2 = 705.95
For peak C:
N = 5.54 * (14.1 / 1.16)^2 = 666.26
For peak D:
N = 5.54 * (21.6 / 1.72)^2 = 1152.57
(b) To calculate the mean and standard deviation for N, we can use the following formulas:
Mean (μ) = (N1 + N2 + N3 + N4) / 4
Standard Deviation (σ) = sqrt((1/3) * ((N1 - μ)^2 + (N2 - μ)^2 + (N3 - μ)^2 + (N4 - μ)^2))
Mean:
μ = (483.53 + 705.95 + 666.26 + 1152.57) / 4 = 751.82
Standard Deviation:
σ = sqrt((1/3) * ((483.53 - 751.82)^2 + (705.95 - 751.82)^2 + (666.26 - 751.82)^2 + (1152.57 - 751.82)^2)) = 304.99
(c) To calculate the plate height for the column, we can use the following formula:
H = L / N
where H is the plate height, L is the length of packing, and N is the number of plates.
H = 24.7 / (483.53 + 705.95 + 666.26 + 1152.57) / 4 = 0.03 cm
From the data in the problem, we can calculate the retention factor (k) and the distribution constant (K) for A, B, C, and D.
(a) To calculate the retention factor, we can use the formula:
k = (tR - t0) / t0
where k is the retention factor, tR is the retention time, and t0 is the non-retained peak time.
For A:
k = (5.4 - 3.1) / 3.1 = 0.74
For B:
k = (13.3 - 3.1) / 3.1 = 3.29
For C:
k = (14.1 - 3.1) / 3.1 = 3.55
For D:
k = (21.6 - 3.1) / 3.1 = 6.97
(b) To calculate the distribution constant, we can use the formula:
K = VM / VS
where K is the distribution constant, VM is the mobile phase volume, and VS is the stationary phase volume.