Question

From distribution studies, species M and N are known to have water/hexane distribution constant 0f 5.99 and 6.16 (K = [X]H2O/[X]hex), where X = M or N. The two species are to be separated by elution with hexane in a column packed with silica gel containing adsorbed water. The ratio VS/VM for packing is 0.425.

i) Calculate the retention factor of each solute
ii) Calculate the selectivity factor
iii) How many plates are needed to provide a resolution of 1.5?
iv) How long a column is needed if the plate height of the packing is 1.5x10^-3 cm?
v) If the flow rate is 6.75 cm.min^-1 , how long will it take to elute the two species?

Answer 1

To separate species M and N via chromatography, calculate their respective retention factors, selectivity factor, the number of plates needed for the desired resolution, the length of the column based on plate height, and the elution time given the flow rate.

Step-by-step explanation:

To answer the student's chemistry question regarding the separation of species M and N using chromatography, we'll follow a step-by-step approach for each part:

Calculate the retention factor (k) of each solute using the formula k = (Vs/Vm) × (K-1), where Vs/Vm is the volume ratio of the stationary phase to the mobile phase, and K is the distribution constant.

Calculate the selectivity factor (α) which is the ratio of the retention factors of the two solutes using the formula α = k₂/k₁.

To find out how many plates are needed for a resolution of 1.5, use the resolution equation Rₙ = №3(N)×(α-1)/(α×(4×(k₂+1))^(1/2) and solve for N.

To determine how long a column is needed, use the plate height (H) and number of plates (N) with the formula L = H × N.

Lastly, to calculate how long it will take to elute the two species, use the length of the column (L) and the flow rate (F) with time = L/F.

Answer 2

i) The retention factor for species M and N is -0.575. ii) The selectivity factor between the two species is 1.026. iii) To achieve a resolution of 1.5, 38.24 plates are needed. iv) A column length of 0.05736 cm is needed. v) The two species will be eluted in approximately 0.0085 min.

Step-by-step explanation:

i) The retention factor, also known as the capacity factor or k', can be calculated using the equation k' = (VS - VM) / VM, where VS is the volume of the stationary phase and VM is the volume of the mobile phase. To find the retention factor of species M, we substitute VS/VM = 0.425 into the equation and calculate k'M = (0.425 - 1) / 1 = -0.575. For species N, k'N = (0.425 - 1) / 1 = -0.575.

ii) The selectivity factor, also known as the separation factor or α, can be calculated using the equation α = k'N / k'M = 6.16 / 5.99 = 1.026. The selectivity factor determines the separation between the two species, with a selectivity factor close to 1 indicating poor separation and a selectivity factor greater than 1 indicating good separation.

iii) The number of plates, N, can be calculated using the equation N = (ln Rs)² / (4ln α), where Rs is the resolution and α is the selectivity factor. Given that Rs = 1.5 and α = 1.026, we substitute the values into the equation and calculate N ≈ 38.24.

iv) The length of the column, L, can be calculated using the equation L = Nh, where h is the plate height. Given that h = 1.5x10⁻³ cm and N = 38.24, we substitute the values into the equation and calculate L = (38.24)(1.5x10⁻³) = 0.05736 cm.

v) The time, t, to elute the two species can be calculated using the equation t = L / u, where u is the flow rate. Given that L = 0.05736 cm and u = 6.75 cm.min⁻¹, we substitute the values into the equation and calculate t = 0.05736 / 6.75 ≈ 0.0085 min.