Question

Albumin is being separated from Immunoglobin G (IgG) in a chromatography column
having a stationary phase fraction of 0.25. The mobile phase retention time is 10
min. The distribution coefficients for albumin and IgG are 0.1 and 1, respectively. If
the albumin peak has a characteristic width of 0.52 minutes, predict the selectivity
and resolution.

Answer 1

the volume of the column is 39ml calculated using the given data

the mobile phase retention time can be calculated using equation

t_M = $\frac{V_Cε}{Q}$ $\implies$ $\frac{39(0.25)}{10}$ = 0.975 min

the retention times can be calculated using equation

t_R = t_M {1+ ( $\frac{1-ε}{ε}$ ) K}

t_R,alb = 0.975 { 1 + ($\frac{1-0.25}{0.25}$ ) 0.1 } = 1.25 min

t_R,IgG = 0.975 { 1 + ($\frac{1-0.25}{0.25}$) 1 } = 3.9 min

the number of theoretical plates in the column can be calculated from albumin retention time data using equation

N = 16($\frac{t_g}{w}$ )² $\implies$ 16 ($\frac{1.27}{0.52}$)² = 95

the peak width of IgG can be calculated using equation

W_IgG = $\frac{t_{R.IgG}}{\sqrt\frac{N}{16}}$ $\implies$ $\frac{3.9}{\sqrt\frac{95}{16}}$ = 1.6 min

the resolution of separation can be calculated using equation

R = $\frac{t_{R2}-t_{g1}}{0.5(w_1+w_2)}$ $\implies$ $\frac{3.9-1.27}{0.5(1.6+0.52)}$ = 2.58

the selectivity can be calculated using equation

α = $\frac{K_2}{K_1}$ = $\frac{t_{R2}-t_M}{t_{R1}-t_M}$ $\implies$ $\frac{1}{0.1}$ = 10

the height of the theoritical plate can be calculated using equation

H = $\frac{l}{N}$ = $\frac{50}{95}$ = 0.526 cm