Theory of Chromatography - Biagini

Question 1

What is the peak terminology regarding a chromatogram?

Answer 1

T₀ = dead-time volume

T₁ = retention time of component 1

T₂ = retention time of component 2

W = width of peak

W_1/2 = width of peak at half the height.

Question 2

What is the capacity factor from retention times?

Answer 2

Retention factor, or capacity factor k^’ of an analyte is measured experimentally as shown:

k^’ = (t_r-t₀) / t₀

The capacity factor describes thermodynamic basis of the separation and its definition is the ratio of the amounts of solute at the stationary and mobile phases within the analyte band inside the chromatographic column. See Image.

Question 3

What are the individual components of the capacity factor equation?

Answer 3

• C_s is the concentration of solute at stationary phase
• C_m is the concentration of solute at mobile phase
• Phi is the ratio of the stationary and mobile phase volumes all within the chromatographic band.

The retention/capacity factor is useful because it can be used to compare the retention of a solute between two chromatographic systems, normalising it to the column’s geometry and system flow rate.

Question 4

What is the relative retention time?

Answer 4

If t₀ is uncertain, then one known component can be used as a retention marker for the other peaks.

In such cases, ratio between retention time of any peak in the chromatogram and the retention time of the marker is used:

(t_{R (Peak)} / t_{R (Marker)})

This is known as the relative retention time.

Question 5

What is a ‘theoretical plate’?

Answer 5

• There is no such thing as a theoretical plate. Practically it relates to the width of a band to distance travelled.
• The smaller the plate height the narrower the band width
• Formulae include N = 16 (t_r)²/w² and H = L/N
  
  • t_r = retention time
  • w = width
  • L = column length
  • N = number of theoretical plates
  • H = plate height.
• If half peak height is used: N = 5.54(t_r)²/W_1/2²

Question 6

How can resolution be calculated from peak widths?

Answer 6

Resolution = (delta)t_r/W_av

(delta)t_r = difference in retention time

W_av = 1/2 (width of peak 1 + width of peak 2)

For quantitative analysis, a resolution of > 1.5 is desirable.

Question 7

Why does overloading and tailing of the peaks occur?

Answer 7

Overloading occurs when the concentration of solute in stationary phase increases, causing an increase in K’

Tailing of the peak occurs when the concentration of solute in the mobile phase inscreasesm causing a decrease in K’

Question 8

Should gradient or isocratic elution be chosen?

Answer 8

• Begin with gradient elution using 10-90% acetonitrile in aqueous buffer over 40 mins
• To decide mathematically:
  
  • Let (delta)t be the difference in retention times between first and eluted peaks. t_g is the time over which the solvent composition is changed.
• If (delta)t / t_g > 0.25 use gradient elution.
• If < 0.25, use isocratic elution.

Question 9

How is resolution linked to theoretical plates?

Answer 9

For equation, see picture.

N = number of plates

alpha = separation factor

k = retention (capacity) factor

Question 10

What is selectivity?

Answer 10

Selectivity, alpha, is the ability of an HPLC method to separate two analytes from each other.

Selectivity is calculated as:

alpha = k₂ / k₁