Question

A mixture of benzene (C6H6), toluene (CH3C6H5) and methane (CH4) was injected into a gas chromatograph column that is12.5 m long. The peaks were observed at 40 s (methane), 260 s (benzene), and 272 s (toluene).

(a) Calculate the adjusted retention time (tS) and capacity factor (k) for each solute.

(b) Find the relative retention () of toluene and benzene.

(c) If the width at the base (w) of the peaks for toluene and benzene is 16 and 20 s, respectively, calculate the resolution of the two peaks.

(d) Calculate the number of theoretical plates and the theoretical plate height for toluene and benzene in this experiment.

Answer 1

Given

Column length L – 12.5 m

Retention time of methane (t m) = 40 S

Retention time of benzene (t _b) = 260 S

Retention time of Toluene (t t) = 272 S

width at the base (w) of the peaks for toluene and benzene is W1= 16 and W2 20 s

Adjusted retention time (tS)

      Adjusted retention times of benzene and toluene are

In Benzene   tS = t _b - t m = 260-40 = 220 s

In Toluene tS = t _t - t m = 272-40 = 232 s

Capacity factor (k) for benzene and toluene are

capacity factor (k) = t b - t m / t m

Benzene = 260-40 / 40 = 5.5

Toluene = = 272-40 /40 = 5.8

Relative retention (a) of toluene and benzene

relative retention (a)    = t t / t _b   = 1.046

Resolution of the toluene and benzene peaks.

Resolution is the difference between peak retention times divided by the average peak width

R = t t - t b / ½( W1+W2)= 272-260/ ½( 16+20)= 12/ 18 = 0.67   

Number of theoretical plates and the theoretical plate height for toluene and benzene.

Number of theoretical plates for toluene N_t = 16 t _t²/ W2 ²

= 16 (272)² / (20)²

  = 2959

Theoretical plate height for toluene= L/ N_t = 12.5/2152 = 0.004 m

Number of theoretical plates for Benzene N_b = 16 t _b²/ W1 ²

= 16 (260)² / (16)²

= 4225

Theoretical plate height for Benzene= L/ N_b = 12.5/4225 = 0.003 m