Question

A mixture of hydrocarbons was separated on a nonpolar, 95% methyl, 5% phenylpolysiloxane column of internal diameter 3.2 mm and of length 2.0 m. The experimental conditions are given here:

Inlet pressure 50.0 psi.

Room pressure 755.6 mm Hg.

Column temperature 250.0 ^oC.

Room temperature 23.2 ^oC.

He gas flow 30.5 mL/min (measured using a soap bubble flow meter at the column outlet)

( 760 mm Hg = 14.7 psi;     p_H2O = 21.2 mm Hg at 23.2 ^oC )

The results of the chromatographic separation are given in the table below.

Compound	Retention Time tR (min)	Peak Width w (min)
air	1.56	----
benzene	3.22	0.204
toluene	4.71	0.298
ethyl benzene	7.83	0.495
para-xylene	8.13	0.514
meta-xylene	8.69	0.550
ortho-xylene	9.53	0.602

Calculate the following showing clearly all calculations and equations used:

a) The average number of theoretical plates (N), and the average plate height.

b) The capacity factor, k', for ethyl benzene.

c) The selectivity, a, for benzene and toluene.

d) The resolution between para-xylene and meta-xylene. Is base line resolution achieved?

e) If baseline resolution is achieved, go to question (f). If baseline resolution is not achieved, how many theoretical plates would be required in order to achieve baseline resolution?

f) The average volumetric carrier gas flow rate in the column.

g) The corrected retention volume for ortho-xylene.

Answer 1

(a) Avg no of plates=(no of plates of benzene+no of plates of toluene+no of plates of ethylbenzene+no of plates of paraxylene+no of plates of meta xylene+no of plates of orthoxylene)/6

No of plates (N) can be calculated as N=16(t_r/w)²

N (benzene)=16(3.22/0.204)²

=16x(15.78)²=3984.1

N (toluene)=16(4.71/0.298)²=3994.2

N (ethylbenzene)=16(7.83/0.495)²=3999.3

N (paraxylene)=16(8.13/0.514)²=4004.3

N (metaxylene)=16(8.69/0.550)²=3994.2

N (orthoxylene)=16(9.53/0.602)²=4009.4

now, N_avg=(3984.1+3994.2+3999.3+4004.3+3994.2+4009.4)/6=23985.5/6=3997.6

plate geaght (H) = L/N

where, L=column length, N=no of plates

L = 2m in each case,

Average Height =(2/3984.1+2/3994.2+2/3999.3+2/4004.3+2/3994.2+2/4009.4)/6

(b). Capacity factor K' for ethylbenzene=(t_r-t_o)/to

where, t_r=retention time, t_o =dead timr of column

for ethyl benzene, k'=(7.83-1.56)/1.56=4.019

(c) Selectivity (a) for benzene and toluene=k₂/k₁=(tr (benzene)-t₀)/(tr (toluene)-t₀)

=(3.22-1.56)/(4.71-1.56)=1.66/3.15=0.527

(d)resolution between p-xylene and m-xylene (R_s)

=2X t_R (m xylene)-t_R (p xylene)/(baseline width of m xylene+baseline width of p xylene)

=2X(8.69-8.13)/0.550+0.514)=2X 0.56/1.064=1.052

As R_s is less than 1.5, so base line resolution has been achieved

(f) Average volumetric carrier gas flw rate (Q)=linear flow rate (u)Xpi r2

Q=u (pi r²)

where u=L/t_r, pi r²=3.14X1.6 mmX 1.6 mm=0.0803 m²

for benzene it is 2m/3.22 minX0.0803 m²=0.05ml³/min

similarly, we can calculate flow rate individually for ethylbenzene, toluene, o, p and m xylene by just putting their value of t_r in the given formula and then calculating the average value.

(g) corrected retention volume for ortho xylene (Vr^')=(V_r-V_o)=Q/(t_r-t_o)

where Q is flow rate=L/t_{r X} pi r²

^{for o-xylene,} 2/9.53 X0.0803 m²/(9.53-1.56)

=0.0168/7.97=0.0021 m³