The following data were obtained by gas-liquid chromatography on a 40-cm packed column: Compound tR, min W, min
Air 1.9 —
Methylcyclohexane 10 0.76
Methylcyclohexene 10.9 0.82
Toluene 13.4 1.06

Calculate:
a. an average number of plates from the data.
b. the standard deviation for the average in (a).
c. an average plate height for the column.

a)

For Methylcyclohexane  N₁ = 2770

For Methylcyclohexene N₂ = 2827

For Toluene N₃ = 2557

b) the standard deviation for the average in (a) is 143.31

c)

For Methylcyclohexane; H₁ = 0.01444 cm

For Methylcyclohexene; H₂ = 0.01415 cm

For Toluene; H₃ = 0.01564 cm

Explanation:

Given the data in the question;

Gas-liquid chromatography on a 40-cm packed column:

Compound                   tR, min                           W, min

Air                                   1.9                                    —

Methylcyclohexane      10.0                               0.76

Methylcyclohexene      10.9                               0.82

Toluene                        13.4                                1.06

a)

an average number of plates from the data;

To get the Number of plates N, we use the following expression;

N = 16( tR / W )², we use it for Methylcyclohexane, Methylcyclohexene and Toluene

-

For Methylcyclohexane  N₁ = 16( 10 / 0.76 )² = 16( 173.13 ) = 2770.08 ≈ 2770

-

For Methylcyclohexene N₂ = 16( 10.9 / 0.82 )² = 16( 176.7 ) = 2827.2 ≈ 2827

-

For Toluene N₃ = 16( 13.4 / 1.06 )² = 16( 159.8078 ) = 2556.9 ≈ 2557

b) standard deviation for the average in (a).

First we get the mean;

Mean N" = ( N₁ + N₂ + N₃ ) / 3 = ( 2770 + 2827 + 2557 ) / 3 = 8154 / 3 = 2718

Next we determine the deviation

d₁² = (N₁ - N")² = (2770 - 2718)² = (52)² = 2704

d₂² = (N₂ - N")² = (2827 - 2718)² = (109)² = 11881

d₃² = (N₃ - N")² = (2557 - 2718)² = (-161)² = 25,921

∴ ∑d² = 40506

Standard Deviation S = √( ∑d²  / ( n-1 ) )

Standard Deviation S = √( 40506 / ( 3-1 )

Standard Deviation S = √( 40506 / 2 )

Standard Deviation S = √( 20253 )

Standard Deviation S = 143.31

Therefore, the standard deviation for the average in (a) is 143.31

c)

an average plate height for the column

Given that; Gas-liquid chromatography on a 40-cm packed column, L = 40 cm

-

For Methylcyclohexane; H₁ = L/N₁ = 40 / 2770 = 0.01444 cm

-

For Methylcyclohexene; H₂ = L/N₂ = 40 / 2827  = 0.01415 cm

-

For Toluene; H₃ = L/N₃ = 40 / 2557 = 0.01564 cm