Answer:
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[tex]_i[/tex] = 40506
Standard Deviation S = √( ∑d²[tex]_i[/tex] / ( 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
