Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 100

Relative Partial Pressure ψ i Ether Adsorbed (mg/g soil)

0.10 6.74

0.28 13.27

0.44 15.32

0.56 18.04

0.63 23.49

0.80 32.28

0.90 46.09

Use the above data to obtain (i) the BET isotherm constants and (ii) the surface area of
the soil (in m 2 /g).

Since the data are given directly in terms of ψ i and Γ i , a plot of ( 1 / Γ i )( ψ i / 1 − ψ i )

versus ψ i values

of 0.01 and 0.63 were considered for this plot. A good linear fit with an r 2 of 0.9776
was obtained. The slope S was 0.1142 and the intercept I was 0.00211. Hence

ψ i can be made as shown in Figure 3.19a. Only the data between

m
i

Γ =

1 /(S 55.1. Using these parameters, the

BET isotherm was constructed and compared with the experimental plot of

+ I) = 8.59 mg/g and K BET = (S/I) + 1 =

Γ i versus
ψ i . An excellent fit to the data was observed as in Figure 3.19b. The transition from
a monolayer to a multi-layer adsorption is clearly evident in this example.
From the value of

m

i , one can calculate the total surface area of the soil if the
molecular area occupied by ether on the surface is known. In order to do this, we shall
first express

Γ

10 − 4 mol/g. The surface area occupied
by a molecule of ether in the monolayer is given by A m = ϕ

m
i

10 − 3 / 74 Γ as 8.59 × = 1.16 ×

N) 2 / 3 , where is

the packing factor (1.091 if there are 12 nearest neighbors in the monolayer), M is
the molecular weight of ether (

(M/ ρ ϕ

0.71 g/cm 3 ) ,

= ρ =

74), is the liquid density of ether (

10 23 ) . In this example, substituting these

= ×

and N is the Avogadro number ( 6.023

(a) 0.08 (b)

90
80
70
60
50
40
30
20
10
0

0.07

0.06

0.05

0.04

0.03

0..02

0.01

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

y i y i

FIGURE 3.19 (a) Linear BET plot to obtain isotherm constants and (b) BET isotherm and
the experimental points.