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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 651
(1) Adsorption cannot proceed beyond monolayer coverage.
(2) All sites are equivalent and the surface is uniform.
(3) �e ability of a molecule to adsorb at a given site is independent of the
occupation of neighbouring sites.
For the BET isotherm assumption (1) is removed so that multi-layer coverage
is possible. In the derivation of this isotherm a distinction is made between the
energetics involved in forming the �rst and subsequent layers.
Solutions to exercises
E19B.1(b) �ere is an error in the Exercise: the volume at the lower pressure should be
1.52 cm3.
�e Langmuir isotherm is [19B.2–833], θ = αp/(1 + αp), with α = ka/kd.�e
surface coverage may be written in terms of the volume of gas adsorbed V ,
θ = V/V∞, where V∞ is the volume corresponding to complete coverage. For
two di�erent pressures
V1
V∞
= αp1
1 + αp1
V2
V∞
= αp2
1 + αp2
Inverting both sides
V∞
V1
= 1
αp1
+ 1 V∞
V2
= 1
αp2
+ 1
To eliminate α �rst multiply the le�-hand equation by 1/p2 and the right-hand
equation by 1/p1
V∞
p2V1
= 1
αp1p2
+ 1
p2
V∞
p1V2
= 1
αp1p2
+ 1
p1
Subtracting the two equations gives then eliminates α
V∞
p2V1
− V∞
p1V2
= 1
p2
− 1
p1
hence V∞ = 1/p2 − 1/p1
1/p2V1 − 1/p1V2
= p1 − p2
p1/V1 − p2/V2
where for the last step top and bottom are multiplied by p1p2.
With the data given
V∞ = p1 − p2
p1/V1 − p2/V2
= (56.4 kPa) − (108 kPa)
(56.4 kPa)/(1.52 cm3) − (108 kPa)/(2.77 cm3)
= 27.4 cm3