PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 453

Note:This isotherm can be derived on condition that:

• Only one single layer of adsorbed molecules is formed.


• The adsorbent surface is homogeneous.


• The adsorbed molecules do not influence each other.

Example

Nitrogen adsorption on charcoal at 0◦C in the pressure range up to 100 kPa is expressed by

the Langmuir isotherm with the parametersamax= 36cm^3 g−^1 ,b= 0. 053 kPa−^1 (the adsorbed

amount of nitrogen is expressed by volume converted toTref= 273. 15 K, and pressurepref=

101. 32 kPa). Calculate the amount of nitrogen adsorbed per 10 g of charcoal at a pressure of

5 kPa.

Solution

From relation (13.39) we obtain

av= 36

0. 053 · 5

1 + 0. 053 · 5

= 9. 54 cm^3 g−^1 ,

n=madsorbent

avpref

RTref

= 10

0. 00954 · 101. 32

8. 314 · 273. 15

= 0. 004256 mol.

13.2.5 Langmuir isotherm for a mixture of gases

For ak-component mixture of gases we obtain by expanding equation (13.39)

ai=amax,i

bipi

1 +

∑k

j=1bjpj

, (13.40)

wherepiis the partial pressure of componentiin the mixture.