Langmuir equation
Langmuir derived a relationship for q and C based
on some quite reasonable assumptions. These are: a uniform surface, a single
layer of adsorbed material, and constant temperature. The rate of attachment
to the surface should be proportional to a driving force times an area.
The driving force is the concentration in the fluid, and the area is the
amount of bare surface. If the fraction of covered surface is 
,
the rates per unit of surface are:
the rate going on to the surface = k1 C
( 1 - )
The evaporation from the surface is proportional to
the amount of surface covered, so
the rate leaving the surface = k2
where k1 and k2 are rate coefficients
C = concentration in the fluid
= fraction
of the surface covered
At equilibrium, the two rates are equal, and
we find that:
By dividing the numerator and denominator by k1,
Since q will be proportional to ,
the useful form of the equation is:
where q
= q for a complete
monolayer
K
= a coefficient
Taking reciprocals and rearranging: ( details
of math for sleepy people)
A plot of 
versus 
should indicate a straight line of slope 
and an intercept of 
. The
graph shows data points and lines fitted to both Freundlich and Langmuir
equations.
Equations Fitted to Data
Try this yourself. Do not get confused by two values
for each slider bar. The equations are handled separately. The idea is
to imagine a data set and to observe that either equation can usually fit
pretty well if you fiddle with the coefficients.
NEXT
Back to outline