##
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 *
F* , the rate per unit of surface is:
*
rate going on = k*_{1} C ( 1 - F )

The evaporation from the surface is proportional to the amount
of surface covered:

*
rate leaving = k*_{2} F

where k_{1} and k_{2} are rate coefficients

C = concentration in the fluid

*F *= fraction of the surface
covered

Animation of finding adsorption sites

At equilibrium, the two rates are equal, and we find that:

By dividing the numerator and denominator by k_{1}, and making use of the fact that
q will be proportional to F,
the useful form of the equation is:

where q_{m} = q for a complete
monolayer

K_{a} = 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. 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.

**How to relate graphs to equations**

Go **"with the flow"**or to **Main
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