## 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 = k1 C ( 1 - F )

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

rate leaving = k2 F

where k1 and k2 are rate coefficients
C = concentration in the fluid
F = fraction of the surface covered

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

By dividing the numerator and denominator by k1, and making use of the fact that q will be proportional to  F, the useful form of the equation is:

where qm = q for a complete monolayer
Ka = 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

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