Chemistry Langmuir adsorption isotherm( Derivation constant)



Langmuir isotherm

Hello friends welcome to our blog, today we are going to discuss Langmuir adsorption isotherm.
We know that pressure and the temperature are the two main factors which can influence(effect) the extent of adsorption of gas on the solid surface. if the temperature is kept constant(same) the amount of gas(x/m) adsorb on the surface of adsorbent and corresponding pressure are known as adsorption isotherms

Remember

1. Reversible Process

To study the effect of pressure on adsorption of gas on the surface of solid we must bear in mind
that adsorption is a reversible process (i.e desorption also taking place simultaneously).In case adsorbent and adsorbate are enclosed in closed container stage reached when amount of gas at adsorbedt become equal to amount of gas desorbed we called this stage is equilibrium stage the surface of the adsorbent gets saturated with the adsorbed gas and no more adsorption occur

2. Adsorption isotherm

iso- (means) -same                                therm-(means)- temperature


The main features of adsorption theory are as follow

This theory was studied by a Langmuir in 1916 and a Nobel Prize was awarded to the scientist. The scientist studied the concept of adsorption. Lets see what he found in experiment and relate with the mathematics and drive an expression for this isotherm the main features are
1. The layer of gas absorbs only one molecule thick(i.e unimolecular) in nature since this type of adsorption is noticed only in case of chemisorption
Note- Langmuir adsorption isotherm is applicable only to chemisorption

2. Adsorption process having two opposite tendencies that is condensation(adsorption of gas molecules) on the surface of the solid and evaporation(desorption of these molecules) back to gaseous state

3. The rate of condensation of gas is proportional to uncovered surface of adsorbent while that of evaporation to its covered surface


Derivation


To start with the entire surface of solid is uncovered and the rate of condensation is very high while that of evaporation is negligible with the passage of time more and more surface becomes covered as a result rate of condensation decreases while evaporation increases when the two are equal.

Suppose  a one centimeter of surface of solid exposed to gas maintaining pressure p. Let at any time the surface covered by the adsorbate molecules (theta) square centimeter therefore uncovered surface of adsorbent will be (1 - theta) square centimeter



Graph

A graph between log (x/m) and log C is a straight line for small ranges of concentrations.
The values of constants “a” and “b” depends upon the nature of adsorbate, nature of solid
adsorbent, and temperature. “p” is equilibrium pressure



limitations


Lagmuir theory has limitations. This theory of unimolecular adsorption is valid only at low pressure and high temperature. As the pressure is increases or temperature is lowered, additional layer starts forming . This leads to multilayer adsorption.







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