# Freundlich and Langmuir Adsorption Isotherms

• Adsorption Isobar: The graphs relating the extent of adsorption of adsorbate with temperature, at constant pressure are called adsorption isobars.
• Isoster: We can keep x/m constant by increasing temperature and pressure both the graph between temperature and pressure for a given extent of adsorption is called isoster.
• Freundlich adsorption isotherm:(\frac{x}{m} = f(p) at constant T.)
The mathematical relations of extent of adsorption \left(\frac{x}{m}\right) with pressure at constant temperature and corresponding graphs, as studied by Freundlich are called Freundlich adsorption isotherms.
• Graphs {Freundlich}:
• Langmuir adsorption isotherms:
• (i)
\frac{x}{m}=\frac{ap}{1+bp}
\frac{P}{(x/m)}=\frac{b}{a}p+\frac{1}{a}
(ii) At low pressure 1+ bp ≈ 1
\therefore \frac{x}{m}=ap
\therefore \frac{x}{m}\propto p
(iii) At high pressure 1+ bp ≈ bp
\therefore \frac{x}{m}=\frac{ap}{bp}=\frac{a}{b}
• Applications of adsorption:
(i) Activated charcoal is used to adsorb coloring matter from sugar-cane juice during the manufacture of cane-sugar(sucrose)
(ii) Activated charcoal is used in gas masks to adsorb poisonous gases.
(iii) In heterogeneous catalysis, gaseous reactants are adsorbed on the surface of same solid catalyst.
(iv) Moisture can be removed from a chamber by adsorbing it on silica gel.
(v) The process of chromatography is based on adsorption of substances.
(vi) Nickel is used as adsorbent for H2 gas to activate it during the hardening of vegetable oil to vegetable ghee.
(vii) Al3+ ion is tested based on the capacity of Al(OH)3 to adsorb blue litmus in "lake test"
• Adsorption from solutions:
(i) Solutes can be adsorbed from solids eg: charcoal adsorbs acetic acid from solution.
(ii) The extent of adsorption decreases with increase in temperature.
(iii) The extent of adsorption increases with increase in surface area of the adsorbent.
(iv) The extent of adsorption depends upon concentration.
\frac{x}{m}=kC^{1/n}. C is equilibrium molar concentration X = Cinitial − Cfinal
(v) The extent of adsorption depends upon the nature of adsorbent and adsorbate.

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1. Freundlich Adsorption Isotherm
\tt \Rightarrow\log\frac{x}{m}=\log k+\frac{1}{n}\log p

2. Langmuir Adsorption Isotherm
\tt \frac{x}{m}=\frac{ap}{1+bp}