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If x is amount of adsorbate and m is amount of adsorbent, which of the following relations is not related to adsorption process?
A
$\frac{x}{m} = p\times T$
B
$\frac{x}{m} = f(p)$ at constant T
C
$\frac{x}{m} = f(T)$ at constant p
D
$p = f(T)$ at constant $\left(\frac{x}{m}\right)$
Detailed Solution
$\frac{x}{m} = f(p)$ at constant T is the adsorption isotherm (e.g., Freundlich isotherm $\frac{x}{m} = kp^{1/n}$).
$\frac{x}{m} = f(T)$ at constant p is the adsorption isobar.
$p = f(T)$ at constant $\frac{x}{m}$ is the adsorption isostere.
$\frac{x}{m} = p\times T$ would mean that adsorption increases in direct proportion to both pressure and temperature. This is not true: adsorption is exothermic and decreases with rise in temperature.
Hence the relation not related to adsorption is $\frac{x}{m} = p\times T$.
$\frac{x}{m} = f(T)$ at constant p is the adsorption isobar.
$p = f(T)$ at constant $\frac{x}{m}$ is the adsorption isostere.
$\frac{x}{m} = p\times T$ would mean that adsorption increases in direct proportion to both pressure and temperature. This is not true: adsorption is exothermic and decreases with rise in temperature.
Hence the relation not related to adsorption is $\frac{x}{m} = p\times T$.