Surface Chemistry - Result Question 17

####17. Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent at pressure $p \cdot \frac{x}{m}$ is proportional to

(2019 Main, 9 Jan I)

(a) $p^{2}$

(b) $p^{1 / 4}$

(c) $p^{1 / 2}$

(d) $p$

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Answer:

Correct Answer: 17. (d)

Solution:

  1. According to Freundlich adsorption isotherm,

$$ \frac{x}{m} \propto p^{1 / n} \Rightarrow \frac{x}{m}=K p^{1 / n} $$

On taking $\log$ on both sides, we get

$$ \log \left(\frac{x}{m}\right)=\log K+\frac{1}{n} \log p $$

On comparing with equation of straight line, $y=m x+c$, plot of $\log \frac{x}{m} v _s \log p$ gives,

$$ \begin{array}{lc} & \text { Slope } \frac{\left(y _2-y _1\right)}{\left(x _2-x _1\right)}=\frac{1}{n} \Rightarrow \frac{2}{4}=\frac{1}{2} \ \therefore & \frac{x}{m} \propto p^{1 / 2} \end{array} $$



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