Question

For Freundlich adsorption isotherm, a plot of \(\log(x/m)\) (y-axis) and \(\log p\) (x-axis) gives a straight line. The intercept and slope for the line is 0.4771 and 2, respectively. The mass of gas, adsorbed per gram of adsorbent if the initial pressure is 0.04 atm, is ______ \(\times10^{-4}\) g.
(\(\log 3 = 0.4771\))

Hint:

Freundlich isotherm: \(\log(x/m) = \log k + n\log p\). The intercept is \(\log k\) and the slope is \(n\) (here \(n=2\), taking the slope as given).

Answer 1

Correct Answer: 48

Freundlich isotherm: \(\frac{x}{m} = k\,p^{n}\), so \(\log\frac{x}{m} = \log k + n\log p\).
Slope \(= n = 2\) and intercept \(= \log k = 0.4771 = \log 3\), so \(k = 3\).
\(\frac{x}{m} = 3\times(0.04)^2 = 3\times1.6\times10^{-3} = 4.8\times10^{-3}\ \mathrm{g}\ \mathrm{per\ g\ of\ adsorbent}\).
\(4.8\times10^{-3} = 48\times10^{-4}\).
Answer: 48