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Question

The adsorption of solution on a solid surface follows the equation \(\frac{x}{m} = k.c^{1/n}\).

The plot of log \(\left(\frac{x}{m}\right)\) versus log (c) gives a horizontal line. It means :

The correct answer is

\(\frac{1}{n} = 0\)

The Freundlich isotherm \(\frac{x}{m} = k\,c^{1/n}\) is linearised by taking logarithms: \(\log\frac{x}{m} = \log k + \frac{1}{n}\log c\).

A plot of \(\log(x/m)\) against \(\log c\) is therefore a straight line with slope \(\frac{1}{n}\) and intercept \(\log k\).

A horizontal line has zero slope, so \(\frac{1}{n} = 0\).

Then \(\frac{x}{m} = k\,c^{0} = k\): the amount adsorbed per unit mass no longer depends on concentration, as when the adsorbent surface is saturated.

The concentration itself is the variable on the horizontal axis, so the shape of the line says nothing about c being 0, fixed or equal to \(1/n\).

Therefore the horizontal line means \(1/n = 0\).

Hence, \(\frac{1}{n} = 0\).

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