Among the following the number of curves not in accordance with Freundlich adsorption isotherm is

The Freundlich adsorption isotherm is given by:

$$\mathrm{\frac{x}{m} = kP^{1/n}}$$

where:

$$\mathrm{x = mass\ of\ gas\ adsorbed}$$

$$\mathrm{m = mass\ of\ adsorbent}$$

$$\mathrm{P = pressure}$$

Taking logarithm on both sides:

$$\mathrm{\log\left(\frac{x}{m}\right) = \log\left(kP^{1/n}\right)}$$

$$\mathrm{\log\left(\frac{x}{m}\right) = \frac{1}{n}\log P + \log k}$$

Comparing with:

$$\mathrm{y = mx + c}$$

gives:

$$\mathrm{y = \log\left(\frac{x}{m}\right)}$$

$$\mathrm{x = \log P}$$

$$\mathrm{Slope = \frac{1}{n}}$$

$$\mathrm{Intercept = \log k}$$

Hence, the graph must be a straight line between:

$$\mathrm{\log\left(\frac{x}{m}\right)\ and\ \log P}$$

with positive slope and positive intercept.

Graph (a) plots:

$$\mathrm{\log\left(\frac{x}{m}\right)\ vs\ \log P}$$

but gives a curve instead of a straight line.

Hence, it is incorrect.

Graph (b) plots:

$$\mathrm{\log\left(\frac{x}{m}\right)\ vs\ P}$$

which is not the required relation.

Hence, incorrect.

Graph (c) also plots:

$$\mathrm{\log\left(\frac{x}{m}\right)\ vs\ P}$$

Hence, incorrect.

Graph (d) correctly shows a straight line between:

$$\mathrm{\log\left(\frac{x}{m}\right)\ and\ \log P}$$

with positive intercept.

Thus, graphs not obeying Freundlich adsorption isotherm are:

$$\mathrm{(a),\ (b),\ (c)}$$

Total number of incorrect graphs:

$$\mathrm{3}$$