In an adsorption experiment a graph between $\log \frac{\mathrm{x}}{\mathrm{m}}$ vs $\log \mathrm{p}$ is found to be linear with a slope of $45°$. The intercept of the graph was found to be $0.3010$.

What is the value of $\frac{\mathrm{x}}{\mathrm{m}}$ if the pressure is 0.6 bar $\left(\tan 45°=1\right)$.

From Freundlich isotherm, it can be written as,

$\log \frac{\mathrm{x}}{\mathrm{m}}=\log \mathrm{K}+\frac{1}{\mathrm{n}}\log \mathrm{p}$

Where, $\frac{1}{\mathrm{n}}=\tan \mathrm{\theta }=\tan 45°=1$

Value of K is determined from the value of intercept,

$$\begin{gathered} \log \mathrm{K}=0.301 \\ \mathrm{K}=2 \end{gathered}$$

Another equation from Freundlich isotherm is:

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

$$\begin{gathered} \frac{\mathrm{x}}{\mathrm{m}} =2\times 0.5^{\frac{1}{1}} \\ \frac{\mathrm{x}}{\mathrm{m}} =1 \end{gathered}$$

Hence the value of $\frac{\mathrm{x}}{\mathrm{m}}$ is equal to $1$.