Question

Which of the following is correct for given curve?

• A. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
• B. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)$
• C. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^2$
• D. $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^0$

Answer 1

The correct option is A

$\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Explanation for the correct answer

(A)$\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

1. This curve represent the Freundlich isotherm.
2. Freundlich isotherm is the mathematical expression for adsorption isotherm represents that the change in extent of adsorption $\left(\raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.\right)$ with $\left(\mathrm{P}\right)$ Pressure at a temperature where x is the mass of adsorbate and m is the mass of adsorbent.
3. This can be written mathematically as $\left(\raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right.\right)\alpha {\left(P\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}$ where $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.$ implies 0 to 1 It can further be solved and written as ${\log }_{10}\left(\frac{x}{m}\right)={\log }_{10}\left(k\right)+\frac{1}{n}{\log }_{10}\left(P\right)$ $$\begin{gathered} Slope=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right. \\ Fromgraph\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.=\tan \frac{2}{4} \\ \frac{2}{4}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right. \\ \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right. \end{gathered}$$

So, this is the correct answer.

Explanation for the incorrect answer

(B)$\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)$

1. This equation does not represent the Freundlich isotherm.
2. Thus, the curve is not for this equation.

(C) $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^2$

1. This equation does not follow the equation of Freundlich isotherm.
2. So, this equation does not fits the curve.

(D)$\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha {\left(P\right)}^0$

1. This equation does not represent the Freundlich isotherm.
2. Thus, the curve is not for this equation.

Thus, $\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$m$}\right.\right)\alpha \left(P\right)\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ is the correct answer. Option A.