Question

For the plot of $\left(\frac{m}{x}\right)vs\frac{1}{P}$ of the Langmuir adsorption isotherm, the slope and y-intercept are respectively:
where,
$\frac{x}{m}$ is extent of adsorption
$P$ is temperature
$a$ and $b$ are Langmuir parameters

• A. $a$ and $b$
• B. $\frac{1}{a}$ and $\frac{b}{a}$
• C. $\frac{1}{a}$ and $\frac{1}{b}$
• D. $\frac{1}{a}$ and $b$

Answer 1

The correct option is B $\frac{1}{a}$ and $\frac{b}{a}$

By langmuir adsorption isotherm,
$\frac{x}{m}=\frac{aP}{1+bP}$

where,
$a=K_{1}K=K_1\frac{k_a}{k_d}$
$b=K=\frac{k_a}{k_d}$
$k_a$ and $k_d$ are rate constant of adsorption and desorption respectively.
$\frac{x}{m}=\frac{aP}{1+bP}$

$\frac{m}{x}=\frac{1+bP}{aP}$
$\frac{m}{x}=\frac{1}{aP}+\frac{b}{a}$
Now, the plot of $\frac{m}{x}vs\frac{1}{P}$ will give a straight line.
Slope = $\frac{1}{a}$
Intercept = $\frac{b}{a}$