Question

Which type of graph gives straight line in Langmuir adsorption isotherm?

• A. $\frac{x}{m}\to \frac{1}{P}$
• B. $\frac{m}{x}\to \frac{1}{P}$
• C. $log\left(\frac{x}{m}\right)\to \frac{1}{P}$
• D. $log\left(\frac{x}{m}\right)\to P$

Answer 1

The correct option is B $\frac{m}{x}\to \frac{1}{P}$

Langmuir adsorption isotherm is mathematically given by $\frac{x}{m}=\frac{aP}{1+bP}$ .

Upon dividing this equation by P in both numerator and denominator we get $\frac{x}{m}=\frac{a}{\frac{1}{P}+b}$ which can also be written as $\frac{m}{x}=\frac{\frac{1}{P}+b}{a}=\frac{1}{a}\times \frac{1}{P}+\frac{b}{a}$ or $\frac{m}{x}=\frac{1}{a}\times \frac{1}{P}+\frac{b}{a}$

From this, we can deduce that graph between $\frac{m}{x}$ and $\frac{1}{P}$ will yield a straight line as the equation is in the form of $y=mx+c$ where $y=\frac{m}{x};x=\frac{1}{P};m=\frac{1}{a};c=\frac{b}{a}.$

So the correct option is B.