Question

Adsorption of a gas on a metal oxide surface follows Freundlich adsorption isotherm. At $300\text{ K}$, the slope and intercept of this isotherm are 2 and 1.0 respectively. What is the value of $\frac{x}{m}$ when the pressure of the gas is 4 bar?

• A. 200
• B. 180
• C. 160
• D. 20

Hint:

Always double check if the intercept given is using base 10 logarithm or natural logarithm.
In standard textbooks, Freundlich log-plots are plotted with $\log_{10}$ by default, meaning Intercept = $1.0 \implies k = 10$.

Answer 1

The Correct Option is C

Step 1: Write the Freundlich isotherm in its log form.
\[ \log\left(\frac{x}{m}\right) = \log k + \frac{1}{n}\log P \]
Step 2: Substitute slope and intercept directly, no need to isolate k first.
Slope $1/n = 2$, intercept $\log k = 1.0$, and $\log 4 \approx 0.602$: \[ \log\left(\frac{x}{m}\right) = 1.0 + 2(0.602) = 2.204 \]
Step 3: Undo the logarithm.
\[ \frac{x}{m} = 10^{2.204} \]
\[ \boxed{\frac{x}{m} \approx 160} \]