Question

The following graph is obtained for the adsorption of a gas on a metal surface at 300K. What is the value of $x/m$ when the pressure of gas is 2 bar?

• A. 100
• B. 400
• C. 200
• D. 10

Hint:

Slopes and intercepts in logarithmic plots reveal adsorption constants.

Answer 1

The Correct Option is B

Step 1: Recall the Freundlich isotherm.
Gas sticking on a solid surface follows $\dfrac{x}{m} = k\,P^{1/n}$, where $x/m$ is the amount adsorbed per gram of solid and $P$ is the gas pressure.

Step 2: Make it linear with logarithms.
Taking log on both sides gives \[ \log\frac{x}{m} = \log k + \frac{1}{n}\log P \] So a plot of $\log(x/m)$ against $\log P$ is a straight line.

Step 3: Read the line from the graph.
The graph gives the slope $\dfrac{1}{n} = 2$ and an intercept $\log k$. So $\log(x/m) = \log k + 2\log P$.

Step 4: Insert the pressure value.
At $P = 2$ bar, $\log P = \log 2 \approx 0.3$. So the slope part adds $2 \times 0.3 = 0.6$ to the intercept.

Step 5: Use the intercept from the plot.
The intercept read off the graph leads to $\log(x/m) \approx 2.6$ when the pressure term is added.

Step 6: Take antilog and conclude.
$\log(x/m) = 2.6$ gives $x/m = 10^{2.6} \approx 400$. So the value is $400$.
\[ \boxed{400} \]