Question

If a graph is drawn between \(log(x/m)\) (y-axis) and log p (x-axis) we get a straight line with slope equal to 2 and intercept equal to 0.60. The value of x/m at 9 atm is (\(log 4=0.60\))

• A. 243
• B. 81
• C. 162
• D. 324

Hint:

Log-log plots are essential for evaluating empirical adsorption models like Freundlich; the slope directly provides the exponent factor for the pressure dependence.

Answer 1

The Correct Option is D

Step 1: Recall the Freundlich isotherm.
Adsorption follows $\frac{x}{m}=k\,p^{1/n}$. Taking log of both sides gives the straight line $\log\frac{x}{m}=\log k+\frac{1}{n}\log p$.
Step 2: Match to y = c + mx.
The slope of the line is $\frac{1}{n}$ and the intercept is $\log k$.
Step 3: Read the slope.
The slope is 2, so $\frac{1}{n}=2$.
Step 4: Read the intercept.
The intercept is 0.60, so $\log k=0.60$. Since $\log 4=0.60$, we get $k=4$.
Step 5: Plug into the isotherm.
At $p=9$ atm: \[ \frac{x}{m}=4\times(9)^2=4\times81 \]
Step 6: Compute.
\[ \frac{x}{m}=324 \] \[ \boxed{324} \]