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 (\(log 4=0.60\))
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 (\(log 4=0.60\))
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Log-log plots are essential for evaluating empirical adsorption models like Freundlich; the slope directly provides the exponent factor for the pressure dependence.
Updated On: Jun 8, 2026
- 243
- 81
- 162
- 324
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The Correct Option is D
Solution and Explanation
Concept:
The Freundlich adsorption isotherm is given by the equation: \(\frac{x}{m} = k \cdot p^{1/n}\). Taking the logarithm on both sides yields the linear equation: \(\log(\frac{x}{m}) = \log k + \frac{1}{n} \log p\). This matches the form \(y = c + mx\), where the slope is \(1/n\) and the intercept is \(\log k\).
Step 1: Determine the constants from the graph.
The slope is given as 2, so \(1/n = 2\). The intercept is 0.60, which equals \(\log k\). Given \(\log 4 = 0.60\), we find \(k = 4\).
Step 2: Calculate the value of \(x/m\) at p = 9 atm.
Using the isotherm equation \(\frac{x}{m} = k \cdot p^{1/n}\): \[ \frac{x}{m} = 4 \cdot (9)^2 = 4 \cdot 81 = 324 \]
Step 1: Determine the constants from the graph.
The slope is given as 2, so \(1/n = 2\). The intercept is 0.60, which equals \(\log k\). Given \(\log 4 = 0.60\), we find \(k = 4\).
Step 2: Calculate the value of \(x/m\) at p = 9 atm.
Using the isotherm equation \(\frac{x}{m} = k \cdot p^{1/n}\): \[ \frac{x}{m} = 4 \cdot (9)^2 = 4 \cdot 81 = 324 \]
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