Which of the following curves is in accordance with Freundlich adsorption isotherm ?

Options

A.
B.
C.
D.

Answer

To determine which curve is in accordance with the Freundlich adsorption isotherm, we need to understand the relationship defined by this isotherm. Here's a step-by-step solution:

### Step 1: Understand the Freundlich Adsorption Isotherm
The Freundlich adsorption isotherm describes how the quantity of gas adsorbed (X) by a unit mass of solid adsorbent (M) relates to the pressure (P) of the gas at a constant temperature. The equation is given by:

\[ \frac{X}{M} = K \cdot P^{\frac{1}{n}} \]

Where:
- \(X\) = mass of gas adsorbed
- \(M\) = mass of adsorbent
- \(K\) and \(n\) = constants
- \(P\) = pressure

### Step 2: Take the Logarithm of Both Sides
To analyze the relationship graphically, we take the logarithm of both sides:

\[ \log\left(\frac{X}{M}\right) = \log(K) + \frac{1}{n} \log(P) \]

This can be rearranged to:

\[ \log\left(\frac{X}{M}\right) = \log(K) + \frac{1}{n} \log(P) \]

### Step 3: Identify the Graph Type
This equation indicates that if we plot \(\log\left(\frac{X}{M}\right)\) (y-axis) against \(\log(P)\) (x-axis), we should get a straight line. The slope of this line will be \(\frac{1}{n}\) and the y-intercept will be \(\log(K)\).

### Step 4: Analyze the Given Options
Now, we need to analyze the provided curves (options 1, 2, 3, and 4) to see which one represents a linear relationship between \(\log\left(\frac{X}{M}\right)\) and \(\log(P)\).

- **Option 1**: \(\log\left(\frac{X}{M}\right)\) vs. \(P\) (not correct, should be vs. \(\log(P)\))
- **Option 2**: \(\log\left(\frac{X}{M}\right)\) vs. \(P\) (not correct, same reason)
- **Option 3**: \(\log\left(\frac{X}{M}\right)\) vs. \(\log(P)\) (correct, should show a linear relationship)
- **Option 4**: \(\log\left(\frac{X}{M}\right)\) vs. \(\log(P)\) (correct, but we need to verify if it represents the same relationship as option 3)

### Step 5: Conclusion
After analyzing the options, we find that **Option 3** is the correct representation of the Freundlich adsorption isotherm, as it shows the expected linear relationship between \(\log\left(\frac{X}{M}\right)\) and \(\log(P)\).

### Final Answer
The curve that is in accordance with the Freundlich adsorption isotherm is **Option 3**.

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