The mass of argon adsorbed per unit mass of carbon surface is plotted against pressure. Which of the following plots is correct if x and m represent the masses of argon and carbon respectively ? (………. Represents extrapolated data)

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the correct plot for the mass of argon adsorbed per unit mass of carbon surface against pressure, we can follow these steps:

### Step 1: Understand the Concept of Adsorption
Adsorption is the process by which atoms, ions, or molecules from a gas, liquid, or dissolved solid adhere to a surface. In this case, argon is the adsorbate and carbon is the adsorbent.

### Step 2: Apply the Freundlich Adsorption Isotherm
The Freundlich adsorption isotherm describes how the amount of adsorbate on the adsorbent varies with pressure. The relationship can be expressed as:
\[ \frac{x}{m} = k \cdot p^{\frac{1}{n}} \]
where:
- \( \frac{x}{m} \) is the mass of argon adsorbed per unit mass of carbon,
- \( p \) is the pressure,
- \( k \) is a constant,
- \( n \) is a constant that typically lies between 0 and 1.

### Step 3: Analyze the Equation
From the equation, we can see that as pressure \( p \) increases, \( \frac{x}{m} \) also increases. However, the rate of increase will diminish as \( p \) continues to rise because of the exponent \( \frac{1}{n} \) (where \( n > 1 \) implies a decreasing rate of adsorption).

### Step 4: Graphical Representation
When plotting \( \frac{x}{m} \) against pressure \( p \):
- Initially, as pressure increases, \( \frac{x}{m} \) will increase rapidly.
- After a certain point, the increase will slow down and approach a plateau, indicating that the surface is becoming saturated with adsorbate.

### Step 5: Identify the Correct Plot
The correct plot will show an initial steep increase followed by a gradual leveling off. This behavior is characteristic of the Freundlich isotherm.

### Conclusion
The correct option that represents this kind of graph is option 4, which shows the expected behavior of the adsorption process according to the Freundlich adsorption isotherm.

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