The plot representing Langmuir's adsorption isotherm is :

Options

A.
B.
C.
D.

Answer

To solve the question regarding the plot representing Langmuir's adsorption isotherm, we will follow these steps:

### Step 1: Understand Langmuir's Adsorption Isotherm
Langmuir's adsorption isotherm describes how gas molecules adsorb onto a solid surface. It is based on the assumption that adsorption occurs at specific homogeneous sites within the adsorbent. The equation for Langmuir adsorption isotherm is given by:

\[ \theta = \frac{kP}{1 + kP} \]

where:
- \( \theta \) is the fractional coverage of the adsorbent (extent of adsorption, \( \frac{x}{m} \)),
- \( P \) is the pressure of the gas,
- \( k \) is the Langmuir constant related to the affinity of the binding sites.

### Step 2: Identify the Variables
In the equation, as pressure \( P \) increases, the extent of adsorption \( \theta \) will also change until it reaches a maximum value (saturation). Beyond this saturation point, further increases in pressure will not lead to an increase in adsorption.

### Step 3: Analyze the Behavior of the Plot
- At low pressures, the extent of adsorption increases linearly with pressure.
- As pressure increases, the adsorption continues to increase but at a decreasing rate.
- Eventually, the plot will level off, indicating that all available adsorption sites are filled (saturation).

### Step 4: Determine the Shape of the Plot
The plot of \( \theta \) (or \( \frac{x}{m} \)) versus \( P \) will initially rise steeply and then plateau as it approaches saturation. This characteristic shape is typical of Langmuir isotherm plots.

### Step 5: Identify the Correct Option
Given the options, the correct plot representing Langmuir's adsorption isotherm will show:
- An initial increase in \( \theta \) with increasing \( P \),
- A leveling off at higher pressures, indicating saturation.

Thus, the correct answer is **Option C**, which depicts this behavior.

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