According of Langmuir adsorption isotherm amount of gas adsorbed at very low pressure

Options

A. Directly proportional to the pressure
B. Proportional to `P^(1//n)` (where ` n gt 1` )
C. Inverself proportional to the pressure
D. Independent to the pressure of the gas

Answer

To solve the question regarding the Langmuir adsorption isotherm and the amount of gas adsorbed at very low pressure, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Adsorption**:
- Adsorption is the process where gas molecules (adsorbate) accumulate on the surface of a solid (adsorbent).
- In this context, we denote the mass of the adsorbate as \( x \) and the mass of the adsorbent as \( m \).

2. **Langmuir Adsorption Isotherm Equation**:
- The Langmuir adsorption isotherm can be expressed as:
\[ \frac{x}{m} = \frac{ab}{1 + bb} \]
- Here, \( \frac{x}{m} \) is the extent of adsorption, \( a \) is a constant related to the adsorption capacity, \( b \) is a constant related to the adsorption energy, and \( P \) is the pressure of the gas.

3. **Analyzing the Condition of Very Low Pressure**:
- At very low pressure, the term \( bb \) becomes negligible compared to 1. Therefore, we can simplify the equation:
\[ 1 + bb \approx 1 \]
- This leads to the modified equation:
\[ \frac{x}{m} = ab \]

4. **Graphical Representation**:
- When we plot \( \frac{x}{m} \) (extent of adsorption) against \( P \) (pressure), at low pressures, the graph will be a straight line.
- The slope of this line is equal to \( a \), indicating a linear relationship between \( \frac{x}{m} \) and \( P \).

5. **Conclusion**:
- Thus, at very low pressure, the amount of gas adsorbed (\( \frac{x}{m} \)) is directly proportional to the pressure \( P \). This means that as the pressure increases, the amount of gas adsorbed also increases linearly.

### Final Answer:
According to the Langmuir adsorption isotherm, at very low pressure, the amount of gas adsorbed is directly proportional to the pressure.

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