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

Options

A. Directly propoftional 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

### Step-by-Step Solution:

1. **Understanding Adsorption**:
- Adsorption is the process where particles (solid, liquid, or gas) accumulate on the surface of a solid. The particles that accumulate are called adsorbates, while the solid surface is called the adsorbent.

2. **Langmuir Adsorption Isotherm**:
- The Langmuir adsorption isotherm describes how the amount of gas adsorbed on a solid surface varies with pressure at a constant temperature. The mathematical expression for the Langmuir isotherm is given by:
\[ \frac{x}{m} = \frac{aP}{1 + bP} \]
where:
- \( x \) = mass of the adsorbate (gas)
- \( m \) = mass of the adsorbent (solid)
- \( P \) = pressure of the gas
- \( a \) and \( b \) are constants.

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

4. **Conclusion**:
- From the simplified equation, we can see that 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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