According to 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. Inversely proportional to the pressure
D. Independent to the pressure of the gas .

Answer

**Step-by-Step Solution:**

1. **Understanding Langmuir Adsorption Isotherm:**
The Langmuir adsorption isotherm describes the equilibrium between the adsorbent and the adsorbate (gas) on a surface. It assumes that adsorption occurs only on specific sites within the adsorbent and that each site can hold only one molecule of the adsorbate.

2. **Mathematical Expression:**
The Langmuir adsorption isotherm can be expressed mathematically as:
\[ \frac{x}{m} = \frac{aP}{1 + bP} \]
where:
- \( x \) = mass of gas adsorbed (in grams)
- \( m \) = mass of adsorbent (in grams)
- \( P \) = pressure of the gas
- \( a \) and \( b \) = Langmuir parameters

3. **Behavior at Low Pressure:**
At very low pressures, the term \( bP \) becomes very small (much less than 1). Therefore, we can simplify the equation by ignoring \( bP \):
\[ \frac{x}{m} \approx \frac{aP}{1} = aP \]

4. **Proportionality:**
From the simplified equation, we can see that:
\[ \frac{x}{m} \propto P \]
This indicates that the amount of gas adsorbed (\( x \)) is directly proportional to the pressure (\( P \)) at very low pressures.

5. **Conclusion:**
Therefore, according to the Langmuir adsorption isotherm, the amount of gas adsorbed at very low pressure is directly proportional to the pressure of the gas.

**Final Answer:**
The amount of gas adsorbed at very low pressure according to the Langmuir adsorption isotherm is directly proportional to the pressure.

---