If adsorption of a gas on a solid is limited to monolayer formatin , then which of the following statement are ture ?

Options

A. At low pressures `x/m` varioes proportionately with P
B. At moderate pressures, `x/m` varies less than proportiontely with P
C. At high pressure ,` x/m` becomes inderpendent of P
D. at high pressue , `x/m` varies more than proportiontely with P

Answer

To solve the problem regarding the adsorption of a gas on a solid limited to monolayer formation, we will analyze the statements based on the principles of adsorption and the corresponding graph.

### Step-by-Step Solution:

1. **Understanding Monolayer Adsorption**:
- Monolayer adsorption refers to the scenario where gas molecules adhere to the surface of a solid until a single layer is formed. This means that once the surface is fully occupied, no additional gas can be adsorbed.

2. **Adsorption Isotherm**:
- The relationship between the amount of gas adsorbed (x/m) and the pressure (p) can be described by the adsorption isotherm. For monolayer adsorption, it is often represented as:
\[ \frac{x}{m} = k p^{1/m} \]
- Here, \(x/m\) is the mass of gas adsorbed per unit mass of adsorbent, \(k\) is a constant, and \(p\) is the pressure of the gas.

3. **Analyzing the Graph**:
- The graph of adsorption (x/m) versus pressure (p) typically has three regions:
- **Low Pressure**: At low pressures, the graph shows a linear relationship, indicating that \(x/m\) varies proportionally with \(p\).
- **Moderate Pressure**: As pressure increases to moderate levels, the relationship becomes less than proportional, meaning that the rate of adsorption starts to slow down.
- **High Pressure**: At high pressures, the graph levels off, indicating that \(x/m\) becomes independent of \(p\) as the surface becomes saturated.

4. **Evaluating the Statements**:
- **Statement A**: At low pressure, \(x/m\) varies proportionally with \(p\). **(True)**
- **Statement B**: At moderate pressure, \(x/m\) varies less than proportionally with \(p\). **(True)**
- **Statement C**: At high pressure, \(x/m\) becomes independent of \(p\). **(True)**
- **Statement D**: At high pressure, \(x/m\) varies more than proportionally with \(p\). **(False)**

5. **Conclusion**:
- The true statements regarding the adsorption of a gas on a solid limited to monolayer formation are A, B, and C. Statement D is false.

### Summary of True Statements:
- A: True
- B: True
- C: True
- D: False