In Freundlich adsorption isotherm, adsorption is proportional to pressure P as

Options

A. `P^0`
B. P
C. `P^n`
D. `P^(1//n)`

Answer

To solve the question regarding the Freundlich adsorption isotherm and its relationship with pressure \( P \), we can break it down into a step-by-step explanation.

### Step-by-Step Solution:

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

2. **Freundlich Adsorption Isotherm**:
- The Freundlich adsorption isotherm is an empirical relationship that describes how the amount of adsorbate on the adsorbent surface varies with pressure at a constant temperature.

3. **Mathematical Expression**:
- The Freundlich isotherm can be expressed mathematically as:
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]
where:
- \( \frac{x}{m} \) is the amount of adsorbate per unit mass of adsorbent,
- \( P \) is the pressure,
- \( k \) is a constant,
- \( n \) is a constant that indicates the nature of the adsorption process.

4. **Proportionality to Pressure**:
- From the equation, it can be observed that \( \frac{x}{m} \) is proportional to \( P^{\frac{1}{n}} \). This means that as pressure \( P \) increases, the amount of adsorbate on the adsorbent also increases, but the relationship depends on the value of \( n \).

5. **Behavior at Different Pressures**:
- For low pressures, when \( P \) is small, the value of \( \frac{1}{n} \) approaches 1, leading to a linear relationship between \( \frac{x}{m} \) and \( P \).
- For high pressures, \( \frac{1}{n} \) approaches 0, indicating that \( \frac{x}{m} \) becomes constant, meaning that the adsorption reaches a saturation point.

6. **Graphical Representation**:
- The graph of \( \frac{x}{m} \) versus \( P \) will show a linear increase at low pressures, transitioning to a plateau as pressure increases, indicating saturation.

### Final Answer:
In the Freundlich adsorption isotherm, adsorption is proportional to pressure \( P \) as:
\[ \frac{x}{m} \propto P^{\frac{1}{n}} \]
where \( n \) is a constant between 0 and 1.