Frendlich adsorption isotherms are properly represented as in

Options

A.
B.
C.
D.

Answer

To solve the question regarding the Freundlich adsorption isotherms, we will follow these steps:

### Step 1: Understand the Freundlich Adsorption Isotherm
The Freundlich adsorption isotherm describes how the amount of adsorbate (x) adsorbed on a solid adsorbent (m) varies with the pressure (p) of the adsorbate in the gas phase. It is mathematically represented as:
\[ \frac{x}{m} = k p^{\frac{1}{n}} \]
where:
- \( x \) = mass of adsorbate
- \( m \) = mass of adsorbent
- \( p \) = pressure of the adsorbate
- \( k \) = constant
- \( n \) = constant that varies between 0 and 1

### Step 2: Analyze the Relationship
From the equation, we can see that \( \frac{x}{m} \) is directly proportional to \( p^{\frac{1}{n}} \). This implies that as pressure increases, the amount of adsorbate per unit mass of adsorbent also increases, but the rate of increase diminishes as \( n \) varies.

### Step 3: Graphical Representation
The graphical representation of the Freundlich isotherm is typically a curve that starts at the origin and rises, indicating that with increasing pressure, the amount of adsorbate increases. However, it will eventually level off as saturation is approached.

### Step 4: Consider Temperature Effects
It is important to note that adsorption is generally an exothermic process, meaning that as temperature increases, the amount of adsorption tends to decrease. Thus, if temperature is increased, \( \frac{x}{m} \) should decrease.

### Step 5: Evaluate the Options
Given the options:
- Option 1 suggests that with increased temperature, \( \frac{x}{m} \) increases, which is incorrect.
- Option 2 is also incorrect based on the same reasoning.
- Option 3 correctly states that as temperature decreases, \( \frac{x}{m} \) increases, aligning with the principles of adsorption.
- Option 4 is incorrect for similar reasons.

### Conclusion
The correct representation of the Freundlich adsorption isotherm is found in option 3, where it correctly reflects the relationship between temperature and adsorption.