The slope and intercept of Freundlich adsorption isotherm will be respectively:

Options

A. 1/n and K
B. 1/n and log K
C. n and k
D. n and log K

Answer

To determine the slope and intercept of the Freundlich adsorption isotherm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm describes how the amount of adsorbate (the substance being adsorbed) on the adsorbent (the surface on which adsorption occurs) varies with pressure at a constant temperature. The mathematical expression is given by:
\[ \frac{x}{m} \propto P^{\frac{1}{n}} \]
where \( x \) is the mass of the adsorbate, \( m \) is the mass of the adsorbent, \( P \) is the pressure, and \( n \) is a constant.

2. **Convert Proportionality to an Equation**:
To express the relationship in a linear form, we can introduce a constant \( k \):
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]

3. **Take the Logarithm of Both Sides**:
Taking the logarithm of both sides gives:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(P) \]

4. **Identify the Linear Form**:
This equation can be rearranged to fit the linear equation format \( y = mx + c \):
- Let \( y = \log\left(\frac{x}{m}\right) \)
- Let \( x = \log(P) \)
- The slope \( m \) is \( \frac{1}{n} \)
- The intercept \( c \) is \( \log(k) \)

5. **Conclusion**:
Thus, from the above analysis, we can conclude:
- The slope of the Freundlich adsorption isotherm is \( \frac{1}{n} \)
- The intercept is \( \log(k) \)

### Final Answer:
- **Slope**: \( \frac{1}{n} \)
- **Intercept**: \( \log(k) \)