For a linear plot of log `(x//m)` versus log [ in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are consists)

Options

A. 1/n appears as the intercept.
B. Only 1/n appears as the slope
C. log (1/n) appears as the intercept.
D. Both k and 1/n appear in the slope term.

Answer

To solve the question regarding the linear plot of log(x/m) versus log(p) in the context of the Freundlich adsorption isotherm, we can follow these steps:

### Step 1: Understand the Freundlich Isotherm Equation
The Freundlich adsorption isotherm is given by the equation:
\[ x/m = k p^{1/n} \]
where:
- \( x \) is the amount of adsorbate,
- \( m \) is the mass of the adsorbent,
- \( k \) is the Freundlich constant,
- \( p \) is the pressure of the adsorbate,
- \( n \) is a constant that indicates the adsorption intensity.

### Step 2: Take the Logarithm of Both Sides
Taking the logarithm of both sides of the Freundlich equation gives:
\[ \log(x/m) = \log(k) + \frac{1}{n} \log(p) \]

### Step 3: Rearranging the Equation
We can rearrange the equation to fit the linear form \( y = mx + c \):
\[ \log(x/m) = \frac{1}{n} \log(p) + \log(k) \]
Here, we can identify:
- \( y = \log(x/m) \)
- \( x = \log(p) \)
- Slope \( m = \frac{1}{n} \)
- Intercept \( c = \log(k) \)

### Step 4: Identify the Slope and Intercept
From the rearranged equation:
- The slope of the line is \( \frac{1}{n} \).
- The intercept of the line is \( \log(k) \).

### Conclusion
Based on the analysis:
- Option A (1/n appears as an intercept) is incorrect.
- Option B (1/n appears as a slope) is correct.
- Option C (log(1/n) appears as intercept) is incorrect.
- Option D (both k and 1/n appear in the slope term) is incorrect.

Thus, the correct answer is **Option B**: 1/n appears as the slope.