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

### Step 1: Understand the Freundlich Isotherm Equation
The Freundlich adsorption isotherm describes how the amount of gas adsorbed (x) on a surface relates to the pressure (P) of the gas. The equation is given by:
\[ x = k \cdot m \cdot P^{\frac{1}{n}} \]
where:
- \( x \) = amount of gas adsorbed
- \( m \) = mass of the adsorbent
- \( P \) = pressure of the gas
- \( k \) and \( n \) = constants specific to the gas and adsorbent at a given temperature.

### Step 2: Rearranging the Equation
We can rearrange the equation to express it in a linear form. Dividing both sides by \( m \):
\[ \frac{x}{m} = k \cdot P^{\frac{1}{n}} \]

### Step 3: Taking Logarithms
To linearize this equation, we take the logarithm of both sides:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(P) \]

### Step 4: Identifying the Linear Form
This equation can be compared to the standard linear equation \( y = mx + c \), where:
- \( y = \log\left(\frac{x}{m}\right) \)
- \( x = \log(P) \)
- \( m = \frac{1}{n} \) (slope)
- \( c = \log(k) \) (intercept)

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

### Final Answer
Thus, the slope and intercept of the Freundlich adsorption isotherm are:
- **Slope**: \( \frac{1}{n} \)
- **Intercept**: \( \log(k) \)

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