The intercept on Y - axis in the graph of log `(x)/(m)` versus log P gives

Options

A. `(1)/(n) (n gt 1)`
B. k
C. log k
D. Temperature

Answer

To solve the question regarding the intercept on the Y-axis in the graph of log \((x/m)\) versus log \(P\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Frode-Litz Absorption Isotherm**:
The Frode-Litz absorption isotherm states that:
\[ \frac{x}{m} = k P^{1/n} \]
where \(x\) is the mass of the adsorbate, \(m\) is the mass of the adsorbent, \(P\) is the pressure, \(k\) is a constant, and \(n\) is a constant that characterizes the system.

2. **Take the Logarithm of Both Sides**:
To analyze the relationship, we take the logarithm of both sides:
\[ \log\left(\frac{x}{m}\right) = \log(k P^{1/n}) \]

3. **Apply Logarithm Properties**:
Using the properties of logarithms, we can expand the right side:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \log(P^{1/n}) \]
This simplifies to:
\[ \log\left(\frac{x}{m}\right) = \log(k) + \frac{1}{n} \log(P) \]

4. **Rearrange the Equation**:
The equation can be rearranged to fit the linear form \(y = mx + c\):
\[ \log\left(\frac{x}{m}\right) = \frac{1}{n} \log(P) + \log(k) \]
Here, we can identify:
- \(y = \log\left(\frac{x}{m}\right)\)
- \(x = \log(P)\)
- The slope \(m = \frac{1}{n}\)
- The intercept \(c = \log(k)\)

5. **Identify the Intercept on the Y-axis**:
From the rearranged equation, the intercept on the Y-axis (when \(x = 0\)) is:
\[ \text{Intercept} = \log(k) \]

### Conclusion:
Thus, the intercept on the Y-axis in the graph of \(\log\left(\frac{x}{m}\right)\) versus \(\log(P)\) is \(\log(k)\).