By plotting log x/m on y-axis and log P on x-axis we s hould get

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Answer

To solve the problem, we need to analyze the relationship between the degree of adsorption (x/m) and the pressure (P) using the Freundlich isotherm equation. We will derive the equation step by step and understand what the plot of log(x/m) versus log(P) will look like.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Let \( x \) be the mass of the adsorbate.
- Let \( m \) be the mass of the adsorbent.
- The degree of adsorption is given by \( \frac{x}{m} \).

2. **Freundlich Isotherm Equation**:
- According to the Freundlich isotherm, the relationship between the degree of adsorption and pressure is given by:
\[ \frac{x}{m} \propto P^{\frac{1}{n}} \]
- This can be expressed as:
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]
- Here, \( k \) is a constant.

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

4. **Rearranging the Equation**:
- We can rearrange the equation to fit the linear form \( y = mx + c \):
\[ \log\left(\frac{x}{m}\right) = \frac{1}{n} \log(P) + \log(k) \]
- Here, we identify:
- \( y = \log\left(\frac{x}{m}\right) \)
- \( x = \log(P) \)
- Slope \( m = \frac{1}{n} \)
- Intercept \( c = \log(k) \)

5. **Graph Interpretation**:
- When we plot \( \log\left(\frac{x}{m}\right) \) on the y-axis and \( \log(P) \) on the x-axis, we will obtain a straight line.
- The slope of this line will be \( \frac{1}{n} \) and the y-intercept will be \( \log(k) \).

### Conclusion:
By plotting \( \log\left(\frac{x}{m}\right) \) on the y-axis and \( \log(P) \) on the x-axis, we will get a straight line. The slope of the line is \( \frac{1}{n} \) and the y-intercept is \( \log(k) \).