A plot of log x/m versus log p for the adsorption of a gas on a solid gives a straight line with slope equal to:

Options

A. – log K
B. n
C. `1/n`
D. Log K

Answer

To solve the problem regarding the slope of the plot of log(x/m) versus log(p) for the adsorption of a gas on a solid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Freundlich Adsorption Isotherm**:
The Freundlich adsorption isotherm describes how the amount of gas adsorbed (x) on a solid surface relates to the pressure (p) of the gas. The equation is given by:
\[ x/m = k p^{1/n} \]
where:
- \(x\) = amount of gas adsorbed,
- \(m\) = mass of the solid,
- \(k\) = Freundlich constant,
- \(n\) = Freundlich exponent.

2. **Rearranging the Equation**:
To analyze this equation in terms of logarithms, we can take the logarithm of both sides:
\[ \log(x/m) = \log(k) + \frac{1}{n} \log(p) \]

3. **Identifying the Linear Form**:
The equation can be rearranged to fit the linear form \(y = mx + c\):
- Let \(y = \log(x/m)\)
- Let \(x = \log(p)\)
- The equation now looks like:
\[ y = \log(k) + \frac{1}{n} x \]
Here, \(\log(k)\) is the y-intercept and \(\frac{1}{n}\) is the slope.

4. **Determining the Slope**:
From the linear equation, we can see that the slope (m) of the line is:
\[ \text{slope} = \frac{1}{n} \]

5. **Conclusion**:
Therefore, the slope of the plot of \(\log(x/m)\) versus \(\log(p)\) is equal to \(\frac{1}{n}\).

### Final Answer:
The slope of the plot of log(x/m) versus log(p) is \(\frac{1}{n}\).

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