For a adsorption of gas on solid surface, the plots of log x/m vs. log P is linear with a slope equal to 

Options

A. K
B. log K
C. 1/nK
D. 1/n (n being integer)

Answer

To solve the question regarding the slope of the plot of log(x/m) vs. log(P) for the adsorption of gas on a solid surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Adsorption Isotherm**: The adsorption of a gas on a solid surface can be described by the Freundlich adsorption isotherm, which is given by the equation:
\[ \frac{x}{m} = k P^{\frac{1}{n}} \]
where \(x\) is the amount of gas adsorbed, \(m\) is the mass of the solid, \(P\) is the pressure of the gas, \(k\) is a constant, and \(n\) is a constant that indicates the adsorption intensity.

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

3. **Identify the Linear Form**: The equation now resembles the linear form \(y = mx + b\), where:
- \(y = \log\left(\frac{x}{m}\right)\)
- \(m = \frac{1}{n}\) (the slope)
- \(x = \log(P)\)
- \(b = \log(k)\) (the y-intercept)

4. **Determine the Slope**: From the linear equation, we can identify that the slope of the plot of \(\log\left(\frac{x}{m}\right)\) versus \(\log(P)\) is:
\[ \text{slope} = \frac{1}{n} \]

5. **Conclusion**: Therefore, the slope of the plot of \(\log\left(\frac{x}{m}\right)\) vs. \(\log(P)\) is equal to \(\frac{1}{n}\), where \(n\) is an integer.

### Final Answer:
The slope of the plot of \(\log\left(\frac{x}{m}\right)\) vs. \(\log(P)\) is \(\frac{1}{n}\).

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