Based on langmuir adsorption isotherm the interceot in the graph `((m)/(x) "versus" (1)/(P))` is equal to

Options

A. `(1)/(a)`
B. `(b)/(a)`
C. `(a)/(b)`
D. `(1)/("slope ")`

Explanation

To solve the problem based on the Langmuir adsorption isotherm and find the intercept in the graph of \(\frac{m}{x}\) versus \(\frac{1}{P}\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Langmuir Adsorption Isotherm**:
The Langmuir adsorption isotherm describes the adsorption of gas molecules on a solid surface, assuming that the adsorption occurs on a homogeneous surface with a finite number of identical sites. The equation is given as:
\[ \frac{x}{m} = \frac{bP}{1 + bP} \]
where \(x\) is the mass of gas adsorbed, \(m\) is the mass of the adsorbent, \(P\) is the pressure, and \(b\) is the Langmuir constant.

2. **Rearranging the Equation**:
We can rearrange the Langmuir equation to express \(\frac{m}{x}\):
\[ \frac{x}{m} = \frac{bP}{1 + bP} \implies \frac{1}{\frac{x}{m}} = \frac{1 + bP}{bP} \implies \frac{m}{x} = \frac{1 + bP}{bP} \]

3. **Simplifying Further**:
We can separate the terms:
\[ \frac{m}{x} = \frac{1}{bP} + 1 \]

4. **Identifying Variables for the Graph**:
In the graph of \(\frac{m}{x}\) versus \(\frac{1}{P}\), we can let:
- \(Y = \frac{m}{x}\)
- \(X = \frac{1}{P}\)

Thus, we can rewrite the equation as:
\[ Y = \frac{1}{b}X + 1 \]

5. **Identifying the Intercept**:
From the equation \(Y = \frac{1}{b}X + 1\), we can see that the intercept (where \(X = 0\)) is equal to:
\[ \text{Intercept} = 1 \]

6. **Identifying the Slope**:
The slope of the line is \(\frac{1}{b}\).

7. **Final Result**:
Therefore, the intercept in the graph of \(\frac{m}{x}\) versus \(\frac{1}{P}\) is equal to:
\[ \text{Intercept} = 1 \]

### Conclusion:
The intercept in the graph \(\frac{m}{x}\) versus \(\frac{1}{P}\) based on the Langmuir adsorption isotherm is \(1\).