For a certain gas which deviates a little from ideal behaviour, a plot between P/p vs P was found to be non- linear . The intercept on y-axis will be :

Options

A. `(RT)/(M)`
B. `(M)/(RT)`
C. `(MZ)/(RT)`
D. `(R)/("TM")`

Explanation

To solve the problem, we need to analyze the relationship between pressure (P), density (ρ), and the behavior of a gas that deviates slightly from ideal behavior. Here is a step-by-step solution:

### Step 1: Understand the Ideal Gas Law
For an ideal gas, the equation is given by:
\[ PV = nRT \]
However, for real gases that deviate from ideal behavior, we can modify this to account for volume occupied by gas particles:
\[ P(V - nb) = nRT \]
Where \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the temperature, and \( b \) is the volume occupied by one mole of the gas particles.

### Step 2: Rearranging the Equation
From the modified equation, we can express it as:
\[ PV = nRT + Pnb \]
This can be rearranged to express pressure in terms of density.

### Step 3: Relate Density to Pressure
Density (ρ) is defined as:
\[ \rho = \frac{m}{V} \]
Where \( m \) is the mass of the gas. Rearranging gives us:
\[ V = \frac{m}{\rho} \]
Substituting this into our equation gives:
\[ P = \frac{nRT}{V} + Pnb \]

### Step 4: Express P/ρ
Now, substituting \( V \) into the equation, we can express \( P/\rho \):
\[ P = \frac{nRT}{\frac{m}{\rho}} + Pnb \]
This simplifies to:
\[ P = \frac{nRT \cdot \rho}{m} + Pnb \]

### Step 5: Rearranging for P/ρ
Dividing both sides by ρ gives us:
\[ \frac{P}{\rho} = \frac{nRT}{m} + \frac{Pnb}{\rho} \]
This indicates that \( \frac{P}{\rho} \) is a function of \( P \).

### Step 6: Identify the Intercept
In the equation \( \frac{P}{\rho} = \frac{nRT}{m} + \frac{Pnb}{\rho} \), we can identify the y-intercept when \( P = 0 \):
\[ \text{Intercept} = \frac{nRT}{m} \]
This means the intercept on the y-axis (where \( P = 0 \)) is given by:
\[ \text{Intercept} = \frac{RT}{M} \]
Where \( M \) is the molar mass of the gas.

### Final Answer
Thus, the intercept on the y-axis will be:
\[ \text{Intercept} = \frac{RT}{M} \]