For a real gas, behaving ideally, the pressure may be:

Options

A. `a.b.V_(m)`
B. `(V_(m))/(a.b)`
C. `(a)/(V_(m).b)`
D. `(b)/(a.V_(m))`

Explanation

To solve the question "For a real gas, behaving ideally, the pressure may be:", we can follow these steps:

### Step 1: Understand the Ideal Gas Equation
The ideal gas equation is given by:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

### Step 2: Rearranging the Ideal Gas Equation
From the ideal gas equation, we can express pressure \( P \) as:
\[ P = \frac{nRT}{V} \]
This shows that pressure is directly proportional to temperature and the number of moles, and inversely proportional to volume.

### Step 3: Consider Real Gas Behavior
Real gases behave ideally under certain conditions, particularly at high temperatures and low pressures. The concept of Boyle's temperature is crucial here. A real gas behaves more ideally at or above its Boyle's temperature.

### Step 4: Boyle's Temperature
Boyle's temperature (\( T_B \)) is defined as the temperature at which a real gas behaves ideally. It can be expressed in terms of the van der Waals constants \( a \) and \( b \):
\[ T_B = \frac{a}{Rb} \]
Where:
- \( a \) = measure of attraction between particles
- \( b \) = measure of volume occupied by gas particles

### Step 5: Substitute Boyle's Temperature into the Pressure Equation
Using the ideal gas equation and substituting \( T_B \):
\[ P = \frac{nR \left(\frac{a}{Rb}\right)}{V} \]
This simplifies to:
\[ P = \frac{n \cdot a}{b \cdot V} \]

### Step 6: Final Expression for Pressure
If we denote \( V_m \) as the molar volume (volume per mole), we can rewrite the pressure as:
\[ P = \frac{a}{b \cdot V_m} \]
This shows how the pressure of a real gas behaving ideally can be expressed in terms of the van der Waals constants.

### Conclusion
Thus, for a real gas behaving ideally, the pressure can be expressed as:
\[ P = \frac{a}{b \cdot V_m} \]