Homogeneous mixing and compressibility both result from the fact that the molecules are far apart in gases. Mixing occurs because individual gaseous molecules have little interaction with their neighbours, assuming that no reaction taken place, the chemical identities is possible in gases because only about 0.1% of the volume of a typical gas is taken up by the molecules themselves under normal circumstances, the remaining 99.9% is empty space
Compressibility factor of a gas is given by

Options

A. `1(PV)/(R)`
B. `(PV)/(R^(2))`
C. `(R)/(PV)`
D. `(PV)/(nRT)`

Answer

To solve the question regarding the compressibility factor of a gas, we will follow these steps:

### Step 1: Understand the Concept of Compressibility Factor
The compressibility factor (Z) is a measure of how much a gas deviates from ideal gas behavior. It is defined as the ratio of the product of pressure (P) and volume (V) of a gas to the product of the number of moles (N), the universal gas constant (R), and the temperature (T).

### Step 2: Write the Formula for Compressibility Factor
The formula for the compressibility factor (Z) is given by:
\[ Z = \frac{PV}{NRT} \]
Where:
- \( P \) = Pressure of the gas
- \( V \) = Volume of the gas
- \( N \) = Number of moles of the gas
- \( R \) = Universal gas constant
- \( T \) = Temperature of the gas

### Step 3: Identify the Components of the Formula
- **Pressure (P)**: The force exerted by the gas per unit area.
- **Volume (V)**: The space occupied by the gas.
- **Number of Moles (N)**: The amount of substance measured in moles.
- **Universal Gas Constant (R)**: A constant that relates energy scales in physics and chemistry.
- **Temperature (T)**: The measure of thermal energy of the gas.

### Step 4: Conclusion
Thus, the compressibility factor of a gas is expressed as:
\[ Z = \frac{PV}{NRT} \]