The compressibility factor Z for the gas is given by -

Options

A. `Z = PV_(obs)`
B. `Z = (PV_(obs))/(nRT)`
C. `Z = nRT`
D. `Z = PV. nRT`

Answer

To solve for the compressibility factor \( Z \) for a gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Compressibility Factor \( Z \)**:
The compressibility factor \( Z \) is defined as the ratio of the molar volume of a real gas (\( V_{\text{real}} \)) to the molar volume of an ideal gas (\( V_{\text{ideal}} \)):
\[ Z = \frac{V_{\text{real}}}{V_{\text{ideal}}} \]

2. **Relate \( V_{\text{ideal}} \) to the Ideal Gas Law**:
According to the Ideal Gas Law, the volume of an ideal gas can be expressed as:
\[ PV = nRT \]
Rearranging this gives:
\[ V_{\text{ideal}} = \frac{nRT}{P} \]

3. **Substitute \( V_{\text{ideal}} \) into the Equation for \( Z \)**:
Now, substitute \( V_{\text{ideal}} \) into the equation for \( Z \):
\[ Z = \frac{V_{\text{real}}}{\frac{nRT}{P}} = \frac{V_{\text{real}} \cdot P}{nRT} \]

4. **Final Expression for Compressibility Factor \( Z \)**:
Thus, we arrive at the final expression for the compressibility factor:
\[ Z = \frac{PV_{\text{real}}}{nRT} \]

5. **Identify the Correct Option**:
From the derived expression, we can see that the correct answer corresponds to the expression \( Z = \frac{PV_{\text{observed}}}{nRT} \), which matches option 2.

### Final Answer:
The compressibility factor \( Z \) for the gas is given by:
\[ Z = \frac{PV_{\text{observed}}}{nRT} \]