The compressibility factor for an ideal gas is

Options

A. (a) 1.5
B. (b) 1
C. (c) 2
D. (d) `oo`

Explanation

To find the compressibility factor (Z) for an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Compressibility Factor**:
The compressibility factor (Z) is defined by the equation:
\[ Z = \frac{PV}{nRT} \]
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 in Kelvin

2. **Use the Ideal Gas Law**:
According to the ideal gas law, we have:
\[ PV = nRT \]
This equation states that for an ideal gas, the product of pressure and volume is equal to the number of moles multiplied by the gas constant and temperature.

3. **Substitute the Ideal Gas Law into the Compressibility Factor Equation**:
We can substitute \(PV\) from the ideal gas law into the compressibility factor equation:
\[ Z = \frac{PV}{nRT} = \frac{nRT}{nRT} \]

4. **Simplify the Equation**:
When we simplify the equation, we find:
\[ Z = 1 \]

5. **Conclusion**:
Therefore, the compressibility factor (Z) for an ideal gas is:
\[ Z = 1 \]

### Final Answer:
The compressibility factor for an ideal gas is **1**.

---