The compressibility factor of an ideal gas is — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Compressibility Factor of an Ideal Gas **Definition of Compressibility Factor:** The compressibility factor $Z$ is defined as: $$Z = \frac{PV}{nRT}$$ where $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is gas constant, and $T$ is temperature. **For an Ideal Gas:** An ideal gas follows the equation: $PV = nRT$ Substituting into the $Z$ equation: $$Z = \frac{nRT}{nRT} = 1$$ **Physical Interpretation:** - **$Z = 1$**: Gas behaves ideally (negligible intermolecular forces, negligible molecular volume) - **$Z < 1$**: Attractive forces dominate; gas is more compressible than ideal - **$Z > 1$**: Repulsive forces dominate; gas is less compressible than ideal **Conclusion:** The compressibility factor of an ideal gas is **exactly 1** under all conditions of temperature and pressure, since ideal gases satisfy $PV = nRT$ by definition.