Question

Which of the noble gases would not behave ideally under any circumstance? Why?

Short answer

Radon (Rn) would not behave ideally, due to its large size and intermolecular forces.

Step-by-step solution

Understanding the Ideal Gas Law

The Ideal Gas Law is represented as \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. Ideal gases follow these rules under all conditions. Real gases, however, deviate from ideal behavior at high pressures and low temperatures.

Identify Noble Gases

The noble gases are a group of elements in Group 18 of the periodic table. They include Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn). These gases have complete valence electron shells, which makes them mostly non-reactive.

Consider Real Gas Deviations

Real gases deviate from ideal behavior due to intermolecular forces and the volume occupied by the gas particles. Larger atoms with more electrons tend to have greater intermolecular forces, causing more deviation from ideal behavior.

Analyze the Sizes of Noble Gases

Among the noble gases, Radon (Rn) has the largest atomic radius and most electrons. This results in significant van der Waals forces, meaning Radon is more likely to deviate from ideal gas behavior compared to other noble gases.

Conclusion

Due to its larger atomic size and higher intermolecular forces, Radon would not behave ideally under any circumstance, because these factors cause significant deviation from the assumptions made in the ideal gas law.

Key concepts

Ideal Gas Law

The Ideal Gas Law is an important equation in chemistry that relates the four key properties of gases: pressure (\(P\)), volume (\(V\)), temperature (\(T\)), and amount in moles (\(n\)). It is expressed as \( PV = nRT \). This equation implies a straightforward relationship where pressure and volume are directly proportional to the temperature and moles of the gas. However, this law assumes no forces between the molecules and that they occupy no volume themselves. This simplification means that the Ideal Gas Law accurately describes gases only under specific conditions of low pressure and high temperature. When these conditions are not met, discrepancies don’t allow gases to behave ideally.

Real Gas Behavior

Real gases, unlike ideal gases, are not just theoretical constructs but are affected by intermolecular forces and the finite volume of the gas particles. Two main factors lead to this deviation:

• **Intermolecular Forces:** These include attractions between molecules which can range from weak van der Waals forces to stronger dipole-dipole attractions.
• **Finite Volume of Particles:** Unlike ideal gas molecules, real gas particles occupy a significant portion of the gas's volume, affecting their compressibility.

Deviations from ideal behavior become evident at high pressures, where molecules are forced closer together, and at low temperatures, where reduced kinetic energy increases the effect of intermolecular forces, causing gases to behave less like ideal gases.

Intermolecular Forces

Intermolecular forces are the forces that mediate interaction between molecules, including forces of attraction or repulsion which act between molecules and other types of neighboring particles. They are responsible for many properties of substances, such as boiling and melting points. In noble gases, especially, these forces come into play when we discuss deviations from ideal gas behavior. Van der Waals forces, which are a category of intermolecular forces including attractions and repulsions between atoms, increase with larger atomic size and more electrons. Their influence is significant in gases such as Radon, contributing to deviations from ideality since intermolecular forces impact how closely a gas follows the predictions of the Ideal Gas Law.

Periodic Table Group 18

Group 18 on the periodic table is also known as the noble gases. This group includes Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn). Noble gases are characterized by having a complete outer shell of electrons, making them extremely stable and largely non-reactive under normal conditions. This full valence shell renders them almost inert, as they have little tendency to gain or lose electrons. Despite this stability, noble gases can still exhibit non-ideal behavior under certain conditions due to factors like atomic size and intermolecular forces, with Radon notably being the least ideal due to its larger size and greater number of electrons.