Question

Does \(\mathrm{SF}_{6}\) (boiling point \(=16^{\circ} \mathrm{C}\) at 1 atm) behave more ideally at \(150^{\circ} \mathrm{C}\) or at \(20^{\circ} \mathrm{C}\) ? Explain.

Short answer

\(\mathrm{SF}_{6}\) behaves more ideally at \(150^{\circ} \mathrm{C}\) than at \(20^{\circ} \mathrm{C}\).

Step-by-step solution

Understand Ideal Gas Behavior

Under ideal gas behavior, a gas follows the ideal gas law: \[ PV = nRT \]Here, P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Gases behave more ideally at higher temperatures and lower pressures because interactions between molecules are minimized.

Compare Given Temperatures to Boiling Point

Compare the given temperatures to the boiling point of \(\mathrm{SF}_{6}\), which is \(16^{\circ} \mathrm{C}\). The two temperatures given are \(150^{\circ} \mathrm{C}\) and \(20^{\circ} \mathrm{C}\). Both are above the boiling point, meaning \(\mathrm{SF}_{6}\) will be in a gaseous state at both temperatures.

Determine Influence of Temperature on Ideal Gas Behavior

Gases behave more ideally at higher temperatures due to increased kinetic energy, which reduces intermolecular interactions. Therefore, compare the given temperatures: \(150^{\circ} \mathrm{C}\) is significantly higher than \(20^{\circ} \mathrm{C}\). This means molecular interactions are minimized more at \(150^{\circ} \mathrm{C}\).

Conclusion Based on Temperature

Since gases behave more ideally at higher temperatures, \(\mathrm{SF}_{6}\) will behave more ideally at \(150^{\circ} \mathrm{C}\) than at \(20^{\circ} \mathrm{C}\).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a foundational principle in chemistry and physics. It is represented by the equation \[ PV = nRT \]. Here:

• P stands for pressure
• V represents volume
• n indicates the number of moles
• R is the gas constant
• T is temperature

This law describes how these variables interact and relate to one another. According to the Ideal Gas Law, gases perform ideally under specific conditions: high temperatures and low pressures. These conditions reduce the chance of molecules interacting closely. When molecules are heated, they gain kinetic energy, moving more rapidly and behaving in a more 'ideal' manner.

Temperature Influence on Gases

Temperature plays a crucial role in the behavior of gases. Higher temperatures increase the kinetic energy of gas molecules. This means gas particles move faster and are less likely to experience significant intermolecular forces. For instance, consider the provided temperatures: 150°C is significantly higher than 20°C. At 150°C, the kinetic energy of the sulfur hexafluoride (SF6) molecules would be much higher than at 20°C.
This is why gases tend to behave more ideally at elevated temperatures; their enhanced motion makes intermolecular interactions even less significant.

Intermolecular Interactions

Intermolecular interactions refer to the forces between individual molecules in a substance. These forces can include:

• Van der Waals forces
• Dipole-dipole interactions
• Hydrogen bonds (unlikely in nonpolar SF6)

In the realm of ideal gases, these forces are considered negligible. However, in real gases, they can influence behavior. When temperature increases, intermolecular interactions decrease. This is due to the fact that molecules have increased kinetic energy, making it easier for them to overcome any attracting or repelling forces between them.

Sulfur Hexafluoride (SF6)

Sulfur hexafluoride (SF6) is a gas frequently used in electrical insulation and in medical imaging. Its boiling point is 16°C at 1 atm, meaning it becomes a gas above this temperature. Both 20°C and 150°C are above this threshold. Therefore, SF6 will be in its gaseous form at both temperatures. However, at 150°C, SF6 will exhibit more ideal behavior compared to 20°C due to its high kinetic energy and reduced molecular interaction. This aligns with the Ideal Gas Law, confirming that higher temperatures make gases behave more ideally.