Question

A gas will approach ideal behaviour at (1) Low \(T\) and high \(P\) (2) Low \(T\) and low \(P\) (3) High \(T\) and low \(P\) (4) High \(T\) and high \(P\)

Short answer

Best ideal gas behavior is observed at high T and low P: option 3.

Step-by-step solution

Understand Ideal Gas Behavior

An ideal gas follows the ideal gas law perfectly: \( PV = nRT \). Under ideal conditions, the gas particles have negligible volume and no intermolecular forces.

Ideal Conditions for Gases

From kinetic molecular theory, ideal gas behavior is observed when gas molecules are far apart (low pressure) and moving fast enough to overcome intermolecular forces (high temperature).

Determine the Answer

From our analysis ideal behaviour in gases is best at high temperature and low pressure. Hence, the best answer is option 3: High T and low P.

Key concepts

ideal gas law

The **ideal gas law** is a fundamental equation in chemistry and physics that describes the behavior of an ideal gas. The equation is given by \[ PV = nRT \] where:

• \(P\) is the pressure of the gas
• \(V\) is the volume of the gas
• \(n\) is the number of moles of the gas
• \(R\) is the ideal gas constant (\[8.314 \quad J/(mol \, K) \]
• \(T\) is the temperature of the gas in Kelvin

This law assumes ideal conditions where gas molecules do not attract or repel each other, and the volume of the individual gas molecules is negligible compared to the volume of the container.
It is crucial to understand that real gases deviate from ideal behavior under conditions of high pressure and low temperature because intermolecular forces and molecular sizes become significant. Under these conditions, the assumptions of the ideal gas law do not hold, and corrections need to be made using the van der Waals equation.

kinetic molecular theory

The **kinetic molecular theory** explains the behavior of gases by considering their molecular composition and motion. According to this theory:

• Gas molecules are in constant, random motion.
• The average kinetic energy of gas molecules is directly proportional to the temperature in Kelvin.
• Gas molecules collide with each other and with the walls of their container, exerting pressure.
• Molecules do not attract or repel each other; there are no intermolecular forces in an ideal gas.
• The volume of the gas molecules themselves is negligible compared to the volume of the container.

The kinetic molecular theory helps explain why gases behave ideally under certain conditions. Specifically, at high temperatures, gas molecules move faster, overcoming any attractive forces. At low pressures, the molecules are far apart, minimizing interactions and making the volume occupied by the gas molecules themselves negligible compared to the overall volume of the gas.

temperature and pressure effects on gases

The **temperature and pressure effects on gases** are significant in determining whether a gas behaves ideally or deviates from ideal behavior. Here is a closer look at these effects:

• High Temperature: At high temperatures, gas molecules have higher kinetic energy, which means they move faster. This increased motion helps the molecules overcome any intermolecular forces, making the gas behave more ideally.
• Low Pressure: At low pressures, gas molecules are spread out over a larger volume, reducing the interactions between molecules. This spacing is why gases tend to follow the ideal gas law more closely at low pressures.
• Low Temperature: At low temperatures, gas molecules have less kinetic energy and move more slowly, causing them to interact more through intermolecular forces. This condition can lead to deviations from ideal behavior.
• High Pressure: At high pressures, gas molecules are forced close together, amplifying the effects of intermolecular forces and the actual volume of the molecules. Under these conditions, gases do not behave ideally and require corrections.

For these reasons, gases approach ideal behavior most closely at high temperatures and low pressures. Understanding these effects helps predict and explain the behavior of gases in different environmental conditions, providing valuable insights for various scientific and industrial applications.