Question

A gas approaches an ideal behaviour when (1) Temperature is raised keeping the volume constant (2) Compressed to a smaller volume at constant temperature (3) More gas is introduced into the same volume and at the same temperature (4) Volume is increased keeping the temperature constant

Short answer

Option 1: Temperature is raised keeping the volume constant.

Step-by-step solution

Understanding Ideal Gas Conditions

An ideal gas follows the equation of state \( PV = nRT \) where pressure (P), volume (V), and temperature (T) relate linearly. Ideal behavior is approached when the interactions between gas molecules are negligible, which is typically achieved under specific conditions.

Analyze Option 1

Increasing the temperature while keeping the volume constant increases the kinetic energy of the molecules, reducing intermolecular attractions. This aids in approaching ideal behavior.

Analyze Option 2

Compressing the gas to a smaller volume at constant temperature increases the pressure and intermolecular forces, moving away from ideal gas behavior.

Analyze Option 3

Introducing more gas into the same volume at constant temperature increases the number of interactions between gas molecules, moving away from ideal gas behavior.

Analyze Option 4

Increasing the volume at constant temperature decreases the pressure, which in turn reduces the intermolecular forces. This aids in approaching ideal behavior.

Conclusion

Options 1 and 4 are conditions that bring the gas closer to ideal behavior, but increasing temperature while keeping volume constant (option 1) is typically considered more effective in minimizing intermolecular attractions.

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 law is expressed as:
\( PV = nRT \)
Here:

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

The formula shows a relationship between pressure, volume, temperature, and the amount of gas. Under ideal conditions, gas molecules do not interact with each other, and they occupy no volume themselves. This law is extremely helpful for predicting how a gas will behave under different conditions.

Temperature Effects on Gases

Temperature is a crucial factor that affects the behavior of gases. When the temperature of a gas is increased:

• The kinetic energy of the gas molecules increases
• This increase in kinetic energy makes the molecules move faster
• The faster movement reduces attractions between molecules

Raising the temperature while keeping the volume constant can foster conditions that are closer to ideal gas behavior. This is because the increased molecular speeds mean that interactions and collisions between molecules become less significant. Thus, option 1 from the exercise, which involves increasing temperature at constant volume, helps the gas approach ideal behavior.

Intermolecular Forces

Intermolecular forces (IMFs) are forces that occur between molecules. These forces can significantly affect a gas's behavior. Common types of IMFs include:

• Van der Waals forces
• Dipole-dipole interactions
• Hydrogen bonding

For a gas to behave ideally, these intermolecular forces need to be negligible. When the temperature is high, the kinetic energy of the molecules is dominant, making it difficult for them to stick together due to IMFs. Therefore, higher temperatures and lower pressures are conducive to ideal gas behavior. This explains why options 1 and 4 in the exercise are conditions that reduce the impact of IMFs and bring the gas closer to ideal behavior.

Volume and Pressure Relationships

The relationship between volume and pressure in the context of gas behavior is described by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are constant. Mathematically, it’s expressed as:
\( PV = k \), where k is a constant.
When the volume of a gas is increased while the temperature is held constant:

• The pressure decreases
• The number of collisions between gas molecules decreases
• The impact of intermolecular forces is reduced

This reduction in pressure and intermolecular forces helps the gas to behave more ideally. In the exercise, increasing the volume at constant temperature (option 4) reduces the pressure, which favors the ideal gas behavior due to fewer molecular interactions and collisions. explicó en la solución, aumentar el volumen a temperatura constante (opción 4) reduce la presión, lo que favorece el comportamiento del gas ideal debido a menos interacciones y colisiones entre moléculas.