Question

How should the conditions be changed to prevent the volume of a given gas from expanding when its mass is increased? (1) Temperature is lowered and pressure is increased (2) Temperature is increased and pressure is lowered (3) Temperature and pressure both arc lowered (4) Temperature and pressure both are increased

Short answer

Lower the temperature and increase the pressure.

Step-by-step solution

Identify the Relationship

Understand that the volume of a gas is influenced by temperature, pressure, and the amount of gas (according to the Ideal Gas Law: \( PV = nRT \)).

State the Scenario

There is an increase in the mass of the gas, which corresponds to an increase in the number of moles (n). To prevent the volume (V) from expanding, other conditions must be adjusted.

Analyze the Options

Evaluate the changes in temperature (T) and pressure (P) for each option: (1) Lowering the temperature and increasing the pressure will help keep the volume constant. (2) Increasing the temperature and lowering the pressure will cause the volume to expand. (3) Lowering both temperature and pressure might not effectively keep the volume constant. (4) Increasing both temperature and pressure might balance out but will depend on the extent of each change.

Conclusion

The best way to prevent the volume from expanding when the mass of the gas increases is to lower the temperature and increase the pressure, as both actions counteract the increase in volume.

Key concepts

Gas Volume

Gas volume is an important parameter in understanding how gases behave under different conditions. According to the Ideal Gas Law, the volume of a gas is directly proportional to the number of moles () and the temperature (T), and inversely proportional to the pressure (P). This can be stated mathematically as PV = nRT. To visualize this:

• If the temperature increases while the pressure remains constant, the volume will increase.
• If the pressure increases while the temperature remains constant, the volume will decrease.

Understanding these relationships is key to manipulating gas volume in practical applications.

Temperature Effects

Temperature has a profound effect on the volume of a gas. According to Charles's Law, volume is directly proportional to temperature when pressure is held constant. This means:

• If you increase the temperature, the gas particles gain more kinetic energy and start colliding with the walls of the container more frequently and with greater force, leading to an increase in volume.
• Conversely, if the temperature is lowered, the gas particles move more slowly, colliding less frequently and with less force, causing the volume to decrease.

Therefore, to prevent the volume from expanding when the mass of the gas is increased, lowering the temperature can help counteract the increase in volume.

Pressure Effects

Pressure exerts a crucial control over gas volume as well. Boyle's Law states that the volume of a gas is inversely proportional to its pressure when temperature is constant. This means:

• Increasing the pressure forces gas particles closer together, reducing the volume.
• On the other hand, lowering the pressure allows the gas particles to spread out, increasing the volume.

By increasing the pressure, you can counteract the tendency for the gas volume to expand. This is especially useful when the mass of the gas (and consequently the number of moles, n) increases.

Molecular Mass

Molecular mass plays a role in how gases behave under different conditions. The mass of a gas is directly related to the number of moles (n) it contains, where more moles mean a greater mass. When the mass increases:

• There is an increase in the number of gas molecules.
• This leads to a higher tendency for the volume to expand if other conditions like temperature and pressure remain constant.

To maintain a constant volume when the mass increases, you must either increase the pressure or decrease the temperature, compensating for the additional gas molecules and keeping the volume stable.