There are 500 molecules in an airtight bucket, and the volume is held constant. Which change would cause the greatest increase in pressure?(1 point)

Responses

adding 100 more molecules and decreasing the temperature by 10K
adding 100 more molecules and decreasing the temperature by 10K

releasing 100 molecules and decreasing the temperature by 10K
releasing 100 molecules and decreasing the temperature by 10K

releasing 100 molecules and increasing the temperature by 10K
releasing 100 molecules and increasing the temperature by 10K

adding 100 more molecules and increasing the temperature by 10K

1 answer

To determine which change would cause the greatest increase in pressure, we should consider the ideal gas law, which states that:

\[ PV = nRT \]

Where:

  • \( P \) = pressure
  • \( V \) = volume (constant in this case)
  • \( n \) = number of moles (number of molecules, since we can consider the volume to be constant and thus relevant for a fixed amount of gas)
  • \( R \) = ideal gas constant
  • \( T \) = temperature in Kelvin

Pressure increases with both the number of molecules (n) and the temperature (T).

Now let's evaluate the provided options:

  1. Adding 100 more molecules and decreasing the temperature by 10K:
    This adds more molecules (increases \( n \)), but decreasing the temperature (decreases \( T \)) has the opposite effect. The net effect here would likely be a moderate increase in pressure since the increase in molecules may outweigh the temperature drop.

  2. Releasing 100 molecules and decreasing the temperature by 10K:
    This decreases both the number of molecules (decreases \( n \)) and the temperature, leading to a decrease in pressure.

  3. Releasing 100 molecules and increasing the temperature by 10K:
    This decreases the number of molecules (decreases \( n \)), but increases the temperature. However, the decrease in molecules will have a dominant effect, leading to a decrease in pressure.

  4. Adding 100 more molecules and increasing the temperature by 10K:
    This adds more molecules (increases \( n \)) and increases the temperature (increases \( T \)), which would lead to a significant increase in pressure.

Comparing the options:

  • The first option theoretically could increase pressure, but the temperature decrease would limit that increase.
  • The second and third options decrease pressure.
  • The fourth option (adding more molecules and increasing temperature) will result in the greatest increase in pressure overall.

Therefore, the answer is:

Adding 100 more molecules and increasing the temperature by 10K.