Question

In the virtual lab demo, a student adds particles to a container. While the
temperature is held constant the initial volume of the container is 10.0 nm. The
pressure fluctuates around what amount?
When the container volume is changed to half its volume (5.0 m), the pressure
く
to
the initial pressure amount. The new pressure is
now about:
~

Answer 1

To analyze the scenario you've described, we'll refer to the ideal gas law which states:

\[ PV = nRT \]

Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles of gas,
- \( R \) is the ideal gas constant, and
- \( T \) is the temperature in Kelvin.

From your description, the initial volume \( V_1 \) is 10.0 nm (which I'll assume is a typo, as it is an improbably small volume and likely meant to be a larger unit), and the pressure fluctuates around a certain value \( P_1 \).

When the volume is decreased to half, \( V_2 = 5.0 nm \), the pressure will increase according to Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure of a gas is inversely proportional to its volume:

\[ P_1 V_1 = P_2 V_2 \]

So, if the volume is halved:

\[ P_2 = \frac{P_1 V_1}{V_2} = \frac{P_1 \times 10.0}{5.0} = 2P_1 \]

This means the new pressure \( P_2 \) is around **twice** the initial pressure \( P_1 \).

In summary:
- Initial Pressure fluctuates around \( P_1 \).
- When the volume is decreased to 5.0 nm (assuming nm was a typo for standard units), the new pressure \( P_2 \) would be approximately \( 2P_1 \).