To answer your questions about the behavior of gas particles in a container according to the ideal gas law, we can use the formula:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant
- \( T \) = temperature (in Kelvin)
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Initial Pressure Calculation: If the volume of the container is initially 100 nm and the temperature is held constant, the exact pressure cannot be determined without knowing the number of particles. However, we can say that the pressure fluctuates around a certain value based on the number of particles present.
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Effect of Halving the Volume: When the volume is reduced to half (5.0 nm), if we assume the number of particles and temperature remain constant, the pressure will increase. According to Boyle's Law, which states \( P_1V_1 = P_2V_2 \) (where subscript 1 refers to the initial state and subscript 2 refers to the final state),
- Initial volume \( V_1 = 100 \) nm
- New volume \( V_2 = 5.0 \) nm
Let's say the initial pressure \( P_1 \) is known. The new pressure \( P_2 \) can be found using:
\[ P_2 = \frac{P_1 V_1}{V_2} \]
So,
\[ P_2 = \frac{P_1 \cdot 100 \text{ nm}}{5 \text{ nm}} = 20 P_1 \]
This means that the new pressure is 20 times the initial pressure amount.
- Final Pressure Value: Without specific initial pressure values, we can only express the answer symbolically. The new pressure is now about 20 times the initial pressure amount.
To summarize:
- Without specific calculations or values for pressure, the initial pressure fluctuates around a value based on the number of particles.
- When the container's volume is halved, the pressure will increase to 20 times the initial pressure.
- The new pressure will be approximately 20P1 where P1 is the initial pressure.
If you provide actual values for the number of particles or initial pressure, I can give you a numerical answer.
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