Final answer:
For part (a), the final pressure inside the container will be 0.50 atm when the piston is moved to the 2.00 L mark while keeping the temperature constant at 20.0 °C. For part (b), the final pressure inside the container will be 40.0 atm when the temperature is raised to 200.0 °C and the piston is not allowed to move. For part (c), the sample of gas is most likely Neon (Ne).
Step-by-step explanation:
For part (a), according to Boyle's Law, the product of pressure and volume is constant when temperature is kept constant. Therefore, the initial pressure (1.00 atm) multiplied by the initial volume (1.00 L) is equal to the final pressure multiplied by the final volume. Plugging in the given values, we get:
Initial pressure imes Initial volume = Final pressure imes Final volume
1.00 atm imes 1.00 L = Final pressure imes 2.00 L
Simplifying the equation, we find that the final pressure is 0.50 atm.
For part (b), according to Gay-Lussac's Law, the pressure of an ideal gas is directly proportional to its temperature when volume is kept constant. Using this relationship, we can calculate the final pressure:
Initial pressure imes Initial temperature = Final pressure imes Final temperature
1.00 atm imes 20.0 °C = Final pressure imes 200.0 °C
Simplifying the equation, we find that the final pressure is 40.0 atm.
For part (c), we can use the ideal gas law (PV = nRT) to calculate the number of moles of the gas. Rearranging the equation, we get:
n = PV / RT
Substituting the given values, we find that the number of moles of the gas is approximately 0.035 moles. Based on the molar mass of the gases given, the most likely monatomic gas is Neon (Ne), which has a molar mass close to the calculated mass.