Final answer:
Using the combined gas law, the new volume of oxygen gas heated to 412°C under a pressure of 0.5 atm is found to be approximately 45.17 L. The correct answer is option: B. 45.17 L
Step-by-step explanation:
The question involves applying the combined gas law, which relates pressure, volume, and temperature of a gas.
According to the combined gas law, P1V1/T1 = P2V2/T2, where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.
To solve this problem, we first need to convert all temperatures to Kelvin (K), since gas law equations require that temperature be expressed in absolute terms.
Therefore, the initial temperature (T1) at Standard Temperature and Pressure (STP) is 0°C or 273.15 K. The final temperature (T2) would be 412°C, which converts to 685.15 K (412 + 273.15).
Plugging in the values into the combined gas law, we have:
(1 atm) * (9.0 L) / (273.15 K) = (0.5 atm) * (V2) / (685.15 K)
Now we solve for V2. Multiplying both sides by 685.15 K and dividing by 0.5 atm gives us a new volume (V2) of approximately 45.17 L, which corresponds to choice B.
Hence, when the oxygen is heated to 412°C and the pressure is decreased to 0.5 atm, its new volume will be 45.17 L.