Final answer:
To find the final volume of a gas when the temperature and pressure change, use the combined gas law. After converting temperatures from Celsius to Kelvin, plug in the known values to get an approximate final volume of 87.9 mL for the given conditions.
Step-by-step explanation:
The question asks for the final volume of a sample of gas after a change in temperature and pressure, starting from specific initial conditions. This type of problem is solved using the combined gas law, which is represented by the equation (P1 × V1) / T1 = (P2 × V2) / T2, where P represents pressure, V represents volume, and T represents temperature in Kelvin.
To solve for the final volume (V2), we first need to convert the temperatures from Celsius to Kelvin by adding 273.15. Thus, the initial temperature T1 becomes 273.15 K, and the final temperature T2 becomes 127 + 273.15 = 400.15 K. Applying the combined gas law and solving for V2 gives:
V2 = (P1 × V1 × T2) / (P2 × T1)
V2 = (1.00 atm × 30.0 mL × 400.15 K) / (0.500 atm × 273.15 K)
V2 = (12000.45 mL × K) / (136.575 atm × K)
V2 ≈ 87.9 mL
Therefore, the final volume of the gas, when the temperature increases to 127 degrees Celsius and the pressure decreases to 0.500 atm, is approximately 87.9 mL.