Final answer:
The final volume of helium in the balloon after 12 hours, with a leakage rate of 0.105 mol/hr, is 13.5 L. This is calculated by determining the amount of helium left after the leak and using Avogadro's law to find the proportional change in volume.
Step-by-step explanation:
We're asked to calculate the final volume of helium in a balloon after a certain amount of helium has leaked out over a period of time. The initial conditions given include a balloon with a volume of 25.0 L containing 2.75 mol of helium. The rate of helium leakage is 0.105 mol/hr. To find out how much helium remains after 12 hours, we multiply the leakage rate by the time period: 0.105 mol/hr * 12 hr = 1.26 mol. This is the total amount of helium that has leaked out, which we then subtract from the original amount to find out how much helium is left in the balloon: 2.75 mol - 1.26 mol = 1.49 mol.
Assuming that the balloon's volume changes directly with the change in the number of moles of gas inside (according to Avogadro's law, under constant temperature and pressure), we now calculate the final volume:
Initial Volume / Initial Moles = Final Volume / Final Moles
25.0 L / 2.75 mol = Final Volume / 1.49 mol
Solving for Final Volume gives us: Final Volume = (25.0 L * 1.49 mol) / 2.75 mol = 13.5 L, which is answer choice A.