Final answer:
The new volume of the balloon will be 1.60 L when an additional 0.20 moles of gas are added to the original 3.00 moles at constant temperature and pressure, according to Avogadro's Law.
Step-by-step explanation:
When additional moles of gas are added to a balloon with pressure and temperature held constant, the volume of the balloon will increase proportionally according to Avogadro's Law. Avogadro's Law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas present.
To calculate the new volume of the balloon when 0.20 moles of gas are added to the original 3.00 moles, under constant temperature and pressure, we can set up a proportion:
V1 / n1 = V2 / n2
Given that V1 = 1.50 L (initial volume), n1 = 3.00 moles (initial moles), n2 = 3.00 moles + 0.20 moles = 3.20 moles. We can solve for the new volume V2 as follows:
V2 = (V1 * n2) / n1 = (1.50 L * 3.20 moles) / 3.00 moles = 1.60 L.
The new volume of the balloon, with the addition of 0.20 moles of gas, will be 1.60 L.