Final answer:
The helium gas from the small tank was able to fill 27 large balloons because it expanded to fill the volume of each balloon until all the helium was used or the balloons were at full capacity.
Step-by-step explanation:
Mr. Allen's concern that 0.4 cubic meters of helium gas would not fill many balloons was unfounded, as it filled 27 large balloons. The reason for this is related to the behavior of gases. Among the options presented, the correct answer is that the helium expanded to fill its new containers, the balloons. This is due to a gas law known as the Ideal Gas Law, which states that the volume occupied by a gas is directly proportional to the number of moles of gas (provided the temperature and pressure are held constant). In essence, the helium gas from the tank, despite seeming like a small amount, will expand to fill up the volume of the balloons until either all the helium is used or the maximum capacity of the balloons is reached. Hence, the volume of gas in the balloons equaled the volume of gas in the tank. The small size of helium molecules and the mixing with air are not directly relevant to how much the balloons can be filled with the gas from the tank.