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A balloon filled with helium gas takes 6 hours to deflate to 50% of its original volume. How long will it take for an identical balloon filled with the same volume of hydrogen gas, instead of helium, to decrease its volume by 50%?

a) 6 hours
b) 3 hours
c) 12 hours
d) 9 hours

1 Answer

3 votes

Final answer:

The identical balloon filled with hydrogen gas will deflate to 50% of its original volume faster than helium due to its lower molar mass, with the closest estimated time being 3 hours based on Graham's law.

Step-by-step explanation:

The time it takes for a balloon to deflate by 50% depends on the rate of effusion of the gas inside it. This rate is governed by Graham's law, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Helium has a molar mass of approximately 4 g/mol, while hydrogen has a molar mass of about 2 g/mol. According to Graham's law, the rate of effusion of hydrogen would be faster than that of helium. Since the square root of 4 (the molar mass of helium) is 2, and the square root of 2 (the molar mass of hydrogen) is about 1.41, hydrogen effuses at a rate ≈ 2/1.41 times faster than helium. If a helium balloon takes 6 hours to deflate to 50%, a hydrogen balloon would take approximately 6 / (2/1.41) hours, which is about 4.24 hours. However, since this is not an option given, and the time must be less than 6 hours due to the faster effusion of hydrogen, the closest correct answer assuming direct proportionality and rounding to the nearest answer choice would be (b) 3 hours.

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