Two identical balloons are filled to the same volume, one...

Two identical balloons are filled to the same volume, one with air and one with helium. The next day, the volume of the air-filled balloon has decreased by $5.0 \%$. By what percent has the volume of the helium-filled balloon decreased? (Assume that the air is four-fifths nitrogen and one-fifth oxygen and that the temperature did not change.)

Key Concepts

Graham's Law of Effusion

Graham’s law states that the rate at which a gas escapes through a small hole is inversely proportional to the square root of its molar mass. This principle is crucial when comparing the escape rates of different gases; lighter gases such as helium will effuse more rapidly than heavier gases like nitrogen or oxygen, helping to explain discrepancies in deflation rates.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. With constant temperature and pressure conditions, the volume of a gas is directly proportional to the number of molecules present. A reduction in the number of molecules due to gas leakage leads directly to a decrease in volume.

Effect of Molecular Mass on Gas Leakage

Molecular mass significantly influences how quickly a gas escapes from a container. Given that helium has a much lower molecular mass than the components of air, it will leak out faster under the same conditions. This concept underpins the explanation for observing a larger percentage loss in the volume of a helium-filled balloon compared to an air-filled balloon.

Transcript

00:01 Question 136.

00:05 Two identical volume are filled with the same volume.

00:09 One with air and the other one with helium.

00:19 The next day the volume of air field volume decreased by 5%.

00:26 That's changing air.

00:31 So we want to calculate changing helium.

00:36 Okay.

00:37 By what percentage would the volume of air fifth helium fill volume will decrease? assuming that the air will.

00:43 There is one fourth nitrogen and one fourth one fifth oxygen four fifth nitrogen and one fifth oxygen and that temperature does not change so every other thing remain the same so this is like the the this after this question is about effusion because even if the volume is puncture and the gas has to effuse out the rate at which the gas we infused out we depend on the rate of the rate that we have to infuse out depend on the molecular weight of the gas it's rate of effusion you know we know that the rate of effusion is proportional to one of a square root of the molecular way so in that case i will have the molar mass of the molar mass of the is 4 gram per more let me calculate the molar mass for air we were told that air contain contains 4 fifth of nitrogen for nitrogen is n2 n2 is 28 14 times 14 times 2 that is 28 gram per more plus 1 fifth of of what oxygen, oxygen is 302, 16 times 2.

02:37 So i will divide by 5, 4 plus 1, 5.

02:41 And that gives the molecular weight of air is 31 .2 gram from up.

02:51 So i will say rate of effusion.

02:55 Rate of effusion is equivalent to the rate of decrease in volume, rate of change in volume...

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