A spacecraft is filled with 0.500 atm of O₂ and 0.500 atm of He. If there is a very small hole in the side of this craft such that gas is lost slowly into outer space, A) He is lost 2.8 times faster than O₂ is lost. B) He is lost 8 times faster than O₂ is lost. C) He is lost twice as fast as O₂ is lost. D) O₂ is lost 2.8 times faster than He is lost. E) O₂ is lost 8 times faster than He is lost.

Question

Quizplus · Accepted Answer

The rate of effusion (loss of gas through a small opening) is directly proportional to the velocity of the gas molecules, which in turn is related to the square root of the molar mass of the gas. He has a molar mass of 4 g/mol, and O₂ has a molar mass of approximately 32 g/mol (assuming it is sulfur hexafluoride). Therefore, the ratio of the effusion rates of He to O₂ is: $\sqrt{\frac{4}{32}} \approx 0.3536$ or He is lost approximately 2.8 times faster than O₂. Therefore, the correct answer is (A).

A Spacecraft Is Filled with 0