Question

Two astronauts are on a space station preparing for a mission to Mars. The space station is powered by the combustion of a mixture of gases released from the high pressure container in which they are both contained. When not in use, the high pressure gas canister is stored in the far corner of the station away from the crew. One of the two gases possesses a high molecular weight, has a strong foul odor but is harmless to humans when inhaled. The second gas has a low molecular weight, no odor but is instantly deadly to humans. The two astronauts are working in the opposite corner of the station when one of them hears a hissing sound and is worried the canister is leaking. The second astronaut states that there is no need to worry because they will smell the foul gas if it is leaking and then can jump into the escape pod to safety.

Will the astronauts live or die?

Use a mathematical expression to describe your reasoning for your answer. You can make up values to help support your answers. Funny answers are appreciated but sadly worth no credit. No numerical answer required, but justify your answer with an equation. please show me details and answer all questions!

Answer 1

We should know about graham's law of diffusion before understanding the question.

Graham's law of diffusion says that rate of diffusion of gas in air is inversely proportional squate to molar mass of gas

Rate1 / Rate2 =

where rate 1 and rate 2 are rate of diffusion of gases 1 & 2 and

M1 and M2 are Molar mass of gas 1 & 2 respecitvely

so according to graham's law

gas with high molar mass will diffuse slower than gas with low molar mass

in the given question we have

Gas 1 odour harmless High molar mass    => Rate of diffusion will be slow

Gas 2 no odour deadly low molar mass => Rate of diffusion will be high

so it means Gas 2 willl reach before the gas 1 can reach that means they cant smell gas 1 which will reach them first and hence literally they will die as Gas 2 is deadly.