Hi Neil,

Do you mean that, if you could label all the molecules of the air in your house (I think painting them purple would be a good way to do it) and then you left the house, how long would it be before there were no purple molecules left?

If so I think the answer is never. If you emptied out the air- say you opened the windows on a windy day- and then mixed all the purple air with the rest of the atmosphere and refilled your house there would always be some of the purple molecules in your house.

The atmosphere weighs something like 14.7 pounds per square inch. That's about 50 tons to the square metre. It covers something like 150,000,000 square km so, in total it weighs about 7.5x10^18 Kg (Google seems to give an answer rather less than that, but it hardly matters).

A cubic metre of air weighs about 1.2Kg so my house (I don't know how big your house is) holds about 300Kg of air. So the atmosphere is about 2x10^16 houses full. If you painted a houefull of air purple and mixed it up with the rest of the air about in molecule in 2X10^16 would be purple

However a house contains something like 6x10^27 molecules, so if one in 2x10^16 is purple, then a housefull would contain something like 3x10^11 purple molecules.

Of course, you can't really label the molecules, but the maths is the same anyway.

By the way the diffusion rates for gases (all other things being equal) vary as the reciprocal of the square root of the molecular weight; it's called Graham's law.