Warm, clear, sunny day. Relatively smog-free environment. You’re outside.
There’s a huge explosion, say, three miles away, in your line of sight. You hear it.
How long, under these conditions, before the very first odor molecules reach your nose?
In what direction and how fast is the wind blowing?
GOOD QUESTION. Assume there’s essentially no wind, that the major propellent is the blast itself.
Also, what kind of explosion and what’s nearby to it? Those factors would affect what kind of scents and odors are released, which would bear on the question since they have very different thresholds of… (pauses, rereads the original question.)
Okay, does it count if an ‘odor molecule reaches your nose’ but is under the threshold of detectability??
I’d say for my purposes whether the scent is actually detected by the human olfactory system is more or less immaterial.
Well, I have no cites for this, but as a wild guess I’d say that the first molecules get there SURPRISINGLY fast… say, ten or fifteen seconds, which works out to around 900 mph. Actual sniff factor would lag behind by a few minutes at least.
It’s pretty mind-boggling just how small molecules really are, and how chaotically they act in a gaseous atmosphere. A few particles will travel very quickly in just about any direction you could name, while most of the rest will just hang around and bump against each other. 
Okay; I’ll buy that. It’s faster than the speed of sound, which means the first molecules would reach you slightly slower than the report from the explosion.
Let’s assume the odor is something really pungent and noticeable, like burning construction plastic. You’re still standing in the same spot. Now the question is, what’s the threshold of detectability? About how long would that take for you to first smell it after your first see it, in a really big explosion spewing out trillions of odorants? More than five minutes? Less?
nope - I won’t buy that. That would mean that you’d smell the explosion before you heard it. Does that make sense to you? Not me. Whatever molecules are propelled outward - pieces of the item exploding - or tiny pieces of the item exploding (molecules that we could smell) would, if anything, get to us at the same time as the sound wave, I’d think. Also, since you’re quite distant from the explosion, and since the energy is exploded in all directions, I’d imagine that you’d get pretty few molecules to detect. As an example, I live about 4-5 miles from a sanitary district plant. When you drive by, it smells like…shit. Here, I"ve never smelled it, regardless of wind direction.
Would that speed be different for different-sized molecules?
I’m thinking of a highly deceased whale that was beached next Highway One, when I was driving my convertible upwind toward it. The road wove back and forth through the plume, and let me tell you, the first pass through the plume was astonishing.
The air seemed greasy, for one thing. Knowing the whale was there, the strategy I used was to keep going and hold my breath when needed.
The wind might have been 25 mph. Perception in this one case was that air near the plume (more like an invisible river) had not enough whale effluvia to be smelled, but you can see that no precise science was done here.
Would ammonia, say, diffuse faster than general whale gasses? and how big would whale-gas molecules be, anyway?
Oddly enough, James Clerk Maxwell did some experiments concerning the rate of diffusion of gases. Here’s his description of one such:
If you have access to the software, plug your hypothetical into CAMEO (Computer Aided Management of Emergency Operations). We use it for HazMat releases to make decisions regarding evacuation/shelter-in-place, etc.
I hadn’t actually thought of the speed of sound… :smack: but I do think it’s possible for individual gas particles to exceed the sound. It’s organized vibration that doesn’t exceed that limit… or something.
In any event, I don’t think a very detectable proportion of particles would be able to exceed the shock wave… probably only a few molecules in any direction, after a mile or so. If they hang around and dawdle to explore their surroundings, they’d get caught up in the wave again. 
Boy I really, really wish some smart person would take a crack at some of the follow up questions asked – particularly #7. It’s not often I have to bump up a thread again to get a question answered. Try again?