A mysterious gap in posting? Must be finals time! As of now I’m done. We’ll see how they went. One of them went well for sure, the other sort of depends. My own students are having their own exams as well, and I’ve got my fingers crossed for them.
One of the things that’s going to be on the exam (or at least it in a chapter they covered) is the speeds of molecules in a gas. Like people milling around in a crowd, as the molecules fly around and bump into each other they’ll be exchanging energy and moving at different speeds. Some molecules will have just been hit in just the right way to go very fast until they get hit again and slow down. And some get hit just right to be brought temporarily to a near halt. On average we can calculate how fast the molecules are moving. The equation to do this is called the Maxwell-Boltzmann distribution and it’s a doozy:
That gives you the probability density of finding a gas atom or molecule at a particular speed. A graph will make things more clear. Here’s a graph for nitrogen at 30 degrees Celsius. That’s a fairly warm temperature in the mid 80s for us Americans. Nitrogen molecules (two nitrogen atoms bound together) are the most common component of air.
You can see that most nitrogen molecules are percolating along at around 400 m/s or so. The vast majority (more than 90%) are between about 100 and 800 m/s. Above 1000 m/s or so the odds of a molecule being hit in just the right way to reach such high speeds are slim indeed. Only about 1 in 1000 molecules are above 1200 m/s, and it falls off absurdly fast beyond that. Up in the 3000+ range the fraction is too small to bother with – one in trillions of trillions.
Hydrogen molecules are much lighter in mass. So at the same temperature they’ll be moving much faster. I’ll run the numbers and graph the hydrogen speeds on the same graph as the nitrogen. In the graph below, the hydrogen speeds extend to the right much farther:
The average speed is in the neighborhood of 1500 m/s, and while nearly no nitrogen is moving at 3000+ m/s, almost 7% of the hydrogen is. As high as 10 km/s, hydrogen still has a respectable fraction (small, but more than 10 million per mole) of molecules which are at that speed. This is pretty much the escape velocity of earth, and so a hydrogen molecule at this speed that’s at a high enough altitude not to hit any more molecules on the way out will be gone for good. Essentially no nitrogen molecule ever manages to get fast enough to escape.
There’s a lot of nitrogen in our atmosphere but not much hydrogen. This is the main reason why.