This is a way of understanding the density of gases, and why Avogadro’s number is the same for large or small molecules, and also some other things about molecules in a gas. First of all, I would like you to see how large Avogadro’s number is, and what proportions it implies about molecules and the space they inhabit in a gas.
6.02 x 1023 is Avogadro’s #
There are 6.02 x 1023 molecules of gas in 22.4 liters of gas at STP (which means Standard Temperature and Pressure, which means 0º Celsius or 32º Fahrenheit and “one atmosphere” which means the air pressure at sea level.)
So, how many molecules in one liter of gas?
Avogadro’s number means as 602 x 1021 molecules of gas per 22.4 liters at STP. (I just moved the decimal and subtracted from the exponent.)
And that means there are 26.875 x 1021 molecules of gas per liter. (Divide 602 by 22.4.)
Or to put it another way, there are 26,875 x 1018 molecules of gas per liter. (Again, I just moved the decimal — three places forward — and subtracted 3 from the exponent.)
What would that look like?
Suppose, just to visualize these things, we make an image that is 8 orders of magnitude larger, putting it into the realm of things we can see. (Hereinafter, “orders of magnitude,” which increase by powers of ten, will be called ooms.)
Eight ooms up from an atom is the size of a large bug; let’s say a bee. (I know I’ve been saying molecule; but let’s talk about atoms for a while since most molecules in the atmosphere are just two or three atoms and therefore lie in the same size range as atoms. I’ll bring the molecule back at the end.)
Eight ooms up from one liter is the Earth.
So it’s like 26,875 x 1018 bees in the volume of the Earth.
What does that look like?
Well, it’s like 26,875 x 1015 bees in a California-width cube … Or it’s 26,875 x 1012 bees in Ireland up to the lower edge of the aurora. (Yes, auroras are rarely seen in Ireland, but I just mean 60 miles up, so we have an Ireland-size cube.)
And that is like 26,875 x 109 bees in a city such as Sioux Falls from the quarries up to the cirrus clouds.
That, in turn is like 26,875 x 106 bees in your half mile or one km neighborhood — but also the same height which is really higher than bees ever fly; hang in a minute to see if that’s really so many…
It would be like 26,875 x 103 bees in pair of football fields surrounded by sequoia trees — but bees don’t really fly that high either, so let’s make it just a tenth as high, surrounded by maple trees for example, and it’s just 26,875 x 102 bees flying around a couple of football fields within one 10 meters of the ground.
Now, a tenth of that (26,875 x 10) would be the same density of bees within 1 meter of the ground, which is their more usual flying zone, and a tenth of that (26,875) would be that density of bees at about the height of the clover which is where they get their honey.
Consider 26,875 bees in the clover
Now, I used football fields, whose length is 120 yards and width is 53 yards, so a pair of them have a length of 120 yards and a width of 106 yards. That means (120 x 106) there are 12,720 square yards of field, with 26,875 bees foraging in a football field? What does that look like?
It’s about two bees per square yard. I suppose if you had 2 or 3 bees on your table, it would make you nervous, but it’s really not so many, is it? In fact, if it were a little plot of clover and grass that large, 2 bees would hardly be noticeable until they started flying. That’s the density of bees in the football field. I don’t suppose you’d want to play football, but just to take a walk wouldn’t be so bad.
Bees and hummingbirds
Finally, let us imagine that our football field has a mixture of bees and hummingbirds (the hummingbirds represent the larger molecules, of course) in just the same numbers. It might even have a few robins (representing very large gas molecules.) The bees fly very fast and the hummingbirds, who fly a lot slower, are bigger, of course, so they do bump into stuff just as often as the bees. If you became a bee yourself and flew into the field blind, you would be about as likely to be struck by a bee as by a hummingbird, because the one is larger and the other is faster.
Anyway, the sum of it all is the peculiar fact that the vapor pressure of a gas (the power of molecules bumping) at STP (cold air by the ocean near Greenland) is about the same whether the gas is composed of big molecules or little ones. Unlike marbles in a bag, all the molecules really have a lot of room, just like the bees and the hummingbirds, and while the big ones bump heavier, the little ones bump with more zing, but if they weren’t moving, they would have a ridiculous amount of space.
I must admit, at the end of all this, that gas molecules move a few hundred times faster than bees and hummingbirds; so they bump all the time, but that’s another story.
…In fact… (ahem!) They all bump so much that if you gave a message to one of them, and if it were passed each time one bumped another, it would cross our paired fields in less than one second unless they were all hummingbirds.
That’s what happens when you shout.
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