Collisional cross sections

The kinetic theory¹ of gases connects the properties of individual molecules with the behavior of the bulk gas.  For example, if you know the mass of a particular gas present in a bottle of known volume and temperature, the idea gas law (PV=nRT) lets you predict the pressure in the bottle.  Since the pressure of a gas is related to how often the molecule hit the walls of the container, collision rates are a fundamental part of the theory.

How often molecules collide is of interest to chemists because getting molecules close together (really close together, within tenths of nanometers) is fundamental to their ability to react, to change into other things.  Molecules bump into each other more often when the temperature is high (they are moving faster and so cover more territory) and when the pressure is high (there are more of them to hit).  But collisions also increase when the target area is larger.  Think about trying to move through a crowded grocery store with a big cart versus when you just need to grab a gallon of milk.  The surface area you present to other shoppers is large when you have that cart and you are more likely to run into other things.²  This surface area is the collisional cross section.

I've been moving fast lately and the pressure has been high, which if I were a gas would mean I would be having more collisions, but in reality has left me feeling like all I do is wave as I race past people in the hallway or on campus. Sorry, can't talk now, have to run. Whoosh.  The semester is winding down, with the gift of a Friday with no classes or meetings on it.  Not only that, but this was the very same Friday that The Egg is singing as part of a quartet at his SoCal college. A most welcome collision on my calendar.  

I booked a flight, and now I am here. Not only that, but Math Man figured out he could take a day off and come, too.  So this morning, I met The Egg on campus and as we walked to get breakfast, we "ran into" Math Man on the sidewalk.  Surprise!

But there was more collisional fun to be had. A delightful colleague was in Philly to give a talk which I couldn't go to (vide infra).  We booked a time for tea and Skype later in the month, a moment to virtually collide, if not literally.  But on Thursday evening, while headed to my gate at PHL, my phone rang. The number was delightful colleague's.  "Are you by any chance at PHL?" she asked.  "I am."  We were flying out from adjacent gates.  Which resulted in two women running (literally) into each other at PHL, and we enjoyed twenty wonderful minutes to hug, hang out and catch up on the really big things that had happened to each other.  And some of the small delights. 

A high collisional cross section?  Almost worth the pressure.

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1. Theory in the sense scientists use it, meaning a coherent system of ideas used to explain something,  not theory as it is often used outside of scientific circles, where it carries the connotation of something unlikely to be realized in actual practice, or notions that are not yet and probably won't  proved true. 

2.  To get a sense of how lightly populated a gas is, a molecule at room temperature on average travels about 300 times its length before hitting another molecule, the equivalent of my walking 500 yards without getting close enough to anyone to shake their hand.  Not my experience of the grocery store after work!