Monday, January 04, 2016

What is the motion of one molecule diffusing?

I survived my first semester as a professor. I really enjoyed it and am looking forward to the next semester.

The only complaint that I had was with the text. We are using "Chemistry - The Central Science" by Brown, LeMay et al. and it drives me nuts at times. Such how it only mentions 3 states of matter - solid, liquid and gas - and overlooks plasmas. Plasmas are not some exotic state of matter completely void of chemistry. Light a Bunsen burner and you have a plasma. It's possible that one or more the students has seen a plasma TV as well. To not mention plasmas is really surprising, especially since the text has no problem in mentioning more esoteric topics, such as Noble gas compounds and ionic compounds.

The section on polymers has too many mistakes to even list, but I think I did a good job of keeping those thoughts to myself.

But what really had me livid (and my students will verify this since it was I spent time in lecture on it, covered it again in the chapter synopsis and even asked about it on the final exam) is this illustration:
The expression "throwing out the baby with the bathwater" has never been more aptly applied.

This figure is a snippet of a random walk and as such, the molecule pictured is most likely to end up right where it started. The molecule is bouncing around at random - there are no signs to indicate which way it is suppose to diffuse and so a single molecule by itself won't diffuse. To call a random walk "diffusion" is a horrible misrepresentation of diffusion. A single molecule won't diffuse anywhere. It will just wander around at random and go nowhere.

So then how do we get diffusion from a collection of random walking molecules? Diffusion is the result of concentration gradients - differences in concentration over a distance. If there is a higher concentration of molecule A on the left and a smaller concentration of molecule A on the right, the odds are better (and yes, diffusion is the result of statistical phenomena) that more molecules from the left will move to the right than from the right to the left since there are more A molecules on the left. There is nothing special about this. The molecules on the left have no clue that they should go to the right - it's just that since there are more of them on the left than the right, they are more likely to overwhelm the molecules on the right moving to the left. But at all times, molecules on the left are each moving to the right and even further to the left while molecules on the right are moving to the left and even further to the right. They have to move in both directions since they are moving randomly without any guidance. The diffusion we observe is based on the statistical outcome of this game of chance and nothing more.

Over time, diffusion lessens the gradient which means that diffusion will lessen over time until eventually the gradient is gone and so is the diffusion. No gradient, no diffusion.

So how can Figure 10.18 above illustrate diffusion when there is only a single molecule in it? It can't. It's not possible. Even if the other molecules were added to the picture, there would still be no diffusion without a concentration gradient. The Zen koan asks "what is the sound of one hand clapping?" to which there is no answer. This picture asks "what is the motion of one molecule diffusing" to which there is no answer, despite the authors claiming to have one.

Previous Years

January 4, 2021 - How will the Law and Chemistry Interact? - The Sheri Sangji Case

January 4, 2011 - Extruder Philosophy

Janaury 4, 2010 - A new year, a change to the comments

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