Electronic Design

# What's All This Dilution Stuff, Anyhow?

One of my friends sent me a wee bottle of scotch whisky to take on my trek in Nepal. He planned to bring the rest of the whisky to a 45th school reunion on June 9. He would drink a toast with our fellow alumni in Mount Hermon, Mass., at 11 p.m. on June 9, and we would drink a toast at the same time at 9:15 a.m. in Nepal on June 10, when we went over the great pass Thorong La, at 17,771 ft. Cheers!

After we drained the bottle carefully and rinsed it with tea and water, what to do with the bottle? We were in Muktinath, where there's a very holy temple. The big shrine there has 108 little spouts in the form of bull's heads, with a little stream of water spouting from each of the bulls' mouths. I decided to collect a few drops from each stream in the little bottle. So that's what I did. Now I could give a sample of this water to any Nepali friends who would like to have it.

But how much water would each person get? First of all, you know Avogadro's number. When I went to school, it was 6.023 × 1023. That's what my Handbook of Chemistry & Physics said. But I had to mark it up to change it to the new accepted value of 6.022. Why was it changed? I guess the chemists who supported the new value (~1986) had better arguments than the physicists who had derived the old value.

That number is the number of molecules in 1 mole of an element or compound. So 18 grams of water would have 6.022 × 1023 molecules of water. That is a large number of molecules. I estimated that if I put about six drops of water from each spout into my little bottle, that would fill it to about 2 ounces—which is about 56 grams. Thus, I'd capture about 0.5 grams from each spout, but at least 0.2 grams. So the original sample would have about 6 × 1021 molecules from each spout.

Then if I diluted the sample by 10× and then by 10× again, each sample would have at least 6 × 1019 molecules—at least 60 million million million molecules from each bull's head spout. I figured that would be enough to make any devout Nepali happy. This shrine is holy to both Buddhists and Hindus, I'm told. (This isn't exactly the same as saying that the air I now breathe probably contains one molecule from the last breath that Julius Caesar breathed. But the math is comparable. Details later.)

A couple of days later, I washed my socks. I washed them with a little soap to get out the mud (and donkey-doo). I rinsed them several times. Each time I'm sure I got a dilution factor of e = ~ 2.71828. Hey, I was just squeezing them by hand in a flow of water. After about four rinses, the water was hardly colored at all. So I did four more rinses, and put my socks in a mesh bag to dry. We rode all day, and by about 4 p.m. they were nearly dry.

Suddenly I heard a thrumming sound. The mesh bag had flopped off the top of my panniers—and had rubbed against my spokes. It had "cleaned" all the mud off the spokes. And the socks were completely dirty and gritty again! Oh, well....

I rewashed the socks and inspected the color of the rinse water. It was exactly the color of the great Khali Gandaki River that flowed along our route: muddy and grey-brown-white. So my socks had very quickly regained all the color of the mud. After about four rinses, they were almost clean. After four more rinses, were they clean enough to put out to dry? How much dilution is enough? I'll be darned if there is any specific answer. But eight rinses is enough for me.

Later that night I had to sew up my shoes. I'd taken some old shoes on this trek because I couldn't find any new ones of the right size and shape and traction. I bought these shoes for about \$20, about five years ago, and I bought two pairs. They were quite comfortable and had excellent traction, which is why I brought them, even if they were somewhat worn. Halfway through the trek, some of the glue began to lose hold. The heel began to flop around on the left shoe, and the sole on the right. I pulled out my trusty thread and needle. Where to begin?

First, I washed the shoes six times. I wanted all of the surplus dirt washed away. But down in the crevices of the shoes, surely there was a lot of dirt, germs, and filth not accessible to any washing. Could I possibly get them clean enough? Would 12 rinses really be any better than six? I decided not. After six rinses, I decided to get down to work. I stitched and knotted using some very heavy thread and a semicircular needle.

I must say it's very satisfying to see the glint of the needle come out from the shoe, over my thumb nail, which is much better than under my thumb nail. I was quite careful to never poke my needle under my thumb nail. After all, what is the "dilution factor" that's safe when you stick a needle into your finger, after it has come through a shoe that was washed just six times? How few molecules of filth will probably not give you any infection? That's an unanswerable question.

But I used all the lessons that my mother ever taught me about sewing, and more. My finger never got punctured, and the stitches held. And I walked and rode out the rest of the trek.

All for now. / Comments invited!

Mail Stop D2597A
National Semiconductor
P.O. Box 58090
Santa Clara, CA 95052-8090