I Am Your Density

I've given away some test tubes and now for some ideas on how to use them. This is the first of those posts.

Density is a measure of the mass of something for a given volume, or in other words how much stuff is smashed into some space. It has a formula of ρ=m/v where:

ρ = density
m = mass
v = volume

Different materials have different densities. Old home chemistry books encouraged you to run to the drug store and get some mercury, carbon tetrachloride, water, oil, iron, a rubber stopper, and a cork. Pour the liquids in in order and then drop in the solids and you have a seven layer density column. This particular column is now very difficult to recreate because both mercury and carbon tetrachloride are no longer sold at the drug store. Steve Spangler has a great description of another 7 layer column that can be created from things found around the house.

Our set up for today is even easier. We are going to make a four layer column using three sugar solutions and plain water. So start by getting five test tubes and a pipette. Three test tubes will have sugar solutions one will have plain water and the last will be used for making the column. In the first tube put two mL of sugar, one drop of red food coloring, and fill it to the 10mL mark with water. In the second tube place four mL of sugar, one drop of green food coloring, and fill it to the 10mL mark with water. In the third tube add six mL of sugar, a drop of blue food coloring , and fill it to the 10mL mark with water. Lastly, in the fourth tube fill it with water. Now shake them until they are all dissolved. One mL of granulated sugar has a mass of about 0.8 g while one mL of water has a mass of 1 g. So your solutions have densities of:

plain water:(10g H₂O+ 0g sugar)/10 mL =1 g/mL
red: (10g H₂O+ 1.6g sugar)/10 mL =1.16 g/mL
green: (10g H₂O+ 3.2g sugar)/10 mL =1.32 g/mL
blue:(10g H₂O+ 6.4g sugar)/10 mL =1.64 g/mL

Now take a pipette full of the blue solution and add it to the empty fifth test tube. Now take a pipette full of the green solution and add it very carefully to the column. To do this you will need to slowly dribble it down the edge of the test tube. It should form a layer on top of the first one. Now do the same with the red layer and the water layer. It should look something like this.


Amazingly it will stay this way for quite a while. The next picture is the column after 12 hours. You can see that the plain water and the weakest concentration have begun mixing.


They will slowly go on mixing and after a week mine looks like this

You can still see separation between the top two and bottom two layers. After another few days in the window some mold started growing on the top so I washed it down the drain.

Now try playing with the solutions. Can you get them to stack in the wrong order? Can you make a solution dense enough to float a raisin in it? If you make alternating solutions of sugar and salt do they last as long as a column made from just sugar? Do they last longer?

I hope you all enjoy making and playing with your own density columns. Let me know how it goes.

Euclid

Geometry has always been my favorite math class. I always wanted to take a college level geometry class but I've never been able to fit it into my schedule. So I decided to read Euclid's Elements and cover the basics again. I really wanted to see the Greek (I don't read Greek but I wanted to see it) while I read the text in English. Marcelle had read and used the Elements as a text book in her days at St. John's in Santa Fe and I asked her if her text had the Greek. She said that it did not and that as far as she knew an inter-columnar version didn't exist or they would have used it.

I searched on Google and found that in 2007 Richard Fitzpatrick published a completely free and wonderful pdf version of the Elements in both Greek and English along with a Greek-English Lexicon. My plan is to print and bind the book along with blank pages in between the text so that I can work the proofs along with the text. Towards this goal Marcelle bought me a great compass so that I can make it look good to.

While I was searching for information on Euclid I decided that I wanted some old manuscripts of the Elements like this one. So I bought a sheet of papyrus from the local art store and while Marcelle and the kids were visiting her parents I acquired some papyri with parts of the Elements on them. These are pictures of them.

These first two are the definitions from the start of Book 1 "1. A point is that of which there is no part." You can see that this item is a composite of two pieces of papyrus "glued" together to make one larger piece.

This is the end of Proposition 11 from Book 4 inscribing a regular pentagon in a given circle. I haven't decided if I'm going to distress these last two like I did the first one.

This, of course, is the famous start of Proposition 47 from Book 1 proving the Pythagorean Theorem.

Liquid Diet

A few days before Christmas 2003 I had my mouth wired shut after having surgery on my jaw. I was on a liquid diet for a week and then I graduated to things like jello. I am here to tell you that you can only drink so much chicken broth before your body starts screaming "Give me a steak!" and I still gag when I think about drinking Ensure. Remembering this episode got me wondering if it is possible to survive solely on pure chemicals? While searching the literature I found out not only that it is possible but what the perfect recipe is. In a paper entitled "Evaluation of Chemical Diets as Nutrition for Man-in-Space¹" Winitz et al inform us that the perfect diet is:

Amino-acids
l-Lysine·HCl 3.58 g
sodium l-aspartate 6.40 g
l-Leucine 3.83 g
l-Threonine 2.42 g
l-Isoleucine 2.42 g
l-Proline 10.33 g
l-Valine 2.67 g
Glycine 1.67 g
l-Phenylalanine 1.75 g
l-Serine 5.33 g
l-Arginine·HCl 2.58 g
l-Tyrosine ethyl ester·HCl 6.83 g
l-Histidine·HCl·H₂O 1.58 g
l-Tryptophan 0.75 g
l-Methionine 1.75 g
l-Glutamine 9.07 g
l-Alanine 2.58 g
l-Cysteine ethyl ester·HCl 0.92 g

Water-soluble vitamins
Thiamine.HCl 1.00 mg
d-Biotin 0.83 mg
Riboflavin 1.50 mg
Folic acid 1.67 mg
Pyridoxine.HCl 1.67 mg
Ascorbic acid 62.50 mg
Niacinamide 10.00 mg
Cyanocobalamin 1.67 mg
Inositol 0.83 mg
p-Aminobenzoic acid 416.56 mg
d-Calcium pantothenate 8.33 mg
Choline bitartrate 231.25 mg

Salts
Potassium iodide 0.25 mg
Potassium hydroxide 0.83 g
Manganous acetate 18.30 mg
Magnesium oxide 0.38 g
Zinc benzoate 2.82 mg
Sodium chloride 4.77 g
Cupric acetate 2.50 mg
Ferrous gluconate 0.83 g
Sodium glycerophosphate 1.67 mg
Calcium Chloride·2H₂O 2.44 g
Ammonium molybdate·4H₂O 5.23 g
Sodium benzoate 1.00 g

Carbohydrates
Glucose 555.0 g
Glucono-δ-lactone 17.2 g

Fats and fat-soluble vitamins
Ethyl linoeate 2.0 g
α-Tocopherol acetate 57.29 mg
Vitamin A 3.64 mg
Menadione 4.58 mg
Vitamin D 0.057 mg

They point out that these diets are unique because " (a) their essential and nonessential nitrogen is provided in the form of highly pure L-amino-acids; (b) the are administered as single, crystal clear solutions which are nutritionally complete in themselves"

The dry ingredients were dissolved in distilled water to give a solution of 50-75% solids by weight which was completely sterile and had about 2-3cal per mL and could be stored almost indefinitely.

24 inmates from the California Medical Facility volunteered to drink/eat nothing but this liquid diet for 19 weeks. They were allowed to drink as much as they wanted and they could have all the water they wanted too. I can understand why they needed to use inmates because if they were on the outside after a week or so a cheeseburger looks really good.

They found that this diet provided well for these inmates and that there were no ill effects on their health. The authors go on to explain that these diets overcome some of the limitations inherent in alternative space-food sources:

"[These diets provide] high nutritive efficacy in ultra-compact form-1 ft³ of the diet as a 75% solution in water, will provide a 154-lb astronaut with all his required essential and nonessential nitrogen, salts, vitamins, and fats, in addition to his estimated requirement of 2,830 calories per day, for a period of a month; (b) complete water solubility- provides advantages in the administration of the diets in liquid form under conditions that will not permit the use of solids; (c) low bulk reduces low faecal residues and mitigates the critical problem of disposal of solid wastes; (d) complete nutrilite accessibility-allows alteration at will of the amino-acid ratios, carbohydrate content, and levels of all other components, thereby making it possible to tailor formulations to specific dietary needs of individual astronauts; (e) complete digestibility- provides dietary components in the most elemental form in the event of disturbances of the digestive system; (f) good storage stability either in the solid state or as aqueous solution."

This might be worth looking at for food storage...
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¹Winitz, M.; Graff, J.; Gallagher, N.; Narkin, A.; Seedman, D. A.; Nature 1965, 205, 741-743