In order of appearance:
SUGAR
We're talking sucrose here. Every day common granulated table sugar. Sucrose itself is the most abundant pure organic chemical in the world - and is the one that is most widely known by the common man. Sucrose comes from either sugar cane or sugar beets.

Chemically, sucrose is a disaccharide (built of two simple sugars) composed of glucose and fructose.

FRUCTOSE
Fructose is a hexose. 'Hextose' refers to the number of carbon atoms in the ring, in this case 6. Fructose is found in fruits and vegetables. In many cases, the fructose we consume comes from corn syrup. Fructose itself is twice as sweet as sucrose but has only half the calories (its only half the sugar). Fructose also has the property that it is not absorbed into the blood as quickly as other sugars, especially when there is little glucose. This has significant implications for diabetics.

CITRIC ACID (PROVIDES TARTNESS)
HO2CCH2C(OH)(CO2H)CH2CO2H . Try saying that three times real fast. Shoot, just try saying it three times. However it is said, it is known for a 'tart' taste. This acid is found in citrus fruits (and thus the name) and can be extracted by adding lime (calcium oxide, not the fruit) to for calcium citrate. Citric acid can also be obtained by fermenting glucose with the aid of the mold Aspergillus niger or synthesized from acetone or glycerol. Citric acid is also a key part of the critic acid cycle that is one of the metabolic pathways responsible for releasing energy from sugars, amino acids, and fatty acids.

CALCIUM PHOSPHATE (PREVENTS CAKING)
Calcium phosphate is commonly used in baking powder and is a stabilizer in food. It also prevents caking. This is often found in instant soups, cocoa, powdered milk and such. The other option for an anti-caking agent is silicates and sodium ferrocyanide which is used in salt, garlic and onion powder. It all depends on taste - I am quite glad calcium phosphate was used.

POTASSIUM CITRATE (CONTROLS ACIDITY)
If you've noticed, there is a fair bit of acids and forms of acids in Tang. Thats part of what gives it 'tang'. Granted, its nowhere near the point where it gets to eating away the paper cup you drink it out of, however it is considered a 'bad' thing to have the flavor be one that bites too hard or gives heartburn.

ORANGE JUICE SOLIDS
Beyond a food derivative, there isn't much information as to exactly what orange juice solids are. They've got some potassium in them, but beyond that there isn't a whole lot of info on it.

ASCORBIC ACID (VITAMIN C)
On the flip side, it is trivial to find too much information on the Vitamin C. Ascorbic acid is a water soluble vitamin that cannot be stored in the body - it gets constantly flushed out. For this reason, it is necessary to have a source of vitamin C in one's diet. This was often a problem with long sea voyages and lead to scurvy amongst sailors. The British Navy implemented a plan to bring along citrus fruits leading to the name 'limey' for their sailors which still sticks today. Another source of vitamin C that has come into vogue recently is that of wheat grass. Pine needles can also be a rich source of vitamin C, although much less appealing in taste.

NATURAL FLAVOR
Natural flavor - you see it everywhere. Even the Altoids tin that I have lists 'natural flavor', and yet it is not well defined anywhere. For example, the Kraft FAQ says this about the "natural flavor" in Caprisun:
The ingredient "natural flavor" is a fruit extract. For example, wild cherry natural flavor ingredient would be wild cherry extract. The actual natural flavor proportions are a trade secret of the flavor suppliers.
Your guess is as good as mine.

ARTIFICIAL COLOR
All these things we're mixing in don't naturally look orange. That is the magic of artifical color. For the most part at this point, we've got something that looks like a white powder. Make it orange, and keep it orange when water is added. Though, I'm sure some kids would find it neat to have something that started out blue and turned orange when water was added it wouldn't really be that great of a hit.

XANTHAN AND CELLULOSE GUMS (FOR BODY)
Cellulose - recognize that '-ose'? Same as sucrose and fructose above, this is a sugar. However, Cellulose is not a simple, or even a disaccharide. We're talking hundreds or thousands of simple sugars joined together. The simpler the sugar, the sweeter it tastes to us - cotton does not taste that sweet. Cellulose is the building blocks of all plant fibers and forms the cell walls that encase each plant cell in a rigid skeleton.

Xanthan gum is another polysaccharide and has numerous uses from lubricants to filler. Xantham itself is made from the bacterium Xanthomonas campestris and is commonly found on plants in the cabbage family. Xantham is resistant to many enzymes and thus improves shelf life and is soluble in hot and cold water, and a wide range of acidic and alkaline solutions and salt levels. There is also a paper written on the effects of xanthan gum and the size of baked cakes (Miller, R.A. and R.C. Hoseney. 1993. The role of xanthan gum in white layer cakes. Cereal Chemistry 70(5): 585-588.).

YELLOW 5
Also known as Sunset Yellow FCF. This is an acid dye. Although it is difficult to represent the color itself on E2, the colors associated with Yellow #5 are close to that of 0xF47A05 and 0xFAC67F. This is the second most widely used coloring (after red 40) and may cause mild allergic reactions in individuals who are aspirin-sensitive.

YELLOW 6
Another sunset yellow coloring. This one is a bit more touchy and it causes tumors in the adrenal gland and kidney in lab animals. It is also possible that small amounts of carcinogens may contaminate Yellow 6. However, the FDA has concluded that Yellow 6 does not pose any significant cancer risk to humans. What today doesn't cause cancer?

ALPHA TOCOPHEROL ACETATE (VITAMIN E)
Alpha Tocopherol is an antioxidant that is found in whole wheat, rice germ and vegetable oils. However, it is destroyed in flour by the refining and bleaching process. Vitamin E reduces damage to cell membranes, reduces the risk of heart disease and cancer, accelerates healing, eases arthritis, reduces the risk of cataracts, improves the immune system, slows the progress of Parkinsons, improves oxygen use, prevents blood clotting and alleviates fatigue. Egads, thats quite a list. deficiency of vitamin E can result in anemia, rupture of red blood cells, loss of reproductive powers, lack of sexual vitality, abnormal fat deposits in muscles, and degenerative changes in the heart and other muscles.

NIACINAMIDE
Niacinamide is a water soluble form of vitamin B3 (Niacin). The differences beyond its solubility are not clear. Furthermore, I have difficulty trusting all the claims made by various online health stores about the differences between them. In the brief research done, the literature claims daily allowance for adults to be 16 - 19 mg, while the health stores have 500 mg tablets. Whatever the case, niacin and niacinamide are components in several metabolic enzymes. These vitamins occur naturally in lean meat, peanuts and other legumes; and are often part of enriched bread and cereal products.

ARTIFICIAL FLAVOR
And I thought hunting down what was in natural flavors was hard... Artifical flavor is the essence of the trade secrets of a food company and are the key to many tastes.

VITAMIN A PALMITATE
Vitamin A is an important antioxidant and is used in photoreceptors. A fat soluble lipid, Vitamin A is found in such places as liver, egg yolk, cream, and butter. It is also found in beta-carotene (leafy green vegetables and yellow fruits and vegetables). Vitamin A is critical to vision, skeletal growth and reproduction along with the health of the skin and mucous membranes.

VITAMIN B6
Combined with phosphorous in the body, the B6 group of vitamins help form the enzyme pyridoxal phosphate which is part of the metabolism of amino acids, glucose, and fatty acids. Primary sources of vitamin B6 are liver and organ meats, corn, and other seeds.

RIBOFLAVIN (VITAMIN B2)
Riboflavin is one of the components of respiratory enzymes in plants and animals and is an important part of oxidation. The natural sources of this vitamin are plant and animal tissue, milk, and organ meats.

BHA (PROVIDES FRESHNESS)
Butylated hyrdoxyanisole - Similar to citric acid, BHA is an antioxidant and helps preserve food by preventing it from oxidizing. Oxidation is the process that ripens fruits and vegetables, and eventually turns it rancid.

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