Monday, August 17, 2009

Calculation Related to Phosphate vs. Phosphorus

I looked at the ratio of sodium to phosphate/phosphorus in the phosphate supplement I discussed here (http://hardcorephysiologyfun.blogspot.com/2009/08/phosphate-discussion-part-50.html), and the "phosphorus" content in the supplement does, in fact, appear to be elemental phosphorus and not phosphate. I'll put my simple calculations in this posting, below. The fact that the numbers make sense on that supplement should not lead one to think that food phosphorus values refer to elemental phosphorus amounts, however. I went through about five more articles [some of the articles in this type of search, for example, although I can't say which ones I went through: (http://scholar.google.com/scholar?as_q=food&num=100&btnG=Search+Scholar&as_epq=&as_oq=%22dietary+phosphate%22+%22phosphate+content%22+%22phosphate+intake%22&as_eq=%22inositol+phosphate%22&as_occt=any&as_sauthors=&as_publication=&as_ylo=&as_yhi=&as_allsubj=all&hl=en)] in which various authors have referred to "dietary phosphate" or variations on that phrase, and I looked for articles whose authors mention "phosphate" because many authors refer to phosphorus only and because many authors that refer to dietary "phosphate" also discuss dietary choices and supplements and foods in terms of the word "phosphorus." All I can say is that many authors state that a typical dietary phosphate intake is 1500 mg/day or so, and other authors, in other articles, state that the dietary phosphorus intake is around 800-1600 mg/day, etc. In some articles, researchers include precise conversion factors, such as for elemental P vs. phosphate and for serum P in mg/dL vs. mM, and detailed tables of food "phosphorus contents," and then there will be statements, later in the article, stating that milk contains 1 mg of "elemental phosphate"/mL (when the table refers to the phosphorus content of milk as being 1 mg/mL). But I've seen an article whose authors say that dietary phosphorus refers, by "convention," to phosphate, and, even in the absence of that statement, the conservative approach would be to assume that dietary phosphorus means phosphate. This is because, as I've discussed, making that assumption helps to ensure that one does not conclude that 3.066 [94.973 mg/mmol PO4 / 30.97 mg/mmol P] times that amount of phosphate (which would be the phosphate content of a food, assuming that the listed values actually referred to elemental phosphorus) is safe. Here are the calculations for the supplement:

Assuming that the molecular formula is Na2HPO4, it is known that Na2HPO4 (disodium hydrogen phosphate, or DHP) would contain 66.9 percent phosphate. The molar mass of DHP is 141.973 [23 + 23 (molar mass of Na2) + 94.973 (molar mass PO4) + 1 (molar mass of H) = 141.973], with Y referring to some mass of DHP:

(Y mg DHP) x (1 mmol DHP / 141.973 mg DHP) x (1 mmol PO4 / 1 mmol DHP) x (94.973 mg PO4 / 1 mmol PO4) = 0.669 (meaning 66.9 percent phosphate)

DHP is also 32.4 percent sodium (46/141.973) and 0.7 percent hydrogen (1/141.973)

The phosphorus (580 mg per three capsules) can't be referring to phosphate, because 580 mg phosphate + 850 mg sodium + 10.1 mg H [32.4 percent + 66.9 percent = 99.3 percent, and 1430 mg of (Na + PO4) = 1430; 1430 is 99.3 percent of 1440.1 mg] = 1440.1 mg Na2PO4; 580/1440.1 = 0.403, or 40.3 percent phosphate. But we know that Na2HPO4 is 66.7 percent phosphate, and so it's clear that the labeled phosphorus content is actually referring to elemental phosphorus. To calculate the amount of phosphate in each capsule, take one-third of the known amount of elemental phosphorus in three capsules (580 mg/3 = 193.333 mg P per capsule):

(193.333 mg P) x (1 mmol P / 30.97 mg P) x (1 mmol PO4 / 1 mmol P) x (94.973 mg PO4/ 1 mmol PO4) = (3.0666 times 193.333 mg P) = 592.76 mg PO4 = 593 mg phosphate per capsule

In some other context, outside of the context of that supplement, for example, one doesn't know if a given scientist, doing an animal study or clinical trial in humans, using a phosphate supplement, assumed that elemental phosphorus meant phosphate or assumed that elemental phosphorus meant elemental phosphorus. I can't quite tell if it would be possible for a listed "phosphate" amount to be off by a factor of 9 and not 3.066, but I don't think the numbers are usually off by that much. But, depending on which assumption a given scientist made, one could look at any one individual article (without getting the sense of things that one gets from looking at multiple articles) and conceivably see a listed dosage that is either one-third or three times the actual amount of phosphorus or phosphate.

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