Author: Martin A. Erickson III, RPh

**Q:** To make 250 g of 1:1000 triiodothyronine (T-3) trituration, we need to use 250 mg (0.25 g) of T-3 and 249.4 g of Avicel (or lactulose). This formula also calls for some food coloring (blue, 0.35 g), making a total of 250 g. Please verify that 250 mg (or 0.25 g) is the appropriate amount of T-3 to use when making 250 g of 1:1000 T-3 trituration. Additionally, please verify that, if we were to make 100 g of the 1:1000 trituration, only 0.1 g (or 100 mg) of T-3 would be used with 99.55 g of Avicel (or lactulose) and 0.35 g of food coloring.

**A: **Proportionalities and nomenclature are subjects of frequent and great confusion. Sometimes analogies are helpful when describing approaches to problems. Here, a trituration is similar to a solution. For solutions, the United States Pharmacopeia/ National Formulary gives solubility ratios as "x:y" and "x in y" (1:4 and 1 in 4, respectively, for example). The statements mean x part(s) of solute *plus *y parts of solvent to make the solution, and the final product is an "x:(x+y) solution," which contains x part(s) in (x+y) parts **of solution**. For example, if the solubility is 1:3, then the solution described is a "1:4 solution."

In your example, the final product is described as a "1:1000 T-3 trituration," analogous to the 1:4 solution in the answer above. Therefore, the final trituration contains 1 in (1+y) of trituration, but the relationship of the active ingredient to the diluent can be described as x in (1000-x) or 1 in (1000-1) trituration.

If your dilution is to be 250 g trituration, then, from the above, 1:1000:x:250, x = 250/1000 = 0.25. Therefore the **trituration **is 0.25:250, but the ratio of the T-3 ("solute") to the diluent ("solvent") is 0.25 in 250-0.25, or 249.75.

Another method is to use a simple proportionality:

You require 250 g of a 1:1000 trituration.

1:1000:x:250

x = 250/1000 = 0.25

Diluent = 250-0.25 = 249.75

Any minor additional ingredients, such as aluminum lake (insoluble) powder FD&C or D&C dye, are subtracted from the total diluent, 249.75-z = diluent, z = amount of dye.

*Mr. Erickson is director of professional affairs at Gallipot Inc.*

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