Answer to Question #5827 Submitted to "Ask the Experts"

Q

I have a question stemming from the response to question 4609, which outlines the conversion of pCi/L to gram-eq/L. For the problem I'm working on I'm trying to convert a concentration, for example, pCi/ft³ to gram-eq/ft³. Based on the response to 4609, I was able to do so without difficulty. However, as a matter of interest, I decided to convert specific activity, in units of pCi/g to units of g-eq/g. For example, ²²⁶Ra specific activity = 1.0 x 10¹² pCi/g, the decay constant = 1.2 x 10^-6/day, and a conversion factor = 3196.80 disintegrations per day/pCi (converted from 2.22 dpm/pCi). The number of atoms per gram is N_a = 1 x 10¹² x 3196.80 / 1.2 x 10^-6 = 7.58 x 10²⁷ atoms/g g-eq specific activity = 2 x 7.58 x 10²⁷/6.022 x 10²³ = 2.52 x 10⁴ g-eq/g. Reviewing the definition of specific activity: "Specific Activity is the concentration of radioactivity per unit mass of that element." What does this g-eq specific activity theoretically mean, that is, that ²²⁶Ra has 25,200 grams of radioactivity per gram?

A

Before we get to your question, please note that you have an arithmetic error in your calculation. When you calculated the number of atoms you obtained 7.58 x 10²⁷, and this should have been 2.66 x 10²¹. This carries through into the specific activity result which should be 8.85 x 10^-3, rather than 2.52 x 10⁴ g-eq/g. Radium compounds exist only in the +2 oxidation state. You might recall from basic chemistry that, by definition, a gram-equivalent of any substance is a quantity in grams that corresponds, in its chemical reaction, to one gram atomic weight of hydrogen or of hydroxyl ion, or 0.5 gram atomic weights of oxygen, or one gram atomic weight of a univalent ion. In the typical solution reactions that radium might undergo, the radium cation would be associated with two univalent anions or one divalent anion, and one gram molecular weight (one mole) of a radium compound would be equal to two gram equivalent weights of the compound.

Thus, if we use the atomic weight of ²²⁶Ra, namely 226, and specify that one gram-atomic weight of radium is 226 grams, then one gram-equivalent weight (1 g-eq) would be equal to half of 226 g or 113 g. The corrected value of 8.85 x 10^-3 g-eq/g from above can then be converted to grams of radium/gram radium—that is, (8.85 x 10^-3 g-eq/g)(113 g/g-eq) = 1g/g. If radium had been present in solution as RaCl₂ whose molecular weight is 297, then we would require half of 297, or 148.5 grams of RaCl₂, to represent 1 gram-equivalent of radium, and the mass of RaCl₂ associated with the value of 8.85 x 10^-3 g-eq/g would be (8.85 x 10^-3 g-eq/g)(148.5 g/g-eq) = 1.31 g (of RaCl₂)/g (of Ra).
 
George Chabot, PhD, CHP